How this works
A percentage is just a fraction with 100 as the denominator — "25%" means 25 out of 100. This calculator handles the three questions people ask most: what is X% of Y, what percentage is X of Y, and how much did a value change in percent. Pick a tab, enter the two numbers, and the answer updates as you type.
The word percent comes from the Latin *per centum* — "by the hundred". Roman tax collectors used the same scaling 2,000 years ago: the *centesima rerum venalium* was a 1% sales tax, easier to communicate as "1 in 100" than as a fraction. The "%" symbol itself evolved from the abbreviated Italian *per cento* in 15th-century mercantile manuscripts, where scribes shortened it to "p̃c̃o" and eventually to the slash-and-two-circles glyph we use today. The point of all of this is that percentages exist purely to make ratios easier to compare: "30 of 50" and "21 of 35" are both 60%, but you have to do mental work to see that without converting to a percentage first.
Three everyday traps to watch for. (1) "Of" vs "is": "20 is what % of 80" (answer: 25%) sounds the same as "what is 20% of 80" (answer: 16) but produces completely different numbers — make sure you know which question you're asking. (2) Percentage change is asymmetric: rising from 100 to 120 is +20%, but falling from 120 back to 100 is −16.7% (not −20%) because the denominator changed. (3) Percentages don't add directly: a 30%-off sale followed by a 20%-off coupon is not 50% off — it's 1 − (0.7 × 0.8) = 44% off. The calculator gets all of these right; just be careful which numbers you feed in.
The formula
A negative result on the third formula means a decrease; the absolute value in the denominator keeps the sign right when A itself is negative.
Example calculation
- A jacket costs €120 and is on sale at 25% off. What is 25% of 120? (25 / 100) × 120 = €30 saved.
- You scored 42 on a test out of 60. What percentage is that? (42 / 60) × 100 = 70%.
- A stock rose from $80 to $92. What was the % change? ((92 − 80) / 80) × 100 = +15%.
Frequently asked questions
How do I calculate a discount?
Use the "X% of Y" tab. Enter the discount percentage as X and the original price as Y — the result is the amount you save. Subtract that from the original price to get the sale price.
What's the difference between percentage points and percent?
If interest rates rise from 4% to 5%, that's a 1 percentage point increase but a 25% relative increase. This calculator returns the relative percent change in the "% change" tab — fine for most everyday questions; just be careful with rates and probabilities.
How do I work backwards — find the original price before tax?
If a price already includes 20% tax, divide by 1.20 (not by 0.80). Use the "X is what % of Y" tab with the after-tax price as X and 1.20 as Y to verify, or just compute directly: original = total / (1 + rate/100).
Why is "% change" different depending on which value you start from?
A change from 100 to 120 is +20%, but going back from 120 to 100 is −16.7% — not −20%. Percentage change is always relative to the starting value (the denominator). When comparing two periods, be explicit about which one is the baseline.
How do I add a percentage to a number?
Multiply by (1 + rate/100). To add 20% to 80: 80 × 1.20 = 96. This works for VAT, sales tax, salary raises, and any "+X%" question. The single-multiplication shortcut is faster than computing the increase separately and adding it back. Likewise, to subtract a percentage, multiply by (1 − rate/100): a 25% discount on €80 is 80 × 0.75 = €60. This calculator does the work in the "X% of Y" tab — enter 120 and 80 to see the same answer (96), then read it as the new total.
How do I calculate two stacked discounts (30% off + extra 20% off)?
Multiply the discount fractions, don't add them. A 30% discount leaves 70% of the price; an additional 20% off that leaves 80% of 70%. Combined factor: 0.70 × 0.80 = 0.56, so you pay 56% of the original — a total 44% discount, not 50%. On a $100 item: $100 × 0.70 = $70 after the first discount, then $70 × 0.80 = $56 final. The order doesn't matter for percentage discounts — 0.7 × 0.8 = 0.8 × 0.7 — but it does matter for fixed-dollar coupons applied alongside percentages, which is why most retailers spell out the order in their fine print.
How do I work out my exam grade as a percentage?
Use the 'X is what % of Y' tab. Enter the marks you scored as X and the maximum possible as Y. 42 out of 60 = (42/60) × 100 = 70%. If the test has weighted sections, calculate each section's contribution separately and add them: e.g., a 40% essay scored 28/40 contributes (28/40) × 40 = 28 percentage points; a 60% multiple-choice scored 45/60 contributes (45/60) × 60 = 45 points; total grade = 73%. To convert a percentage to a letter grade, check your school's rubric — there's no universal mapping, though 90/80/70/60/<60 = A/B/C/D/F is common in US high schools and 70/60/50/40/<40 = First/2:1/2:2/Third/Fail is the UK university scale.