What this tool does and when to use it
This calculator handles the five percentage sums people need most: a percent of a number (tips, tax, discounts), what percent one number is of another (test marks, budgets), the percentage increase or decrease between two numbers (prices, salaries, stats), the percentage difference between two values that have no "before" and "after", and adding or taking a percent off a price. Every answer shows the formula with your numbers in it, so it doubles as a homework check.
How to calculate a percentage
- Choose the question. Pick Percent of, What percent, Change, Difference or Add or take off.
- Enter the two numbers. Type the values. Decimals and negative numbers work.
- Read the answer. The result updates as you type, with the formula and your numbers shown underneath.
The five percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 80 = 12 |
| X is what percent of Y? | X ÷ Y × 100 | 45 of 60 = 75% |
| Percentage change from old to new | (new − old) ÷ old × 100 | 50 to 65 = +30% |
| Percentage difference | gap ÷ average × 100 | 50 and 65 = 26.087% |
| Price after X% off | price × (1 − X ÷ 100) | $80 with 25% off = $60 |
A quick mental trick: X% of Y is the same as Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.
Percentage increase and decrease
Take the new value, subtract the old one, divide by the old one and multiply by 100. A positive answer is an increase, a negative one a decrease. Real runs:
| From | To | Change |
|---|---|---|
| 50 | 65 | +30% (increase) |
| 80 | 60 | −25% (decrease) |
| $3.49 | $3.99 | +14.3266% |
| $52,000 salary | $54,600 | +5% |
| 180 lb | 171 lb | −5% |
Watch the trap: a rise and a fall of the same percent do not cancel out. A $100 item that goes up 50% costs $150, and 50% off $150 is $75, not $100. The fall is worked out from the bigger number.
Percent off: sale price table
To find a sale price, multiply by what is left: 25% off means you pay 75%, so $80 × 0.75 = $60. For a $60 item:
| Discount | You pay | You save |
|---|---|---|
| 10% off | $54 | $6 |
| 15% off | $51 | $9 |
| 20% off | $48 | $12 |
| 25% off | $45 | $15 |
| 30% off | $42 | $18 |
| 40% off | $36 | $24 |
| 50% off | $30 | $30 |
Two discounts stack on each other, not add up. 20% off and then a further 10% off is 72% of the price (0.8 × 0.9), a total saving of 28%, not 30%. To find the original price from a sale price, divide by what is left: $48 after 20% off was $48 ÷ 0.8 = $60.
Percentage of marks and grades
Divide your score by the total and multiply by 100. 42 out of 50 is 84%. For several subjects, add up all the marks and all the totals first: 480 marks out of 600 across six papers is 80%. Do not average the six percentages unless every paper is out of the same total, because a paper out of 100 should count for more than one out of 50.
| Score | Percent |
|---|---|
| 18 out of 20 | 90% |
| 42 out of 50 | 84% |
| 27 out of 40 | 67.5% |
| 56 out of 80 | 70% |
| 480 out of 600 | 80% |
Percentage difference vs percentage change
Use change when there is a before and an after, like last year's price and this year's. Use difference when the two numbers are equals, like the prices of the same TV in two shops. Difference divides by the average of the two, so the answer is the same whichever order you type them. For 50 and 65 the change is 30%, but the difference is 15 ÷ 57.5 × 100 = 26.087%.
One more term that trips people up: percentage points. If a mortgage rate goes from 4% to 5%, it rose by 1 percentage point, which is a 25% increase in the rate.
Percentages in Excel and Google Sheets
- X% of a number:
=A1*B1with B1 typed as 15%, or=A1*15/100. - What percent:
=A1/B1, then format the cell as a percentage. - Percentage change:
=(B1-A1)/A1, formatted as a percentage. - Percentage difference:
=ABS(A1-B1)/AVERAGE(A1,B1).
Working out a raise or a loan rate? See what a new salary pays after tax with the US paycheck calculator or the UK salary calculator, and what an interest rate really costs with the loan calculator.
