What is a percentage?

A percentage is a way of expressing a number as a fraction of 100. The word comes from “per cent”, meaning “per hundred”. So 25% means 25 out of every 100, or one quarter.

Percentages are useful because they make it easy to compare proportions, discounts, exam scores, growth rates and many everyday figures.

Key formulas

What is X% of Y?

Result = (X ÷ 100) × Y

X is what percent of Y?

Percentage = (X ÷ Y) × 100

Percentage change from A to B

% change = ((B − A) ÷ A) × 100

A positive result is an increase. A negative result is a decrease. The starting value A cannot be zero.

Step-by-step examples

Example 1: What is 15% of 200?

(15 ÷ 100) × 200 = 0.15 × 200 = 30

Example 2: 30 is what percent of 150?

(30 ÷ 150) × 100 = 0.2 × 100 = 20%

Example 3: A price rises from 80 to 100. What is the percentage increase?

((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase

Common mistakes

  • Mixing up “X% of Y” with “X is what percent of Y”.
  • Using the new value instead of the original value when calculating percentage change.
  • Forgetting that percentage change is relative to the starting amount, not an absolute difference alone.

FAQ

Can a percentage be more than 100%?
Yes. For example, 150% of 40 is 60. Percentage increases above 100% simply mean the amount more than doubled.

Is percentage change the same as percentage points?
No. If an interest rate moves from 2% to 3%, that is a rise of 1 percentage point, but a 50% relative increase.

Try the free online tool:

Open Percentage Calculator