How to use the percentage calculator
- Choose the type of calculation from the list.
- Enter the two numbers. For an increase or decrease, enter a negative percentage for a decrease (for example −15 for 15% off).
- The answer appears instantly with every step of the working.
All the percentage formulas
Percentage change = (B − A) ÷ |A| × 100 X% of Y = X ÷ 100 × Y X as a % of Y = X ÷ Y × 100 Y increased by X% = Y × (1 + X ÷ 100) Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100 Original before change = Final ÷ (1 + X ÷ 100)
Worked examples
- Price rise: a subscription goes from $50 to $65 → (65 − 50) ÷ 50 = +30%.
- Sale: 15% off a $150 jacket → 150 × 0.85 = $127.50.
- Test score: 42 out of 50 → 42 ÷ 50 × 100 = 84%.
- Before tax: $108 including 8% sales tax → 108 ÷ 1.08 = $100.
- Pay rise: a 4% raise on a $60,000 salary → 60,000 × 1.04 = $62,400.
Common percentage changes
| From | To | Change | To undo it |
|---|---|---|---|
| 100 | 110 | +10% | −9.09% |
| 100 | 125 | +25% | −20% |
| 100 | 150 | +50% | −33.3% |
| 100 | 200 | +100% | −50% |
| 100 | 80 | −20% | +25% |
| 100 | 50 | −50% | +100% |
Percent vs percentage points
When a rate itself changes, be careful with wording. If a mortgage rate goes from 6% to 7%, it has risen by 1 percentage point, but by 16.7 percent (1 ÷ 6). News reports and financial documents often use “basis points” too: 1 percentage point = 100 basis points.
Where percentages come up every day
- Shopping: discounts, coupons and sales tax.
- Money: pay raises, inflation, interest rates and investment returns.
- School: test scores and grade weights.
- Business: growth, profit margin and markup — use the profit margin calculator for pricing.
- Health and fitness: weight change, body fat and progress over time.
Common mistakes
- Dividing by the wrong number: percentage change always divides by the starting value, not the new one.
- Adding percentages in a row: two 10% increases are 21% in total, not 20%, because the second applies to the bigger number.
- Reversing a discount: to find the original price after 20% off, divide by 0.8 — don’t add 20% back.
Percentages and averages
To find the average percentage change over several years, don’t simply average the yearly figures. If an investment rises 50% one year and falls 50% the next, the simple average is 0%, but you have actually lost 25%. For growth over time, use the compound annual growth rate (CAGR): (final ÷ start)^(1 ÷ years) − 1.