The basic percentage formula
A percentage is just a way of expressing a number as "out of 100." The core formula is:
Example: You scored 18 out of 25 on a test. What's your percentage? 18 ÷ 25 = 0.72, then × 100 = 72%.
Finding X% of a number
This is the one people need most — working out a discount, a tip, or a tax amount.
Example: What's 15% of $80? (15 ÷ 100) × 80 = 0.15 × 80 = $12.
Percentage increase or decrease
Useful for pay rises, price changes, or tracking growth.
Example: Your rent went from $1,000 to $1,150. Change = ((1150 − 1000) ÷ 1000) × 100 = 15% increase. If the result is negative, it's a decrease — just drop the minus sign and call it a decrease.
Skip the maths — get any of these instantly:
Open the Percentage CalculatorReverse percentages (finding the original number)
Sometimes you know the result after a percentage change, and need to find where you started — for example, working backward from a discounted price to the original.
Example: A jacket costs $68 after a 20% discount. What was the original price? 68 ÷ (1 − 0.20) = 68 ÷ 0.80 = $85. Use "+" instead of "−" if the new value came from an increase, not a decrease.
Common mistakes to avoid
- Confusing percentage points with percent. If interest goes from 5% to 7%, that's a 2 percentage-point rise, but a 40% relative increase (2 ÷ 5 × 100). Both are correct — they just answer different questions.
- Averaging percentages incorrectly. You can't just average two percentages of different-sized groups — you need the actual totals first.
- Forgetting the "of what." A 50% increase followed by a 50% decrease does not return you to the start — the decrease applies to a bigger number, so you end up lower.
A quick mental-math trick
To estimate X% of a number fast: find 10% (just move the decimal point one place left), then scale from there. 10% of 240 = 24. So 30% = 24 × 3 = 72, and 5% = 24 ÷ 2 = 12. Handy for tips and quick discount checks without a calculator.