How to Calculate a Percentage: Formulas and Examples

Percentages appear everywhere — discounts, taxes, tips, interest rates, exam scores, statistics. Yet the three core percentage questions are easy to confuse, and reaching for the wrong formula under pressure leads to mistakes. This guide covers all three, with worked examples you can apply immediately.

The word "percent" means "per hundred"

A percentage is just a fraction out of 100. So 25% means 25 out of 100, which equals 0.25 as a decimal or 1/4 as a fraction. Converting between the three is the foundation of every percentage calculation:

25%  =  25/100  =  0.25
50%  =  50/100  =  0.50
7%   =  7/100   =  0.07

To turn a percentage into a decimal, divide by 100 (move the decimal point two places left). That single move unlocks most calculations.

Question 1: What is X% of Y?

This is the most common form — finding a portion of a number, like a discount or a tip.

Formula:  (X / 100) × Y

Example:  What is 15% of 80?
          (15 / 100) × 80
          0.15 × 80 = 12

So 15% of 80 is 12. A handy mental shortcut: 10% of any number is just that number with the decimal moved one place left (10% of 80 = 8), and you can build other percentages from there.

Question 2: X is what percent of Y?

This reverses the first question — you have the part and the whole, and you want the percentage.

Formula:  (X / Y) × 100

Example:  12 is what percent of 80?
          (12 / 80) × 100
          0.15 × 100 = 15%

Use this for "I scored 45 out of 60 — what percentage is that?" (45/60 × 100 = 75%).

Question 3: Percentage change

This measures how much something grew or shrank, used for price increases, growth rates, and statistics.

Formula:  ((new - old) / old) × 100

Example:  A price rose from 50 to 65.
          ((65 - 50) / 50) × 100
          (15 / 50) × 100 = +30%

A positive result is an increase, negative is a decrease. Note the asymmetry that surprises everyone: a 50% drop requires a 100% rise to get back to the start, because the base changes.

Percentage vs percentage points

This distinction matters enormously in news and finance. If an interest rate moves from 10% to 15%, it rose 5 percentage points, but it rose 50 percent (relative to the original 10%). Mixing these up can make a small change sound huge or a huge change sound small. Always check which one is meant.

Common mistakes

1. Forgetting to convert. 15% is 0.15, not 15, in a multiplication.
2. Stacking discounts wrong. 20% off then 10% off is not 30% off — it is 28%, because the second discount applies to the already-reduced price.
3. Confusing the base. Percentage change always divides by the original value, not the new one.

For quick, error-free answers to any of these three questions, the calculator below handles all of them — just pick the type, enter your numbers, and it shows the result along with the formula used.