How to calculate a percentage
A percentage is just a fraction with 100 on the bottom. "20%" means 20 out of every 100, or 0.20 as a decimal. Every calculation on this page comes from that one idea, which is why four different-looking questions all reduce to the same small set of formulas.
1. What is X% of Y?
result = base × (percentage ÷ 100)
This is the everyday case: a discount, a tip, a commission. To find 20% of 150, convert 20% to 0.20 and multiply: 150 × 0.20 = 30. A useful shortcut is that percentages are reversible — 20% of 150 and 150% of 20 are both 30, so you can flip the numbers around if one of them is easier to work with mentally.
2. X is what percent of Y?
percentage = (part ÷ whole) × 100
Use this when you already have both numbers and want to know how they relate. If you scored 45 out of 180 on a test: 45 ÷ 180 = 0.25, and 0.25 × 100 = 25%. The order matters — the number you are measuring goes on top, the total goes on the bottom.
3. Increase or decrease a number by a percentage
result = base × (1 + percentage ÷ 100)
Adding 15% to 120 gives 120 × 1.15 = 138. Removing 15% gives 120 × 0.85 = 102. Note that these do not cancel out: adding 15% and then removing 15% leaves you at 117, not 120, because the second percentage is applied to a larger number.
4. Percentage change between two numbers
change = ((new − old) ÷ old) × 100
Going from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25% growth. Going from 100 back down to 80 is a 20% drop, not 25% — the starting value changed, so the same absolute difference is a different share of it. This asymmetry catches people out constantly and is worth internalising.
Percentage, fraction and decimal reference
The values below come up often enough that recognising them saves you reaching for a calculator at all.
| Percentage | Fraction | Decimal | Quick method |
|---|---|---|---|
| 1% | 1/100 | 0.01 | Move the decimal point two places left |
| 5% | 1/20 | 0.05 | Take 10% and halve it |
| 10% | 1/10 | 0.10 | Move the decimal point one place left |
| 12.5% | 1/8 | 0.125 | Halve 25% |
| 20% | 1/5 | 0.20 | Double 10% |
| 25% | 1/4 | 0.25 | Halve, then halve again |
| 33.3% | 1/3 | 0.333… | Divide by 3 |
| 50% | 1/2 | 0.50 | Halve |
| 75% | 3/4 | 0.75 | Subtract a quarter |
| 100% | 1/1 | 1.00 | The number itself |
| 150% | 3/2 | 1.50 | The number plus half again |
Reading the table in the other direction is just as useful: if someone tells you a price rose "by a third", that is a 33.3% increase, and the multiplier you need is 1.333.
Where percentages show up
Shopping and discounts
A "30% off" sign means you pay 70% of the original price. Stacked discounts multiply rather than add — 20% off followed by another 10% off is 0.8 × 0.9 = 0.72, so 28% off in total, not 30%.
Tips and service charges
Tipping is a straight "X% of Y" calculation on the pre-tax total. The fastest mental method is to find 10% by moving the decimal point, then scale: 15% is 10% plus half of it again.
Tax and VAT
Tax is usually added on top of a net price, so a 21% VAT rate means multiplying by 1.21. Going the other way — extracting tax from a gross price — means dividing by 1.21, not subtracting 21%.
Grades and test scores
A score out of an arbitrary total is the "X is what percent of Y" case. 34 out of 40 is 85%.
Interest and growth
Interest compounds, which means each period applies its percentage to the previous result. 5% a year for three years is a factor of 1.05³ = 1.157, or 15.7% growth overall — noticeably more than the 15% you would get by adding.
Three mistakes worth avoiding
Percent and percentage points are not the same
If an interest rate moves from 4% to 5%, that is a rise of one percentage point but a 25% increase. News reports blur the two constantly, and the difference is large enough to change decisions.
Percentage changes do not reverse symmetrically
A value that falls 50% needs to rise 100% to get back to where it started. In general, recovering from a drop of p% requires a gain of p ÷ (100 − p) × 100 percent.
Averaging percentages ignores the base
A 90% pass rate on a class of 10 and a 50% pass rate on a class of 100 do not average to 70%. Weight each percentage by the size of its group, or work from the raw counts instead.
Frequently Asked Questions
- How do I calculate a percentage of a number?
- Divide the percentage by 100 and multiply by the number. For 20% of 150: 20 ÷ 100 = 0.2, then 150 × 0.2 = 30.
- How do I work out what percentage one number is of another?
- Divide the part by the whole, then multiply by 100. 45 out of 180 is 45 ÷ 180 = 0.25, which is 25%.
- How do I add a percentage to a price?
- Multiply by 1 plus the percentage as a decimal. Adding 21% means multiplying by 1.21. To remove it again, divide by 1.21 rather than subtracting 21%.
- What is the difference between percentage change and percentage points?
- Percentage points measure the raw gap between two percentages. Percentage change measures that gap relative to the starting value. A move from 4% to 5% is one percentage point and a 25% change.
- Why does a 50% loss need a 100% gain to recover?
- Because the gain is calculated on the reduced value. 100 falling by 50% leaves 50, and going from 50 back to 100 is a doubling — a 100% increase.
- Can this calculator use a comma as the decimal separator?
- Yes. The separator control in the header switches between a dot and a comma, and the setting is remembered on your device.
- Do two stacked discounts add together?
- No, they multiply. 20% off then 10% off gives 0.8 × 0.9 = 0.72 of the original price, a 28% total discount.
- Is this percentage calculator free?
- Yes. It is free to use, needs no account, and runs entirely in your browser — the numbers you type are never sent to a server.