Science Calculations
Physics, chemistry and astronomy formulas explained with units, constants and worked examples.
10 calculations published in this category.
Physics
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)
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
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
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
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
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
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
Chemistry
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
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