How the Percentage Calculator Works
"Percent" means "out of 100". 25% is 25 out of every 100, or one quarter. Percentages are used for discounts, tips, taxes, grades, interest and changes in prices. The Percentage Calculator solves the three most common questions, and you choose which one with the tabs.
The three modes
| Mode | Question | Formula |
|---|---|---|
| What is X% of Y? | Find a part of a number | X / 100 x Y |
| X is what % of Y? | Find the share | X / Y x 100 |
| % change from X to Y | Find the rise or fall | (Y - X) / |X| x 100 |
In the second mode, Y (the whole) cannot be 0. In the third mode, the starting value X cannot be 0, because a percentage change from 0 is undefined. A result with a plus sign is an increase, and a minus sign is a decrease.
Worked examples
These are the default numbers in the three tabs:
| Question | Working | Answer |
|---|---|---|
| What is 15% of 200? | 15 / 100 x 200 | 30 |
| 25 is what % of 100? | 25 / 100 x 100 | 25% |
| % change from 80 to 100 | (100 - 80) / 80 x 100 | +25% |
Everyday uses
| Situation | Working | Answer |
|---|---|---|
| 18% tip on a 64 bill | 18 / 100 x 64 | 11.52 |
| 30% off 80 | 30 / 100 x 80 = 24 off | Pay 56 |
| 8% sales tax on 50 | 8 / 100 x 50 | 4 |
| 42 of 60 marks | 42 / 60 x 100 | 70% |
| Price from 50 to 40 | (40 - 50) / 50 x 100 | -20% |
Chart: percentages of 200
The bar shows the value of each percentage of 200:
10% of 200 ████████ 20 20% of 200 ████████████████ 40 30% of 200 ████████████████████████ 60 40% of 200 ████████████████████████████████ 80 50% of 200 ████████████████████████████████████████ 100
Chart: percentage change
Green bars are increases and red bars are decreases:
100 to 125 ██████████ +25% 100 to 200 ████████████████████████████████████████ +100% 100 to 80 ████████ -20% 100 to 50 ████████████████████ -50%
A common trap
A rise and a fall of the same percentage do not cancel out. A price of 100 that falls by 20% becomes 80. To get back to 100 it must rise by 25% (80 to 100), not 20%. This is because the second percentage is taken from a smaller number.
Doing it by hand
- 10% of a number: move the decimal point one place to the left. 10% of 64 is 6.4.
- 5%: half of 10%. 1%: move the decimal point two places.
- 50%: half. 25%: a quarter. 75%: three quarters.
- Percent to decimal: divide by 100. 8.5% = 0.085.
Tips
- Percentage points are not percent. A rate that goes from 4% to 5% rises by 1 percentage point, but by 25% in relative terms.
- Answers are rounded to 4 decimal places (6 for the first mode), and a very small answer is never shown as 0.
This tool gives an estimate for general information only. For taxes, loans or contracts, check the exact amounts.