Percentage Calculator
Calculate percentages six ways — with step-by-step workings and a visual result
// Calculation History
// Percentage Formulas at a Glance
How to Calculate Percentages
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum" — meaning "by the hundred". Percentages are used everywhere — discounts, tax, interest rates, statistics, grades, and more.
All Six Percentage Formulas
Common Percentage Mistakes
Mistake 1: "Adding percentages" — a 50% increase followed by a 50% decrease does NOT return to the original. 100 × 1.5 = 150, then 150 × 0.5 = 75. You end up 25% lower.
Mistake 2: Percentage of vs percentage change — "30 is 20% more than 25" is different from "30 is 20% of 150".
Mistake 3: Reverse percentage — if a price was reduced by 20% to reach £80, the original is NOT £80 + 20% = £96. It's £80 ÷ 0.8 = £100.
Every Percentage Problem Is One of Three
Built and verified by Andrius R. · Updated June 2026
Percentages confuse people because one word covers three different questions. Identify which one you're facing and the calculation is always a one-liner.
The three forms
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 80 → 80 × 0.15 = 12 |
| X is what % of Y? | X ÷ Y × 100 | 12 of 80 → 12 ÷ 80 = 15% |
| X is Y% of what? | X ÷ (Y ÷ 100) | 12 is 15% of → 12 ÷ 0.15 = 80 |
Percentage change — and its famous trap
Change = (new − old) ÷ old × 100. The denominator is always the starting value. From 80 to 100 is +25%; from 100 back to 80 is −20%. Same distance, different percentages — which leads to the trap: a 50% loss needs a 100% gain to recover. A portfolio that drops from $1,000 to $500 must double just to break even. Percentages are not symmetric, and a "+10%, then −10%" sequence leaves you below where you started (×1.1 × 0.9 = 0.99).
Reverse percentages: the question shops rely on you getting wrong
An item costs $120 including 20% tax. The pre-tax price is not 120 − 20% = $96. The $120 is 120% of the original, so divide: 120 ÷ 1.20 = $100. (Check: $100 + 20% = $120 ✓.)
Same logic for "what was the price before the 30% discount": sale price ÷ 0.70.
Percent vs percentage points
If an interest rate moves from 4% to 6%, it rose 2 percentage points — but 50 percent (2 is half of 4). News reports mix these constantly, and the difference is enormous: "unemployment up 1 point" and "unemployment up 1%" describe completely different events. When precision matters, "points" refers to the raw difference between two percentages.
Mental shortcuts worth knowing
- x% of y = y% of x. 8% of 25 feels hard; 25% of 8 = 2 is instant. They're always equal.
- Build from 10%. 10% of anything is one decimal shift. For 35% of 60: 10% = 6, so 30% = 18, 5% = 3 → 21.
- Stacked percentages multiply, never add. Two successive 20% discounts are ×0.8 × 0.8 = 36% off, not 40%.
- 1% first for awkward numbers. 7% of 350: 1% = 3.5, × 7 = 24.5.
From the Blog
// Quick Tricks
To find 10% — move the decimal point one place left. 10% of 350 = 35. Then multiply for other multiples.
// Reverse Sale Price
If an item is on sale at £80 after a 20% discount, the original price is £80 ÷ 0.8 = £100 (not £80 + 20%).
// Percentage Points
"Percentage points" and "percent" are different. Going from 10% to 15% is 5 percentage points but a 50% increase.
// Compound Effect
+20% then −20% does not return to start. 100 → 120 → 96. The order of percentage changes matters!