How this calculator works
This calculator handles the three percentage questions that come up in practice: taking a percentage of a number (discounts, commissions), expressing one number as a percentage of another (test scores, market share), and measuring change between two values (price increases, weight loss).
Switch modes with the buttons at the top. Every result updates as you type, and the share button copies a link that reopens the calculator with your exact numbers.
How do you calculate a percentage?
X% of Y = (X ÷ 100) × YX as a percent of Y = (X ÷ Y) × 100Percent change = ((new − old) ÷ |old|) × 100Percent change is measured against the starting value, which is why going from 100 to 150 is +50% but going from 150 back to 100 is only −33.3%.
Worked example: a 25% discount
- A jacket costs $80 and is 25% off.
- Discount: (25 ÷ 100) × 80 = $20.
- You pay 80 − 20 = $60.
- Check with the reverse question: 20 is what percent of 80? (20 ÷ 80) × 100 = 25%. It matches.
Frequently asked questions
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Going from 120 to 150: (150 − 120) ÷ 120 × 100 = 25% increase.
Why is a 50% increase not undone by a 50% decrease?
Because the base changes. 100 increased by 50% is 150, but 150 decreased by 50% is 75. Each percentage is taken of a different starting value.
What is a percentage point?
The simple difference between two percentages. If interest rises from 4% to 6%, that is 2 percentage points — but a 50% relative increase.
How do I work out a percentage without a calculator?
Break it into easy pieces: 10% is the number divided by 10, 1% is divided by 100. For 35% of 240, take 10% (24) three times plus 5% (12) = 84.
How do I calculate a percentage decrease?
Subtract the new value from the old value, divide by the old value, and multiply by 100 — the mirror image of a percentage increase. Going from 150 to 120: (150 − 120) ÷ 150 × 100 = 20% decrease.