Percentage Calculator
Three of the most common percentage questions, each with the working shown so you can follow the method and not just copy the answer.
Last updated: August 2026 · Written and verified by Akash Pandey
Calculate a percentage
Result
This runs the same calculation engine as the main scientific calculator, entirely in your browser. Nothing you type is sent anywhere.
The formula
A percentage is just a fraction with 100 on the bottom. "15%" means 15 per hundred, or 15/100, or 0.15. Every percentage question is one of three rearrangements of the same relationship:
part = (percent ÷ 100) × whole
- whole - the number you are taking a percentage of (sometimes called the base)
- percent - the rate, written without the % sign
- part - the answer
Rearranging for the other two unknowns gives percent = (part ÷ whole) × 100 and whole = part ÷ (percent ÷ 100). Percentage change is a separate formula because it compares two values rather than splitting one:
percentage change = ((new − original) ÷ original) × 100
- A positive result is an increase, a negative one a decrease.
- The denominator is always the original value - this is the single most common mistake.
Worked examples
Find 15% of 200
15% of 200
- Convert the percentage to a decimal:
15 ÷ 100 = 0.15. - Multiply by the whole:
0.15 × 200. - On the main calculator you can type this directly as
200 × 15%.
= 30
- Convert the percentage to a decimal:
A £68 jacket is reduced by 25%. What do you pay?
68 − 25% of 68
- Find the discount:
0.25 × 68 = 17. - Subtract it from the original:
68 − 17 = 51. - Shortcut: paying 75% of the original is
0.75 × 68, which gives the same answer in one step.
= 51
- Find the discount:
30 is what percentage of 200?
(30 ÷ 200) × 100
- Divide the part by the whole:
30 ÷ 200 = 0.15. - Multiply by 100 to express it as a percentage:
0.15 × 100.
= 15%
- Divide the part by the whole:
A price rises from 80 to 100. What is the percentage increase?
((100 − 80) ÷ 80) × 100
- Find the absolute change:
100 − 80 = 20. - Divide by the original value, not the new one:
20 ÷ 80 = 0.25. - Multiply by 100:
0.25 × 100.
= 25%
- Find the absolute change:
After a 20% discount you paid 64. What was the original price?
64 ÷ 0.8
- You paid 100% − 20% = 80% of the original, so 64 represents 0.8 of it.
- Divide rather than multiply:
64 ÷ 0.8. - Check:
80 × 0.8 = 64. ✓
= 80
Mistakes worth avoiding
A percentage increase and decrease do not cancel out
Increase 100 by 10% and you get 110. Decrease 110 by 10% and you get 99, not 100. The two percentages are taken from different bases - the first from 100, the second from 110. This is why a stock that falls 50% must then rise 100% just to break even.
Percent and percentage point are different units
If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points, but a 50% increase in the rate itself. Newspapers mix these up constantly; in any technical context the distinction matters.
Reverse percentages need division, not subtraction
To undo a 20% discount you divide by 0.8. Adding 20% back to the discounted price gives the wrong answer, because that 20% would be taken from the smaller number.
Common percentages as fractions and decimals
| Percentage | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 5% | 1/20 | 0.05 |
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 33⅓% | 1/3 | 0.333… |
| 50% | 1/2 | 0.5 |
| 66⅔% | 2/3 | 0.666… |
| 75% | 3/4 | 0.75 |
| 100% | 1/1 | 1 |
The 10% trick is worth internalising: 10% of any number is that number with the decimal point moved one place left. 5% is half of that, 20% is double it, and 15% is 10% plus 5%. Most everyday percentages can be assembled from those pieces without a calculator at all.
Frequently Asked Questions
How do I calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. For 15% of 200: 15 ÷ 100 = 0.15, then 0.15 × 200 = 30. On the main calculator you can type 200 × 15% directly.
What is the difference between percentage change and percentage difference?
Percentage change has a direction - it measures a move from an original value to a new one, and divides by the original. Percentage difference compares two values with no before-and-after relationship, and divides by their average instead. Use change for "the price went up"; use difference for "these two measurements disagree".
Why does a 50% loss need a 100% gain to recover?
Because the two percentages are taken from different bases. A 50% fall from 100 leaves 50. Getting from 50 back to 100 is a rise of 50 on a base of 50, which is 100%. The smaller the base becomes, the larger the percentage needed to return.
How do I work backwards from a discounted price?
Divide, do not add back. If a 20% discount left you paying 64, you paid 80% of the original, so the original was 64 ÷ 0.8 = 80. Adding 20% to 64 would give 76.8, which is wrong.
Can a percentage be more than 100?
Yes. 100% is the whole, so 250% simply means two and a half times the original. Percentages above 100 appear routinely in growth figures, markups, and comparisons.
Is this percentage calculator free?
Yes, and it needs no sign-up. It runs entirely in your browser, so nothing you type is sent to a server.
How do I calculate a percentage increase between two numbers?
Subtract the original from the new value, divide by the original, then multiply by 100. For example, from 40 to 50: (50 − 40) / 40 × 100 = 25%.
What is the percentage point difference versus percentage change?
A percentage point is the arithmetic difference between two percentages - if a rate goes from 4% to 6%, that is a 2 percentage point increase but a 50% relative change. The two measure different things.