Percentage
% of, % change, difference
About This Calculator
A percentage expresses a number as a fraction of 100. It is used everywhere from shopping discounts and tax rates to exam grades, interest calculations, and statistical data. This calculator handles the three most common percentage problems: finding a percentage of a number, calculating the percentage change between two values, and finding the original value before a percentage was applied.
Formula
P% of X = (P ÷ 100) × X
% Change = ((New − Old) ÷ Old) × 100
Original = Amount ÷ (1 ± P%)
Use '+' in the denominator if the percentage was added (e.g. tax), '−' if it was subtracted (e.g. discount).
Example Calculation
A jacket costs $85 and is 20% off. How much do you pay?
- Discount = 20 ÷ 100 × $85 = $17.00
- Sale price = $85 − $17 = $68.00
You save $17.00 and pay $68.00
Common Discount Table
| Original | 10% off | 20% off | 25% off | 50% off |
|---|---|---|---|---|
| $50 | $45.00 | $40.00 | $37.50 | $25.00 |
| $100 | $90.00 | $80.00 | $75.00 | $50.00 |
| $200 | $180.00 | $160.00 | $150.00 | $100.00 |
| $500 | $450.00 | $400.00 | $375.00 | $250.00 |
Frequently Asked Questions
How do I calculate 20% of a number?
Multiply the number by 0.20. For example, 20% of 150 = 150 × 0.20 = 30.
What is the formula for percentage change?
% Change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result means an increase; negative means a decrease.
How do I find the original price before a discount?
Divide the sale price by (1 − discount%). For a 20% discount: Original = Sale Price ÷ 0.80.
What is the difference between percentage and percentage points?
A percentage point is an absolute difference between two percentages. If a rate rises from 5% to 8%, that is a 3 percentage-point increase but a 60% relative increase.