What is a Percentage?
A percentage expresses a number as a fraction of 100 — “per cent” literally means “per hundred.” Saying “25% of customers” is the same as saying “25 out of every 100 customers.” Percentages make proportions comparable: a 15% discount means the same relative saving whether the price is $40 or $4,000.
Almost every everyday percentage question is one of three shapes, and this calculator handles all three.
The Three Percentage Questions
1. What is X% of Y? — the discount/tip/tax question. What is 15% of 200? → 0.15 × 200 = 30.
2. X is what percent of Y? — the share/score question. 30 is what percent of 200? → 30 ÷ 200 × 100 = 15%.
3. What is the change from X to Y? — the growth/drop question. From 200 to 250? → (250 − 200) ÷ 200 × 100 = +25%.
Pick the matching mode, type the two numbers, and the answer appears with a plain-language sentence so you can sanity-check that you asked the question you meant to ask.
How to Use This Tool
- Choose the question type with the mode buttons.
- Enter your two numbers — the labels adjust to the selected mode.
- Read the result and the explanation sentence below it.
Quick Mental Math Reference
| To find | Trick | Example |
|---|---|---|
| 10% | move the decimal point left | 10% of 480 = 48 |
| 5% | half of 10% | 5% of 480 = 24 |
| 15% | 10% + 5% | 15% of 480 = 72 |
| 20% | double 10% | 20% of 480 = 96 |
| 25% | divide by 4 | 25% of 480 = 120 |
| 50% | divide by 2 | 50% of 480 = 240 |
| 1% | move the decimal two places | 1% of 480 = 4.8 |
Another handy identity: X% of Y equals Y% of X. 8% of 25 feels hard; 25% of 8 is obviously 2 — same answer.
The Classic Percentage Trap
A 50% increase followed by a 50% decrease does not return to the start: 100 → 150 → 75. Percentage changes compound on the current value, not the original. This is why “the stock dropped 20%, then recovered 20%” still leaves you 4% down, and why comparing percentage changes always needs the question: percent of what?
Related: going from 20% to 30% is a 10 percentage point increase, but a 50 percent increase. News reports mix these up constantly; now you won’t.
Frequently Asked Questions
How do I calculate a discount price?
Use mode 1: enter the discount percent and the price to get the discount amount, then subtract. A 30% discount on 89.90: 30% of 89.90 = 26.97, so you pay 62.93. Shortcut: paying after a 30% discount is the same as paying 70% of the price.
How do I calculate percentage increase between two values?
Use mode 3 with the older value first: from 1,200 to 1,500 shows +25%. Order matters — from 1,500 to 1,200 is −20%, not −25%, because the base changed.
Why is percentage change from zero undefined?
Percentage change divides by the starting value, and dividing by zero has no meaningful answer. Growth “from 0 to 50” is infinite in percentage terms — report it as an absolute change instead.
How do I add a percentage (like tax) to a price?
Compute the percentage with mode 1 and add: 8% of 150 = 12, so 162 total. Faster: multiply by 1 + rate (150 × 1.08 = 162). Careful reversing it — removing 8% tax means dividing by 1.08, not subtracting 8%.
Is my data private?
Yes — all calculation runs in your browser. Nothing you type is sent anywhere.