All Calculations
120 calculations published. Each one shows the formula, works through real numbers, and explains where the method stops applying.
Categories
Published calculations
Finance
How To Calculate 401(k) Growth
A 401(k) projection answers a specific question: at a fixed contribution and a fixed return, what will the account be worth at retirement, and how much of that did the employer match create? The arithmetic is a future-value calculation with two additions a year, yours and the match.
FV = B(1+r)^t + (C + M) x [((1+r)^t - 1) / r]
Health
How To Calculate A Calorie Deficit
A calorie deficit is subtraction: maintenance calories minus the calories you eat. The arithmetic is simple, but the figure you subtract from is a moving estimate rather than a fixed constant, and that is where most of the difficulty lives.
Daily deficit = maintenance calories - intake calories
Finance
How To Calculate A Car Lease Payment
A lease payment is the interest on the whole car plus the depreciation you consume while you drive it. Both halves are set by the price, the residual value and the money factor, so a small change in any of them moves the monthly figure.
Payment = depreciation + finance charge
Everyday Life
How To Calculate A Discount
A discount is a percentage taken off the price before tax, so the sale price and the money saved are two separate numbers that the tag never prints. On an original price of 120 with 25 per cent off, the saving is 30.0, the sale price is 90.0, and with 8 per cent tax the bill is 97.2.
sale price = original x (1 - rate); saving = original x rate
Finance
How To Calculate A Down Payment
A down payment is not only the cash you hand over — it sets the loan-to-value ratio, and that ratio decides whether mortgage insurance attaches to every payment for years. Choosing between 10% and 20% down is therefore a cash decision and an insurance decision at the same time.
Down Payment = Purchase Price x Down Payment Percentage
Finance
How To Calculate A Pay Raise
A raise has three numbers that matter: the new salary, the extra pay per period, and whether the increase beats inflation. A nominal raise that falls below inflation is a cut in real terms, even though the paycheck is bigger.
New salary = old salary x (1 + raise%)
Finance
How To Calculate A Paycheck
Gross pay is what you earn; net pay is what reaches your bank account. The gap is income tax, payroll taxes and any retirement or benefit contributions, and it is often large enough to change how you budget.
Net pay = gross - income tax - payroll tax - contributions
Math
How To Calculate A Percentage
Every percentage question is one of three sentences wearing different clothes. Once you can identify which one you are looking at, the arithmetic is a single multiplication or division, and the common mistakes all come from picking the wrong one.
Part = Whole x Percentage / 100
Education
How To Calculate A Percentile Rank
A percentile rank tells you what fraction of a group sits below a value. For 12th out of 250 there are 238 below, and the two standard conventions give 0.9558232931726908 and 0.952 — answers that differ by less than one person, yet must be kept distinct from the percentage score.
Percentile rank = count below / (n - 1), or count below / n
Everyday Life
How To Calculate A Split Bill
A split bill divides one restaurant bill between several people, and nearly every disagreement about it comes from the order of operations rather than from the arithmetic. The tip is a percentage of the pre-tip bill, it has to be added before anything is divided, and the split only stops being trivial once the shares stop being equal.
tip = bill x rate; total = bill + tip; per person = total / people
Education
How To Calculate A Test Score
A test score is the marks you earned divided by the marks available. The arithmetic is one division, but the answer is reported in three different currencies: the raw mark, the percentage, and the letter grade. Only the first two are yours to compute.
Percentage score = (correct / total) x 100
Everyday Life
How To Calculate A Tip
A tip is just a percentage of a bill, yet most of the arguments around it come from two decisions rather than from arithmetic: what you take the percentage of, and at what point you split it.
Tip = bill x rate; total = bill x (1 + rate)
Math
How To Calculate A Weighted Average
A weighted average answers "what is the typical value?" when some values count more than others. Grades, portfolio returns, inventory costs and survey results are almost never plain averages, which is why the distinction matters.
Weighted Average = Sum of (Value x Weight) / Sum of Weights
Education
How To Calculate A Weighted GPA
A weighted GPA on the school scale adds bonus points to difficult courses before averaging, so an AP A counts as 5.0 and an honours A as 4.5 rather than 4.0. The arithmetic is trivial; the difficulty is keeping this weighting distinct from the credit weighting used elsewhere, and knowing which figure a reader actually wants.
Weighted GPA = Sum of (grade points + bonus) / number of courses
Math
How To Calculate A Z-Score
A z-score restates a value as how many standard deviations it sits from the mean. That rescaling removes the original units, which is exactly what lets you compare things that were never commensurable.
z = (x - mean) / standard deviation
Finance
How To Calculate An Amortization Schedule
An amortization schedule is the month-by-month ledger of a fixed-rate loan: every payment is the same size, but the split between interest and principal shifts a little each month. Early on almost everything goes to interest; near the end almost everything goes to principal. The monthly payment comes from one formula, and from it you can read off the first month's interest, the principal that payment retires, and the balance left afterwards.
M = P x r / (1 - (1 + r)^-n)
Education
How To Calculate An Attendance Rate
An attendance rate is the days a student actually attended divided by the days they were enrolled for. The division is trivial; the two decisions around it are not, namely which days belong in the denominator and what the resulting percentage is being measured against.
Attendance rate = Days attended / Days enrolled
Finance
How To Calculate Annuity Payments
Given a balance, a return and a number of years, the payment that exactly exhausts the account is one algebraic step away. The hard part is not the formula — it is recognising that a level payment for a fixed period is a very specific promise that real markets do not make.
PMT = PV x r x (1 + r)^n / ((1 + r)^n - 1)
Finance
How To Calculate APR
The APR is the interest rate that would produce your loan's cash flows if the fee were rolled into the rate. It answers a fairer question than the advertised nominal rate: what single annual rate, applied to the money you actually received, reproduces the payments you actually make?
Solve for i: P - F = sum of pmt / (1 + i)^k
Finance
How To Calculate APY
The annual percentage yield is what a deposit account actually returns in a year once compounding is counted. Comparing two accounts by their headline rates instead of their APYs is the most common way savers pick the slower one.
APY = (1 + r/n)^n - 1
Finance
How To Calculate Auto Loan Payment
A car loan is an amortizing loan like any other: a fixed payment retires the balance over the term. The car-specific wrinkle is the trade-off between payment size and total cost, and the effect of a trade-in and sales tax on the amount actually financed.
M = P x r / (1 - (1 + r)^-n)
Health
How To Calculate BMI
Body mass index divides weight by height squared and returns a single number that is easy to compute and easy to misread. The arithmetic is trivial. The difficulty is in knowing what the number cannot say about muscle, fat distribution, age and population.
BMI = weight in kilograms / (height in metres)^2
Health
How To Calculate BMR
Basal metabolic rate is the energy your body spends staying alive while you do nothing at all. The number is easy to compute and easy to misuse, because it is deliberately lower than anything you would ever eat.
BMR = 10w + 6.25h - 5a + s
Health
How To Calculate Body Fat Percentage
Body fat percentage splits the body into fat and everything else, and estimates the fat share from a few tape measurements. The US Navy circumference method is the most widely used of these estimates. Its arithmetic is short; its limits are worth understanding before you trust the number.
BF% = 495 / (1.0324 - 0.19077 x log(waist - neck) + 0.15456 x log(height)) - 450 for men
Finance
How To Calculate Bond Yield
A bond's yield is the income it pays divided by what you paid for it. Because bonds trade at prices above or below their face value, two bonds with the same coupon can yield very different amounts, and the price move at maturity is part of the return.
Current yield = annual coupon / price paid
Finance
How To Calculate The Break-Even Point
Break-even is the unit count at which contribution from sales finally covers every fixed cost. Below it each additional unit loses money; above it each one contributes its full margin to profit — which is why the number is more useful as a threshold than as a forecast.
Break-Even Units = Fixed Costs / (Price - Variable Cost Per Unit)
Business
How To Calculate Burn Rate
Burn rate is the speed at which a business spends its cash, and runway is how long that cash lasts at that speed. Both come from one subtraction and one division — and almost every argument about them is really an argument about which numbers belong in the subtraction.
Net Burn = Monthly Expenses - Monthly Revenue; Runway = Cash Balance / Net Burn
Finance
How To Calculate CAGR
CAGR compresses a messy multi-year history into one smooth annual rate. Because it reports the same kind of number for a seven-year stock hold and a five-year revenue line, it is the standard way to put two very different histories on one scale.
CAGR = (Ending Value / Beginning Value)^(1/n) - 1
Finance
How To Calculate CD Return
A certificate of deposit pays a fixed rate for a fixed term in exchange for leaving your money untouched. The growth depends on whether interest compounds and on how early withdrawal penalties would bite, but the core number is simply the deposit grown at the APY.
A = P(1 + r)^t
Business
How To Calculate Churn Rate
Churn rate is customers lost divided by customers at the start of the period. The division is trivial; the trap is everything that follows, because a monthly rate compounds into a yearly one that is far lower than twelve times its size.
Churn Rate = Customers Lost / Customers at the Start
Finance
How To Calculate Compound Interest
Compound interest is interest that earns interest. Once interest is added to your balance, that added amount starts earning too — which is why long horizons grow faster than people expect.
A = P(1 + r/n)^(nt)
Business
How To Calculate Conversion Rate
Conversion rate is conversions divided by visitors. The arithmetic is one division; the discipline is deciding what counts as a visitor, what counts as a conversion, and whether both were counted over the same stretch of time.
Conversion rate = conversions / visitors
Education
How To Calculate Cost Per Credit
Cost per credit is the tuition divided by the credits it buys, and it is the cleanest single rate for comparing one programme against another. Tuition of 12000 spread over 30 credits gives 400 per credit, which scales to 1200 for a three-credit course and 48000 across a 120-credit degree — but only if the tuition line is the whole bill.
Cost per credit = tuition / credits
Finance
How To Calculate Credit Card Payoff Time
Paying a fixed amount every month retires a revolving balance on a predictable schedule — and that schedule can be written as a closed-form equation rather than simulated line by line. The catch is a boundary condition the formula cannot cross: pay only the interest and the balance never falls.
n = -ln(1 - (rm x B) / P) / ln(1 + rm)
Business
How To Calculate Customer Acquisition Cost
Customer acquisition cost divides everything you spent to win demand by the number of customers who actually paid. The arithmetic is trivial; the judgement sits in deciding which costs belong in the numerator and which signups belong in the denominator.
CAC = (Marketing spend + Sales spend) / New paying customers
Business
How To Calculate Customer Lifetime Value
Customer lifetime value estimates how much contribution one customer leaves behind over their whole relationship, not just in the first month. With 50 of monthly revenue, a 70 per cent gross margin and 4 per cent monthly churn, that comes to 875.0.
LTV = ARPU x gross margin / churn
Business
How To Calculate Days Sales Outstanding
Days sales outstanding is the average number of days a business waits to be paid after making a sale. It comes from a single ratio and a single multiplication, yet it decides how much cash is trapped inside receivables — and it is routinely computed with the wrong denominator.
DSO = (Accounts Receivable / Revenue) x Days
Finance
How To Calculate Debt-To-Income Ratio
The debt-to-income ratio answers the question a lender is actually asking: not how much you owe, but whether the monthly payments fit inside your income. It takes two numbers and it decides mortgage approvals.
DTI = Total Monthly Debt Payments / Gross Monthly Income
Science
How To Calculate Density
Density is mass divided by volume, and nearly every practical difficulty comes from units: knowing which pair you are holding and which pair the answer should be in.
Density = mass / volume (rho = m / V)
Finance
How To Calculate Effective Tax Rate
Your effective tax rate is what you actually paid, expressed as one number. It is always lower than your headline bracket on the same tax — and often badly misleading if you stop at federal income tax and ignore payroll.
Effective Tax Rate = Total Tax / Gross Income
Everyday Life
How To Calculate Electricity Cost
Electricity cost is power multiplied by time, converted into the unit the bill actually uses, then priced. Almost every wrong answer comes from confusing the two quantities — watts and kilowatt-hours — before any arithmetic begins.
Cost = watts x hours / 1000 x rate per kWh
Finance
How To Calculate EMI
An equated monthly instalment is the fixed payment that repays both principal and interest over a set term. It stays the same every month, but the split between interest and principal shifts steadily in the borrower's favour.
EMI = P x r x (1+r)^n / ((1+r)^n - 1)
Science
How To Calculate Force
Force is mass times acceleration, but the numbers only make sense once mass and weight are kept apart. A 1200 kilogram car needs 3600 newtons to accelerate at 3 metres per second squared, yet it weighs 11767.98 newtons because gravity is pulling on it constantly.
F = m x a
Everyday Life
How To Calculate Fuel Cost
Fuel cost is two multiplications and one division: distance into litres, litres into money, and money into a rate you can reuse. The only real traps are the units and a consumption figure that runs backwards.
Fuel cost = (distance x consumption / 100) x price per litre
Finance
How To Calculate Future Value
Future value of an annuity projects what a stream of equal contributions becomes. Because every deposit compounds for a different length of time, this is the formula retirement plans actually depend on — not the lump-sum one.
FV = PMT x (((1 + r)^n - 1) / r)
Everyday Life
How To Calculate Gas Mileage
Gas mileage is a rate, and it arrives in two scales that run in opposite directions: litres per 100 kilometres, where lower is better, and miles per gallon, where higher is better. Converting between them is a reciprocal, not a single multiplication.
mpg = 100 / (L/100km) x 3.785411784 / 1.609344
Education
How To Calculate GPA
A grade point average is a credit-weighted average of grade points, not an average of letter grades. Every difficulty with it comes down to two things: which grade point table applies to you, and whether the credits were actually used as weights.
GPA = Sum of (grade points x credits) / Sum of credits
Finance
How To Calculate GST
Goods and services tax is a single tax applied to most supplies of goods and services. Adding it multiplies the base price; removing it divides, and the same rate can be split between national and regional shares.
GST = base x rate
Health
How To Calculate Ideal Body Weight
Ideal body weight is a formula, not a fact about health. It was written in 1974 to help clinicians dose drugs, and every version of it returns a slightly different number.
IBW = base + increment x (height in inches - 60)
Science
How To Calculate The Ideal Gas Law
The ideal gas law ties pressure, volume, amount and temperature into one equation, and the only genuinely awkward part is choosing the right value of R for the units you are holding.
PV = nRT
Finance
How To Calculate Inflation Adjusted Value
Inflation quietly erodes the buying power of money. A sum held in cash loses value every year even though its number stays the same. This calculator converts between nominal amounts and real, inflation-adjusted amounts so you can compare figures honestly across time.
Real value = nominal / (1 + i)^t
Business
How To Calculate Inventory Turnover
Inventory turnover is cost of goods sold divided by average inventory, and it answers one question: how many times did the shelf empty during the period? Everything contentious about it comes from which inventory figure sits in the denominator.
Inventory turnover = COGS / average inventory
Finance
How To Calculate Investment Return
Total return measures how much an investment gained in percentage terms. Annualised return converts that into a per-year rate, which is the only fair way to compare a three-year holding with a ten-year one.
Total return = (final value - initial) / initial; Annualised = (1 + total)^(1/years) - 1
Finance
How To Calculate IRR
The internal rate of return is the discount rate that makes an investment's net present value exactly zero. It is the break-even rate the project must beat, and it lets you compare projects of different sizes on a single percentage scale.
NPV = 0 at the rate r, so r is the IRR
Science
How To Calculate Kinetic Energy
Kinetic energy is one half times mass times the square of speed. The square is what makes the formula interesting: it is why doubling your speed quadruples the energy you have to lose, and why momentum tells a different story.
KE = 1/2 x m x v^2
Finance
How To Calculate Loan Payment
An amortizing loan keeps the payment fixed while the split between interest and principal changes every month. The formula that produces that payment — and the amortization behind it — explains why shortening the term saves so much.
M = P x r(1 + r)^n / ((1 + r)^n - 1)
Business
How To Calculate Markup
Markup is the amount loaded on top of cost to reach a selling price, expressed as a percentage of that cost. Margin divides the very same profit by the price instead, which is why a 40% markup on a cost of 60 produces a price of 84 but a margin of only 28.5714%.
Selling price = Cost x (1 + markup), markup = (Price - Cost) / Cost
Science
How To Calculate Molarity
Molarity is the concentration chemists reach for first: moles of solute per litre of solution. Everything difficult about it lives in two distinctions — moles rather than grams, and solution rather than solvent.
M = n / V
Finance
How To Calculate Net Worth
Net worth is the single number that summarizes a balance sheet: everything owned minus everything owed. It takes about ten minutes to compute and it answers a question no income figure can — whether you would be solvent if every debt came due today.
Net Worth = Total Assets - Total Liabilities
Finance
How To Calculate NPV
Net present value asks a single sharp question: after discounting every future cash flow back at the rate you require, does the investment create or destroy value? It is the most reliable single test in capital budgeting because it works in money rather than in ratios.
NPV = -C0 + sum of CF / (1 + r)^t
Science
How To Calculate Ohm's Law
Ohm's law is one relationship among three quantities, and any two of them determine the third. Everything else in the topic is either a rearrangement of that single equation or a consequence of it.
V = I x R
Health
How To Calculate One Rep Max
A one rep max is the heaviest load you can lift once. Testing it directly is risky, so most lifters estimate it from a lighter set — and the whole topic is really about how much you should trust that estimate.
Epley: 1RM = w x (1 + reps/30) | Brzycki: 1RM = w x 36 / (37 - reps)
Everyday Life
How To Calculate Overtime Pay
Overtime pay is not a single multiplication. It is a split: hours up to a threshold are paid at the base rate, hours beyond it are paid at the base rate times a multiplier, and the two bands are added.
Total pay = min(H, T) x R + max(0, H - T) x R x M
Everyday Life
How To Calculate Paint Coverage
Paint coverage is quoted per litre per coat, so the coat count multiplies the area before you divide. The arithmetic is one multiplication and one division; the judgement lies in reading the coverage figure honestly and turning litres into tins you can actually buy.
Litres needed = (wall area x coats) / coverage per litre
Math
How To Calculate Percent Decrease
Percent decrease is a drop divided by the level it fell from. The denominator decides everything: 120 to 90 is a fall of 25.00%, and the same 30 measured against 90 gives 33.3333%, which answers a different question entirely.
Percent Decrease = (Original Value - New Value) / Original Value x 100
Math
How To Calculate Percent Increase
Percent increase is a gap divided by where you started. Get the denominator right and the rest is arithmetic; get it wrong and every figure downstream is quietly answering a different question.
Percent Increase = (New Value - Original Value) / Original Value x 100
Math
How To Calculate Percentage Change
Percentage change is a difference divided by a starting point. That denominator is where almost every mistake lives — including the one that makes a 90% collapse look recoverable.
Percentage Change = (New Value - Original Value) / Original Value x 100
Science
How To Calculate Power
Power is the rate at which energy is transferred, calculated by dividing work by time. Almost every error in this topic comes from mixing up a rate with a quantity — watts with watt-hours — before any arithmetic begins.
Power = work / time
Finance
How To Calculate Present Value
Present value runs the time value of money backwards: instead of growing today's money forward, it tells you what a future payoff is worth right now. Every bond price, lease valuation and capital budgeting decision rests on this one operation.
PV = FV / (1 + r)^n
Science
How To Calculate Pressure
Pressure is force divided by area, and almost everything interesting about it comes from the area in the denominator. The same push concentrated on a knife edge and spread across a snowshoe produces pressures that differ by orders of magnitude.
P = F / A
Business
How To Calculate Profit Margin
Profit margin is the share of revenue left over after cost, computed as revenue minus cost divided by revenue. Everything contentious about the topic comes from a single choice: which number sits on the bottom of the fraction.
Profit margin = (Revenue - Cost) / Revenue x 100%
Health
How To Calculate Protein Intake
Protein needs are quoted as a rate, not a fixed number: grams per kilogram of bodyweight per day. That single multiplication hides most of the real questions, which are about which rate applies to you and how the daily total is best spread.
Protein (g) = bodyweight (kg) x grams per kg
Finance
How To Calculate Purchasing Power
Purchasing power translates an amount of money into what it can actually buy. Every long-term plan denominated in fixed dollars is quietly wrong until this adjustment is applied.
Real Value = Nominal Amount / (1 + i)^n
Finance
How To Calculate Refinance Savings
Refinancing replaces one loan with another, usually at a lower rate. The monthly saving is the obvious gain, but closing costs and a possibly longer term mean the break-even point and the lifetime interest matter just as much.
Saving = old payment - new payment; Break-even = costs / monthly saving
Business
How To Calculate Revenue Growth Rate
Revenue growth is a gap divided by where the business started. The annualised figure is a different question with a different answer, and collapsing the two into one number is why most growth reports quietly overstate themselves.
Revenue Growth = (Ending Revenue - Starting Revenue) / Starting Revenue
Finance
How To Calculate ROI
Return on investment expresses what you gained as a percentage of what it cost you. That single normalization is why ROI survives every criticism leveled at it: it works on a stock, a rental property, or a training program with exactly the same arithmetic.
ROI = (Current Value - Cost) / Cost x 100%
Finance
How To Calculate Roth IRA Growth
A Roth IRA is funded with money that has already been taxed, and qualifying withdrawals are tax free. The benefit is not a deduction today but decades of compounding that the tax authority never touches.
Future value = sum of contributions x (1+r)^t, plus existing balance grown
Finance
How To Calculate Sales Tax
Sales tax and VAT calculations have one common trap: the rate applies to the net price, not to the gross. Adding tax to a net figure means multiplying; removing tax from a gross figure means dividing, and using the wrong operation gives an answer that is close enough to look right but wrong by the tax amount.
Gross = net x (1 + rate) ; Net = gross / (1 + rate)
Finance
How To Calculate Savings Account Interest
Savings account interest depends on the rate and how often it compounds. Monthly compounding earns a little more than annual compounding at the same headline rate, and regular deposits add to the balance faster than the interest alone.
Balance = principal x (1 + rate/n)^(n x t)
Finance
How To Calculate How Long It Takes To Reach A Savings Goal
A savings goal has three moving parts — what you already have, what you add each month, and what compounding quietly adds on top. The third one is the reason rounding your monthly figure to a nice number can push your finish line out by years.
n = ln((FV x r + PMT) / (PV x r + PMT)) / ln(1 + r)
Finance
How To Calculate Simple Interest
Simple interest pays only on the original principal and never reinvests itself. That makes it the easiest interest calculation to verify by hand — and the right model for most short-term loans, bonds and treasury bills.
I = P x r x t
Math
How To Calculate Slope
Slope is how much a quantity changes vertically for one unit of horizontal movement. It turns two data points into a rate, and once you have it, the whole line follows.
Slope = (y2 - y1) / (x2 - x1)
Science
How To Calculate Speed
Speed is distance divided by time, and almost every error in the topic comes from the units rather than the division. Get the units consistent and the arithmetic is a single line.
s = d / t
Everyday Life
How To Calculate Stacked Discounts
Stacked discounts multiply rather than add. A price of 200 cut by 20% and then by 10% falls to 160.0 and then to 144.0, an effective discount of 0.28, not the 0.30 that adding the two rates would suggest.
Final Price = Price x (1 - first) x (1 - second)
Math
How To Calculate Standard Deviation
Standard deviation is the typical distance of observations from their mean, measured in the original units. The squaring is what makes it algebraically useful — and the n-1 is what makes it honest for a sample.
SD = sqrt(Sum of (xi - Mean)^2 / (n - 1))
Finance
How To Calculate Student Loan Payments
A student loan repaid on the standard plan uses the same annuity formula as any other instalment loan. The balance, the rate and the term set the payment, and the term is usually the most powerful lever on total interest.
Payment = P x r x (1+r)^n / ((1+r)^n - 1)
Health
How To Calculate Target Heart Rate
Target heart rate turns an intensity you can name into a pulse you can check. The arithmetic is short; the interesting part is that almost every input is an estimate.
Target HR = Resting HR + (Max HR - Resting HR) x Intensity
Finance
How To Calculate Tax Bracket
A progressive tax system taxes each slice of income at its own rate. Your bracket is the rate on the last dollar you earn, not the rate on all of it, and the difference between the two is the source of most confusion about taxes.
Tax = sum of (income in each bracket x that bracket's rate)
Math
How To Calculate The Area Of A Circle
Circle area is pi times the radius squared. Everything difficult about the topic sits in two decisions: which length is the radius, and how much precision you carry.
Area = pi x r^2
Math
How To Calculate The Area Of A Triangle
A triangle covers exactly half of whatever parallelogram shares its base and height. Nearly every wrong answer comes from one of two slips: a height that was never perpendicular, or a base and a height borrowed from two different sides.
Area = 1/2 x base x height
Education
How To Calculate The Grade You Need On The Final
The grade you need on the final is not a percentage to aim for but an unknown inside a weighted average. Solve it directly and a comfortable-looking target can turn out to be arithmetically impossible.
Needed on final = (Target - Current x (1 - Final weight)) / Final weight
Finance
How To Calculate The Rule Of 72
The rule of 72 is a mental shortcut for doubling time: divide 72 by the annual return and you get roughly how many years it takes for money to double. It is fast, memorable and close enough for nearly every rate you will meet.
Doubling time = 72 / annual return percent
Math
How To Calculate The Volume Of A Cylinder
Cylinder volume is the area of the circular base multiplied by the height. Nearly every wrong answer comes from one of two places: a diameter used where a radius belongs, or units that were never made consistent before being cubed.
V = pi x r^2 x h
Math
How To Calculate The Volume Of A Rectangular Prism
Volume of a rectangular prism is length times width times height. Nearly every error on this page comes from somewhere else: mismatched units, external instead of internal measurements, or a cubic answer read as a liquid one.
V = l x w x h
Everyday Life
How To Calculate Tile Count
Tile count is the surface area divided by the area of one tile, with a wastage allowance added and the answer rounded up. The only real decisions are how much wastage to allow and which direction to round.
Tiles = (room area / tile area) x (1 + wastage)
Everyday Life
How To Calculate Unit Price
Unit price is the price divided by the quantity, expressed per gram, per litre or per 100 g, and it is the only figure that compares two packs of different sizes fairly. The arithmetic is one division; the discipline is applying it before you trust a label.
Unit price = price / quantity
Finance
How To Calculate VAT
Value added tax is charged on the price of goods and services and is normally included in the price you see. Adding it is a multiplication; removing it is a division, and mixing the two up is the most common VAT error.
Gross = net x (1 + rate)
Health
How To Calculate Waist To Hip Ratio
Waist-to-hip ratio divides one circumference by another and returns a single unit-free number. The arithmetic takes seconds; the judgement lies in measuring at the right landmarks and in reading the result as a screening signal rather than a diagnosis.
WHR = waist / hip
Health
How To Calculate Water Intake
Water intake is estimated from body weight: the common guideline is 35 millilitres for every kilogram you weigh, which is 2450 mL at 70 kg. The number is a starting point rather than a rule, because food, other drinks, heat and exercise all shift it.
mL = bodyweight (kg) x mL per kg
Science
How To Calculate Wave Speed
Wave speed is frequency multiplied by wavelength, written v = f times lambda. The arithmetic is trivial; the insight is that the two factors are locked together by the speed of the medium, so changing one forces the other to compensate.
v = f x lambda
Finance
How To Calculate Your FIRE Number
The FIRE number is your annual spending divided by the withdrawal rate you consider sustainable. At 4% that means twenty-five times a year of expenses — a figure that is easy to compute and very easy to compute on the wrong expenses.
FIRE Number = Annual Spending / Safe Withdrawal Rate
Unit Conversion
How To Convert Acres To Hectares
An acre and a hectare both describe land, and both are casually called about the size of a football pitch, which is exactly why they get confused. The conversion itself is a single exact multiplication: one acre is 0.40468564224 hectare, so five acres is 2.0234282112 hectares.
ha = acres x 0.40468564224
Unit Conversion
How To Convert Celsius To Fahrenheit
Two things are happening in the temperature conversion, and keeping them apart is the whole skill: one scales the size of a degree, the other moves where zero sits.
F = C x 9/5 + 32
Unit Conversion
How To Convert Celsius To Kelvin
Converting Celsius to kelvin looks almost too easy beside the Fahrenheit rule, and the reason is that only the zero point moves while the size of the degree stays exactly the same.
K = C + 273.15
Unit Conversion
How To Convert Feet To Meters
Feet and metres are tied together by a fixed, exact number, so the whole task is one multiplication. Every difficulty that remains comes from how the original measurement was written down.
m = ft x 0.3048
Unit Conversion
How To Convert Gallons To Liters
One decision comes before the arithmetic — which gallon you have — and once that is settled the whole conversion is a single multiplication by an exact factor.
L = gal x 3.785411784
Unit Conversion
How To Convert Inches To Centimeters
Inches to centimetres is the rare conversion where the factor is exact by definition rather than measured, so the whole skill reduces to applying it in the right direction and reporting no more precision than the measurement earned.
cm = in x 2.54
Unit Conversion
How To Convert Kilograms To Pounds
Kilograms to pounds is a single multiplication by 2.2046226218487757. The only real decision is whether you use that exact factor or the familiar 2.2 shortcut, which quietly runs 0.3235835 lb high on 70 kg — about 147 g of avoidable error.
lb = kg x 2.2046226218487757
Unit Conversion
How To Convert Miles To Kilometers
Miles to kilometers is the one everyday conversion where the factor is exact rather than rounded for convenience, which means there is no excuse for a wrong digit and every real error comes from applying the right number in the wrong direction.
km = mi x 1.609344
Unit Conversion
How To Convert Mph To Kph
Miles per hour to kilometres per hour is the simplest kind of rate conversion, because both rates are per hour and the hour cancels, leaving a single exact factor of 1.609344. Almost every mistake in the topic comes from rounding that factor or from changing the time unit when the question did not ask for it.
kph = mph x 1.609344
Unit Conversion
How To Convert Ounces To Grams
Ounces to grams is a single multiplication by an exact factor, and almost every mistake people make comes from confusing the mass ounce with the fluid ounce that shares its name.
g = oz x 28.349523125
Unit Conversion
How To Convert Pounds To Kilograms
Pounds to kilograms is one multiplication. The only real decision is whether you use the exact factor, or a mental shortcut that quietly overshoots by an amount that grows with every pound you add.
kg = lb x 0.45359237
Finance
How To Convert A Salary To An Hourly Rate
The textbook answer divides salary by 2,080 hours. The honest answer divides it by the hours you actually surrender to the job, which for most professional roles is a substantially larger number and a substantially smaller rate.
Hourly Rate = Annual Salary / (Hours Per Week x Paid Weeks Per Year)
Unit Conversion
How To Convert Square Feet To Square Meters
Converting square feet to square metres is a single multiplication, but it is the one conversion where the most common mistake, using the linear factor once instead of squaring it, produces an answer that is wrong by a factor of 3.28.
m2 = sq ft x 0.09290304
Math
How To Find The Sum Of A Geometric Series
In a geometric series each term is the previous one multiplied by a fixed ratio. That single change turns polynomial growth into exponential growth — and turns the sum formula into something with a constraint worth respecting.
S = a1 (1 - r^n) / (1 - r), and S-infinity = a1 / (1 - r) when |r| < 1
Math
How To Find The Sum Of An Arithmetic Series
An arithmetic series adds the terms of a sequence that changes by a fixed amount each step. The sum has a closed form, which means adding a thousand terms costs the same effort as adding five.
S = n/2 x (a1 + an)
Everyday Life
How To Scale A Recipe
Scaling a recipe is one division followed by a great many multiplications. The division is trivial; knowing which ingredients should not be multiplied at all is the actual skill.
Scale factor = desired servings / original servings, then new amount = original amount x factor
Math
How To Solve A Proportion
A proportion says two ratios are equal, which means one unknown journey holds all the information you need. The entire skill is deciding which quantity sits above which in the division.
a / b = c / d, so d = c x b / a
Math
How To Solve A Quadratic Equation
Every quadratic equation has a closed-form solution. The discriminant tells you what kind of answer to expect before you compute anything, which is the part people skip.
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Math
How To Use The Pythagorean Theorem
For right triangles, the squares of the two shorter sides add exactly to the square of the longest. That single relation turns any two known sides into the third.
c^2 = a^2 + b^2, so c = sqrt(a^2 + b^2)