Percentage calculator

The formulas, in plain words

What is X% of Y?

Answer = X ÷ 100 × Y

15% of 200 = 0.15 × 200 = 30.

X is what percent of Y?

Answer = X ÷ Y × 100

30 out of 200 = 30 ÷ 200 × 100 = 15%. This is also how you turn a test score into a percentage: 42 marks out of 50 is 84%.

Percentage change between two numbers

Change = (new − old) ÷ |old| × 100

A price going from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. Going back from 100 to 80 is −20%, not −25%, because the starting value is different. The old value cannot be zero.

Increase or decrease by a percentage

Result = X × (1 + Y ÷ 100)

Use a negative Y for a decrease. 200 increased by 10% is 220; 200 decreased by 10% (Y = −10) is 180.

Reverse percentage (find the original)

Original = X ÷ (1 + Y ÷ 100)

After a 5% rise a price is 126, so the original was 126 ÷ 1.05 = 120. After a 20% discount something costs 80, so it was 80 ÷ 0.8 = 100. Taking 20% off 80 (64) would be wrong.

A common trap

A 10% increase followed by a 10% decrease does not get you back where you started: 100 → 110 → 99. Each percentage is taken of a different number. In the same way, two 10% rises in a row add up to 21%, not 20%.

FAQ

What is the difference between percentage change and percentage points?

If an interest rate goes from 4% to 5%, it rose by 1 percentage point, but by 25% in relative terms (1 ÷ 4 × 100).

What about "percentage difference"?

When neither number is the "starting" one, some people use the difference divided by the average of the two: |A − B| ÷ ((A + B) ÷ 2) × 100. For 80 and 100 that gives about 22.2%. Use percentage change when there is a clear before and after.

How many decimals are shown?

Up to 6 decimal places, with trailing zeros removed.