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A Percentage Calculator

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.

Percent of the base

37.5

Part as a share of the base
15.00%
Base after adding the percentage
287.5
Base after subtracting it
212.5

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

Part = Whole x Percentage / 100

P
The part — the slice being taken
W
The whole — the thing it is a slice of
x
The percentage, expressed as a whole number such as 15
W x x/100
The base multiplied by the decimal form of the percentage

How to check the result by hand

  1. 1

    Decide which of the three sentences you are reading

    Are you given a rate and a base, two amounts, or an amount and a rate you need to reverse? Naming the type first makes the operation obvious and removes the guesswork.

  2. 2

    Identify the whole — the thing after "of"

    In "15% of 250" the base is 250. In "37.5 is 15% of what" the base is unknown. Every percentage attaches to a base, and confusing part with whole is the root of most wrong answers.

  3. 3

    Convert the percentage to a decimal

    Divide by 100. Fifteen percent is 0.15. Multiplying by 15 instead of 0.15 gives an answer one hundred times too large, and it is still the single most common error.

  4. 4

    Multiply or divide depending on the type

    Looking for the part — multiply. Looking for the rate — divide part by whole. Looking for the whole — divide part by the rate. Only one of the three involves multiplication.

  5. 5

    Sanity-check against rough bounds

    Ten percent is a tenth, fifty percent is a half, and a hundred percent is the whole thing. If 18% of $450 looks like $8,100 rather than $81, the decimal step was skipped.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Percentage page.