Percentage formulas
| Problem | Formula | Example |
|---|---|---|
| X% of Y | Y × X ÷ 100 | 20% of 80 = 80 × 20 ÷ 100 = 16 |
| A is what % of B | A ÷ B × 100 | 20 ÷ 80 × 100 = 25% |
| % change from A to B | (B − A) ÷ A × 100 | (40 − 20) ÷ 20 × 100 = 100% |
| Increase A by P% | A × (100 + P) ÷ 100 | 80 × 110 ÷ 100 = 88 |
| Decrease A by P% | A × (100 − P) ÷ 100 | 80 × 90 ÷ 100 = 72 |
| X is Y% of Z | Z = X × 100 ÷ Y | 10 × 100 ÷ 5 = 200 |
| Original value after a P% increase gives V | V × 100 ÷ (100 + P) | 88 × 100 ÷ 110 = 80 |
| Tax on a pre-tax price A | A × rate ÷ 100 | 1,000 × 10 ÷ 100 = 100 |
| Pre-tax price from a tax-inclusive price V | V × 100 ÷ (100 + rate) | 1,100 × 100 ÷ 110 = 1,000 |
What is a percentage?
A percentage (symbol %) is a number expressed as a fraction of 100. For example 20% = 20/100 = 0.2, 111% = 1.11, −0.35% = −0.0035.
Percentages are used every day: shopping discounts, sales tax and VAT, interest rates, tips, revenue growth, exam scores and more. For example, a price going from $40.00 to $42.40 is a 6% increase.
How to enter numbers
Use a dot . for decimals and a comma , as the thousands separator (e.g. 1,250,000.5). Negative numbers are allowed. A ≈ sign means the exact result is a repeating decimal and has been rounded.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 200 = 200 × 15 ÷ 100 = 30.
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value and multiply by 100. A positive result is an increase, a negative one is a decrease. From 50 to 60: (60 − 50) ÷ 50 × 100 = 20% increase.
How do I calculate a 30% discount?
Multiply the original price by (100 − 30) and divide by 100. A $500 item with 30% off costs 500 × 70 ÷ 100 = $350. Use calculator 4 above and choose “decreased by”.
How do I find the price before tax?
Divide the price including tax by (100 + tax rate) and multiply by 100. $110 including 10% tax was $100 before tax. Use calculator 6 above.
Does a 10% increase followed by a 10% decrease give the original value?
No. 100 increased by 10% is 110, and 110 decreased by 10% is 99, because the decrease is applied to the larger number.
What is the difference between percent and percentage points?
An interest rate moving from 5% to 6% rises by 1 percentage point, but by (6 − 5) ÷ 5 × 100 = 20 percent.
Are the results exact?
Yes. All calculations use exact big-integer fractions (BigInt), so there are no floating-point rounding errors. Rounding is applied only when displaying, using the number of decimals you choose.