Percentage calculator

What the result means

Percentages compare a part with a whole, or describe how much a value has changed. The same three numbers — part, whole and percent — can be rearranged depending on which one you already know.

How it is calculated

X% of Y = (X ÷ 100) × Y. Percentage change = (new − original) ÷ |original| × 100

• X: A percentage or a comparison value, depending on the mode.
• Y: The base amount.

Finding a percentage of a number scales it. Reverse percentage asks what fraction one number is of another. Increase and decrease apply 1 + r or 1 − r. Difference reports the signed percentage change from Y to X.

Worked example

A 15% discount on $240

A jacket marked at $240 is advertised at 15% off.

Discount

15% of 240 = 36

Sale price

240 − 36 = 204, or 240 × 0.85

The discounted price is $204. That is a decrease mode calculation, not 15% of a mystery total.

Increase is not the inverse of decrease

A 20% decrease followed by a 20% increase does not return you to the start. 100 decreased by 20% is 80; 80 increased by 20% is 96. Percentage changes multiply, they do not cancel as equal-and-opposite amounts.

When comparing prices, wages or bills, decide whether you want the change relative to the original (the usual percentage change) or a symmetric difference. This calculator uses change relative to the original value Y.

Three questions that look the same and are not

“What is 15% of $240?” is a part of a whole: $36. “$36 is what percent of $240?” is the reverse: 15%. “$240 increased by 15%” is a new total: $276. Mixing the first with the third is how a 15% discount becomes a $276 sale price instead of $204.

GST is a special case of the increase: adding 10% is multiplying by 1.1, but removing GST is dividing by 1.1 (or by 11 for the tax component), not subtracting 10%. Use the GST calculator when that is the question.

Questions