Percentage Calculator

Percentages are just a comparison

"Per cent" means "per hundred", so a percentage is a fraction rewritten with 100 as the bottom number. 15% is the same as 15/100, or 0.15. Every percentage question is therefore a small rearrangement of the same three quantities: the part, the whole, and the rate.

The five questions this page answers

• What is X% of Y? Multiply: Y × X ÷ 100. Example: 15% of 200 = 200 × 0.15 = 30. Use it for tips, tax, commission and discounts.
• X is what percent of Y? Divide, then scale to 100: X ÷ Y × 100. Example: 30 ÷ 200 × 100 = 15%. Use it when a score or a share of a budget needs turning into a percentage.
• Percentage change from A to B. (B − A) ÷ A × 100. A rise from 80 to 100 is +25%; a fall to 60 is −25%. This is the one to use for prices, revenue, weight and traffic.
• Increase or decrease A by P%. A × (1 ± P ÷ 100). Increasing 250 by 12% gives 250 × 1.12 = 280; decreasing it by 12% gives 250 × 0.88 = 220. Handy for adding VAT or removing a discount.
• Percentage difference between A and B. |A − B| ÷ ((A + B) ÷ 2) × 100. Use this when neither number is a natural starting point — for instance comparing two products or two temperatures.

Percentage change vs percentage difference

These two get mixed up constantly. Percentage change has a direction and a fixed base: it measures movement *from* A *to* B. Percentage difference has no direction and is symmetric: swapping A and B gives the same answer, because the average of the two is used as the base. Comparing 100 and 150 is a +50% change (from 100) but a 40% difference.

Percentage points are not percent

A rate that goes from 4% to 5% has risen by 1 percentage point, but by 25% in relative terms. This distinction matters in interest rates, polling and statistics — reporters blur it often, and it is the source of a lot of accidental exaggeration.

Where this shows up in daily life

• Shopping: an item at 240 with 30% off costs 240 × 0.7 = 168.
• Dining: a 15% tip on 86 is 12.90, so the total is 98.90.
• Work: a salary moving from 5,000 to 5,600 is a 12% raise.
• Finance: an investment falling from 1,200 to 900 has lost 25% — note it then needs +33.3% just to get back to where it started, which is why losses hurt more than the equivalent gains.
• Study: 42 correct out of 56 is 75%.

A few common mistakes

• Chaining percentages by adding them. Two successive 10% discounts are not a 20% discount: 100 → 90 → 81, which is 19% off. Always multiply the factors.
• Using the wrong base. The denominator is the value you started *from*, not the value you ended up at.
• Forgetting that increase and decrease are not reversible. +20% then −20% leaves 96, not 100.

Privacy

All five calculators run in your browser as you type — the numbers you enter are never sent anywhere.

FAQ

What is the difference between percentage change and percentage difference?

Percentage change is directional and uses the starting value as the base: (B − A) ÷ A × 100. Percentage difference is symmetric and uses the average of the two values: |A − B| ÷ ((A + B) ÷ 2) × 100. Swapping the numbers changes the first result but not the second.

Why is a 20% rise followed by a 20% fall not back to the start?

Because each step is calculated on a different base. 100 rises to 120, then 20% of 120 is 24, so it falls to 96. Gains and losses are asymmetric: after a 50% loss you need a 100% gain to break even.

Is "percent" the same as "percentage point"?

No. A move from 4% to 5% is 1 percentage point, but a 25% relative increase. Percentage points compare two percentages directly; percent compares amounts. Mixing them up exaggerates or understates changes.

How do I calculate a discount or a tip quickly?

For a discount, multiply the price by (1 − rate): 30% off 240 is 240 × 0.7 = 168. For a tip, use the "what is X% of Y" row: 15% of 86 is 12.90, and add it to the bill for the total.