This is the reverse of taking a percentage: instead of applying a rate you are measuring one. Divide the part by the whole and multiply by 100, and you have the share expressed per hundred. It is the calculation behind exam marks, market share, pass rates and every "out of" figure you have ever seen quoted.
The order matters and is the most common source of error. 30 out of 120 is 25%, while 120 out of 30 is 400% — both are valid statements, but they answer different questions. The rule is that the number after "of" always goes on the bottom of the fraction, so the page reports both directions to make the distinction obvious.
The formula
P- The percentage you are looking for
X- The part — the number being measured
Y- The whole — the number it is being measured against
How to use this calculator
- Enter the part, X — the number that comes before "is".
- Enter the whole, Y — the number that comes after "of".
- Read the percentage on the gauge.
- Check the reversed figure below if you suspect the two numbers are the wrong way round.
Worked examples
30 out of 120
30 ÷ 120 = 0.25, and 0.25 × 100 = 25%. The other direction, 120 out of 30, comes to 400% — the same pair of numbers, a different question.
A test score of 47 out of 60
47 ÷ 60 = 0.783333, so the mark is 78.33%. The shortfall is 13 marks, which is the missing 21.67% of the paper.
How to read your score
Frequently asked questions
Which number goes on the bottom?
The whole — the number that follows the word "of". In "what percent is 30 of 120", the 120 is the whole and goes underneath. Getting this backwards is the single most common percentage mistake.
Can the answer be more than 100%?
Yes, whenever the part is larger than the whole. Sales of 140 against a target of 100 is 140% of target, which is a perfectly normal way to report an overshoot.
What if the whole is zero?
The percentage is undefined, because you cannot divide by zero. There is no meaningful way to say what share of nothing a number represents.
How do I convert the answer back into a fraction?
Put the percentage over 100 and cancel. 25% becomes 25/100, which reduces to 1/4 — exactly the ratio 30:120 you started with.
Common "X out of Y" percentages
| X | out of 10 | out of 16 | out of 20 | out of 25 | out of 50 | out of 60 |
|---|---|---|---|---|---|---|
| 1 | 10.00% | 6.25% | 5.00% | 4.00% | 2.00% | 1.67% |
| 3 | 30.00% | 18.75% | 15.00% | 12.00% | 6.00% | 5.00% |
| 5 | 50.00% | 31.25% | 25.00% | 20.00% | 10.00% | 8.33% |
| 7 | 70.00% | 43.75% | 35.00% | 28.00% | 14.00% | 11.67% |
| 12 | 120.00% | 75.00% | 60.00% | 48.00% | 24.00% | 20.00% |
| 25 | 250.00% | 156.25% | 125.00% | 100.00% | 50.00% | 41.67% |
| 40 | 400.00% | 250.00% | 200.00% | 160.00% | 80.00% | 66.67% |
Each cell is X divided by Y and multiplied by 100.