How to calculate a percentage
"Percent" means "per hundred," so 15% is 15/100 or 0.15. Every percentage problem is a variation of one formula: Part = Percent × Whole. Rearranging it answers all the common questions:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 200 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 30 is 25% of 120 |
| Percentage change from A to B | (B − A) ÷ A × 100 | 80 → 100 is +25% |
| Add X% to Y | Y × (1 + X ÷ 100) | 250 + 20% = 300 |
| Subtract X% from Y | Y × (1 − X ÷ 100) | 250 − 20% = 200 |
Percentage increase vs. decrease
Percentage change always compares to the starting value. That is why a 50% drop followed by a 50% gain does not get you back to where you started: $100 falls to $50, and 50% of $50 is only $25, leaving you at $75. To recover from a 50% loss you need a 100% gain.
Reverse percentages
If a price after a 20% discount is $80, the original price is not $80 + 20%. It is $80 ÷ (1 − 0.20) = $100. Similarly, to remove sales tax from a total, divide by (1 + tax rate) — our sales tax calculator does this automatically.
Mental math shortcuts
- 10%: move the decimal one place left (10% of 64 = 6.4).
- 5%: half of 10%.
- 20%: double 10%. Handy for tips — see our tip calculator.
- Percentages are reversible: 8% of 50 equals 50% of 8 = 4.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 18% of 450 = 450 × 18 ÷ 100 = 81.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 40 to 50: (50 − 40) ÷ 40 × 100 = 25%.
What is the difference between percent and percentage points?
Percentage points measure the simple difference between two percentages (4% to 5% is +1 point). Percent change measures the relative change (+25%).
How do I find the original price before a discount?
Divide the sale price by (1 − discount). A $60 item after 25% off originally cost $60 ÷ 0.75 = $80.