Percentage Calculator
A free tool for the three percentage questions people run into most — find a percentage, find a ratio as a percentage, or find a percentage change.
What is % of ?
is what percent of ?
What is the percentage change from to ?
Increase or decrease by %
| Percentage | Of 100 | Of 200 |
|---|---|---|
| 5% | 5 | 10 |
| 10% | 10 | 20 |
| 15% | 15 | 30 |
| 20% | 20 | 40 |
| 25% | 25 | 50 |
| 50% | 50 | 100 |
| 75% | 75 | 150 |
How to calculate a percentage, step by step
Every percentage question comes down to three numbers: a part, a whole, and a percentage. If you know two of them you can find the third. The formulas below are the ones the calculators above use.
Finding a percentage of a number. Turn the percentage into a decimal by dividing by 100, then multiply. 15% of 80 is 0.15 × 80 = 12.
Finding what percentage one number is of another. Divide the part by the whole and multiply by 100. If 12 out of 80 customers asked for a refund, that is 12 ÷ 80 × 100 = 15%.
Finding the percentage change. Subtract the old value from the new one, divide by the old value, then multiply by 100. A price that goes from 80 to 92 has changed by 12, and 12 ÷ 80 × 100 = 15%, so it rose by 15%.
Increasing or decreasing a number by a percentage. Multiply by 1 plus the percentage to increase, or by 1 minus the percentage to decrease. Adding 15% to 200 is 200 × 1.15 = 230. Taking 15% off 200 is 200 × 0.85 = 170.
| From | To | Change |
|---|---|---|
| 50 | 60 | +20% |
| 80 | 60 | -25% |
| 200 | 250 | +25% |
| 120 | 90 | -25% |
| 40 | 100 | +150% |
Mental maths shortcuts
You can work out most everyday percentages without a calculator by starting from 10% and 1%. To find 10% of any number, move the decimal point one place to the left: 10% of 340 is 34. Half of that gives 5%, which is 17, and adding the two gives 15%, which is 51. To find 1%, move the decimal two places to the left.
A few fractions are worth memorising. 50% is half, 25% is a quarter, 20% is a fifth, and 10% is a tenth. Dividing by the fraction is often quicker than multiplying by the decimal, so 25% of 360 is simply 360 ÷ 4 = 90.
Percentages also swap places. 8% of 50 is the same as 50% of 8, because both equal 4. If one version is awkward to calculate, try the other.
Worked examples from everyday life
A sale price. A jacket costs 60 and is 25% off. The discount is 60 × 0.25 = 15, so you pay 45. In one step, 60 × 0.75 = 45.
Adding VAT. Ireland's standard VAT rate is 23%. A 50 item before VAT costs 50 × 1.23 = 61.50 once VAT is added. To go the other way, divide a VAT-inclusive price by 1.23 to get the price before VAT. There is a dedicated VAT calculator if you want the breakdown.
Working back to the original price. If a price after a 20% discount is 48, the original was not 48 plus 20%. The 48 is 80% of the original, so the original is 48 ÷ 0.8 = 60.
A pay rise. A salary of 42,000 with a 3% raise becomes 42,000 × 1.03 = 43,260. The salary calculator converts that into hourly, daily and weekly pay.
A tip. A 12% tip on a bill of 85 is 85 × 0.12 = 10.20. See the tip calculator for splitting the bill between several people.
Common percentage mistakes
Percentage change is not symmetrical. A rise of 20% followed by a fall of 20% does not bring you back to the start. 100 becomes 120, and 20% off 120 is 96, a net fall of 4%. The fall is calculated from a bigger number.
Percentage points are not percentages. If an interest rate moves from 4% to 6%, it has risen by 2 percentage points, but the rate itself is 50% higher. News stories and bank notices often use the two terms loosely.
The base matters. 10% of 200 and 10% of 500 are different amounts. When comparing two percentages, check they are percentages of the same thing.
FAQ
What is a percentage?
A percentage is a way of writing a number as a portion of 100, marked with the "%" symbol. If 25 out of 100 marbles in a jar are blue, that's 25% of the marbles — the percentage always describes a part relative to a whole of 100.
How do you work out a percentage?
Divide the part by the whole, then multiply by 100. For example, if 20 of 50 apples are red, divide 20 by 50 to get 0.4, then multiply by 100 to get 40%. The same formula — part ÷ whole × 100 — covers most percentage questions, just rearranged depending on which values you already know.
How do you calculate percentage increase or decrease?
Subtract the starting value from the new value, divide by the starting value, then multiply by 100. Going from 200 to 250 is a change of 50, so 50 ÷ 200 × 100 = 25% increase. A negative result means the value went down rather than up.
Where do percentages come up in everyday life?
Restaurant tips, sale discounts, exam scores, interest rates, pay raises, and tracking changes over time (like a stock price or a body-weight goal) are all percentage calculations in disguise — usually one of the three forms this tool covers.
How do you find 20% of a number quickly?
Divide the number by 5 — 20% is the same as one-fifth. So 20% of 200 is 200 ÷ 5 = 40, matching the chart above.
What is 15% of 200?
15% of 200 is 30 (200 × 0.15). See the chart above for other common percentages of 100 and 200.
How do you convert a percentage to a decimal?
Divide by 100 — so 25% becomes 0.25, and 7.5% becomes 0.075. Multiplying a number by that decimal gives you the percentage of it directly.
How do I add a percentage to a number?
Multiply the number by 1 plus the percentage as a decimal. To add 15% to 200, multiply 200 by 1.15 to get 230. The fourth calculator above does this for you and can also subtract a percentage.
How do I take a percentage off a number?
Multiply the number by 1 minus the percentage as a decimal. To take 25% off 60, multiply 60 by 0.75 to get 45. Subtracting the discount (60 × 0.25 = 15) from 60 gives the same answer.
What is the difference between percentage change and percentage points?
Percentage points describe the simple gap between two percentages, while percentage change compares them proportionally. Moving from 4% to 6% is a rise of 2 percentage points, but a 50% increase in the rate.
How do I find the original price before a discount?
Divide the discounted price by 1 minus the discount rate. If a price is 48 after a 20% discount, the original was 48 ÷ 0.8 = 60. Adding 20% back onto 48 would give the wrong answer, because the discount was taken from the larger original price.
Why does a 20% rise followed by a 20% fall not return to the start?
Because each percentage is calculated from a different base. 100 plus 20% is 120, and 20% of 120 is 24, which takes you down to 96. To get back to 100 from 120 you need a fall of about 16.7%.
How do I calculate a percentage of a percentage?
Multiply the two as decimals. 50% of 20% is 0.5 × 0.2 = 0.10, or 10%. This comes up when a discount is applied on top of another discount.
About this calculator
This tool covers the three percentage calculations people need most often: finding a percentage of a number, finding what percentage one number is of another, and finding the percentage change between two values. No sign-up, no data stored — just enter numbers and the answer updates instantly.