Percentage Calculator
Calculate X% of Y, what % X is of Y, and A→B change %.
Percentage calculator
Handles everyday ratio and increase/decrease calculations.
Finds what value a given percentage of a whole is, what percentage a part is of a whole, or the percent change from one value to another.
- Find the value that is a given percentage of a whole.20% of 100 is 20.
- Find what percentage a part is of a whole.20 out of 100 is 20%.
- Find how much a value increased or decreased from a base to a new value.From 100 to 150 is a 50% increase.
- Find the new value after a given percent increase or decrease.100 increased by 20% is 120.
- Percent
- Percent (from Latin per centum "by the hundred") is a ratio expressed as a fraction of 100. The symbol is %. For example, 50% means 50/100, or 0.5. Values above 100% (e.g. 150%) or negative (e.g. -10%) are also used.
- Per mille (‰)
- Per mille (permille, permill) is a ratio per 1,000, denoted by ‰. It is used for things like salinity (e.g. seawater), railway gradients, and some tax rates.
- Basis point (‱)
- A basis point is one hundredth of a percent (1‱ = 0.01%). It is commonly used in finance to describe interest rate or yield changes (e.g. "rates rose 25 basis points").
Why percentages trip people up
Percentage mistakes are rarely arithmetic errors. They come from losing track of what the percentage is being taken of.
Three kinds of calculation
There are really only three. What is X% of a total (15% of 80,000 is 12,000), what percentage is one number of another (12,000 is 15% of 80,000), and how much did something change (80,000 to 92,000 is a 15% increase).
Once you know which one you are doing, the arithmetic is trivial. Get the type wrong and a perfect calculation still gives the wrong answer.
Worked examples
Part of a total: 30% of 45,000 → 45,000 × 0.3 = 13,500
Finding the rate: 9 out of 27 → 9 ÷ 27 = 0.333… → about 33.3%
Change: 120 rising to 138 → (138 − 120) ÷ 120 = 0.15 → +15%
For change, always divide by the original value. Dividing by the new value gives a different, incorrect figure.
Percent versus percentage point
If a rate moves from 3% to 4%, that is a rise of one percentage point (pp) and also a rise of about 33 percent. Both statements are true and they describe very different things.
This is why polling and interest-rate coverage says 'up 2 percentage points' rather than 'up 2 percent'. Use percentage points when comparing two rates, and percent when describing how much a value grew.
Stacked discounts do not add up
30% off followed by a further 20% off is not 50% off. Take 10,000, remove 30% to get 7,000, then remove 20% of that to get 5,600 — a 44% discount overall.
The second discount applies to the already reduced price. For the same reason, a 10% increase followed by a 10% decrease does not return you to the start: 10,000 → 11,000 → 9,900.
Adding tax versus removing it
To add a 10% tax, multiply by 1.1. A net price of 100,000 becomes 110,000.
To work backwards from a tax-inclusive price, divide by 1.1 rather than multiplying by 0.9. 110,000 ÷ 1.1 = 100,000. Multiplying by 0.9 gives 99,000, which is wrong, and this is one of the most common percentage errors in everyday accounting.
| Percentage | Fraction · decimal · shortcut |
|---|---|
| 5% | 1/20 · 0.05 · divide by 20 |
| 10% | 1/10 · 0.1 · shift the decimal one place |
| 12.5% | 1/8 · 0.125 · divide by 8 |
| 25% | 1/4 · 0.25 · divide by 4 |
| 33.3% | 1/3 · 0.333… · divide by 3 |
| 75% | 3/4 · 0.75 · divide by 4, multiply by 3 |
Frequently asked questions
- Which number do I divide by when calculating change?
- Always the original value. Going from 80 to 100 is (100−80) ÷ 80 = 25% increase. Dividing by 100 gives 20%, which is wrong.
- Is 30% off plus 20% off the same as 50% off?
- No, it works out to 44% off. The second discount applies to the reduced price: 0.7 × 0.8 = 0.56, so you pay 56% of the original.
- Does a 10% rise then a 10% fall cancel out?
- No, you end up 1% lower. The rise applies to the smaller starting figure and the fall applies to the larger one.
- When do I say percent and when percentage point?
- Percentage points for the gap between two rates, percent for how much a value changed. From 3% to 4% is 1 percentage point and 33 percent.
- How do I find the pre-tax amount from a tax-inclusive price?
- Divide by 1 plus the rate, not multiply by the difference. At 10% tax, 110 ÷ 1.1 = 100. Multiplying 110 by 0.9 gives 99, which is incorrect.