Math guide

How to Calculate a Percentage

Every percentage problem is one of three questions in disguise: find the part, find the percent, or find the change. Once you can spot which one you're looking at, the arithmetic is one multiply and one divide.

Last reviewed 2026-08-01

The one idea behind all percentages

A percentage is a fraction with a denominator of 100. 40% is 40/100, which is 0.4 as a decimal. Converting between the three forms — percentage, fraction, decimal — is the entire trick.

Percent to decimal: divide by 100 (move the point two places left). Decimal to percent: multiply by 100.

Problem 1: What is P% of X?

Convert the percentage to a decimal and multiply.

What is 15% of 240? → 0.15 × 240 = 36.

Formula: Part = (P ÷ 100) × X
Quick check: 10% of anything is the number with the point moved one place left; 15% is 10% plus half of that.

Problem 2: A is what percent of B?

Divide the part by the whole, then multiply by 100.

42 out of 56 on a test → 42 ÷ 56 = 0.75 → 75%.

Formula: Percent = (Part ÷ Whole) × 100
The whole can't be zero — division by zero is undefined.

Problem 3: What is the percentage change?

Subtract the old value from the new value, divide by the old value, multiply by 100. A positive answer is an increase, negative is a decrease.

Price rises from $80 to $92 → (92 − 80) ÷ 80 = 0.15 → a 15% increase.

Common mistakes

Three errors account for most wrong percentage answers:

Mixing up the base: the base of a percentage change is always the starting value, not the new one.
Adding percentages that should compound: +10% then +10% is +21%, not +20%.
Reversing incorrectly: to undo a 25% increase you divide by 1.25 — subtracting 25% gives a different number.