How to Calculate Percentages: Formulas, Examples & Free Tool
A practical guide to the four most common percentage problems — with formulas, worked examples, and a free online calculator that updates as you type.
Percentages come up constantly — discounts, tax rates, exam scores, salary raises, quarterly reports. Most people know roughly what they mean, but the formulas get slippery fast, especially when you’re trying to figure out percentage change vs. percentage difference. Here are the four problems that come up most often, with exact formulas and examples for each.
What is X% of Y?
The most common case. The formula:
Result = (X / 100) × Y
Examples:
- 15% of 200 = (15 / 100) × 200 = 30
- 8.5% of 1,200 = (8.5 / 100) × 1,200 = 102
- 0.5% of 50,000 = (0.5 / 100) × 50,000 = 250
Where this comes up: calculating a tip, finding the VAT on a purchase, working out a commission.
X is what percent of Y?
This one asks for the ratio of two numbers expressed as a percentage:
Result = (X / Y) × 100
Examples:
- 30 is what percent of 200? → (30 / 200) × 100 = 15%
- 75 is what percent of 300? → (75 / 300) × 100 = 25%
- 1 is what percent of 7? → ≈ 14.286%
Where this comes up: marking a test score, calculating market share, comparing a part to a whole.
Percentage change
Percentage change measures how much a value grew or shrank relative to its starting point. Order matters here — you always need to know which value came first.
Change = ((New − Old) / |Old|) × 100
A positive result is an increase; negative is a decrease.
Examples:
- Price rises from 80 to 100: ((100 − 80) / 80) × 100 = +25%
- Price falls from 100 to 80: ((80 − 100) / 100) × 100 = −20%
- Salary goes from 50,000 to 53,500: +7%
One thing that surprises people: a 25% increase and a 20% decrease don’t cancel out. Going from 80 to 100 is a 25% increase, but going back from 100 to 80 is only a 20% decrease. The math is asymmetric.
Where this comes up: year-over-year revenue, weight change over time, stock price movement.
Percentage difference
Percentage difference is similar to percentage change, but symmetric. It doesn’t care which value is “before” or “after” — it measures how far apart two values are relative to their average.
Difference = (|A − B| / ((|A| + |B|) / 2)) × 100
Examples:
- Difference between 80 and 100: (20 / 90) × 100 ≈ 22.22%
- Difference between 50 and 60: (10 / 55) × 100 ≈ 18.18%
Swapping A and B always gives the same result, which makes this formula right when comparing two peer values with no inherent starting point — like prices at two different stores.
Common mistakes worth knowing
Change vs. difference. If you have a before/after scenario, use percentage change. If the two values are peers with no time order, use percentage difference.
“Of” vs. “off”. “20% of £50” is £10. “20% off £50” means you pay £40 — you subtract the result from the original. They look similar but aren’t.
Chaining percentages. A 10% increase followed by a 10% decrease does not return to the original: 100 × 1.10 × 0.90 = 99. Not 100. This catches people out in financial projections.
Rounding. Round only the final answer. Rounding intermediate steps accumulates errors in multi-step calculations.
Use the free calculator
The Percentage Calculator handles all four formulas above. Type your numbers and the result appears immediately — no button to press, no signup. It runs entirely in your browser, so your numbers stay on your device.
Try the Percentage Calculator for your next calculation.