X is Y% of what number?
Enter the part you know and what percentage of the total it represents, to find the whole.
Finding the whole from a part
This is the third shape of reverse percentage question. You are not undoing a change — you know a slice of something and what fraction of the total that slice represents, and you want the total.
30 students passed, which was 40% of the class.
Unitary method
- 40% = 30
- 1% = 30 ÷ 40 = 0.75
- 100% = 0.75 × 100 = 75 students
Multiplier method
30 ÷ 0.40 = 75 — same answer, one step. The unitary version is slower but shows the working exams award marks for.
When the part is bigger than the whole
A percentage above 100 is not an error. If this year's revenue of £90,000 is 150% of last year's, then last year was 90,000 ÷ 1.5 = £60,000. The "part" exceeds the "whole" because the whole is a baseline being compared against, not a container.
The one case with no answer is 0%. Zero percent of any number is zero, so a part of zero is consistent with every possible total — there is nothing to recover. Negative percentages are rejected for the same reason: a share of a total has no meaningful negative reading here.
Spotting this question type
Three different questions all sound like percentages, and telling them apart is most of the work. Which one you have is decided by what is missing.
"What is 40% of 75?" — you have the whole and want the part. Multiply: 75 × 0.4 = 30. Ordinary percentage work.
"30 is what percent of 75?" — you have both numbers and want the rate. Divide part by whole: 30 ÷ 75 = 40%.
"30 is 40% of what number?" — you have the part and the rate, and the whole is missing. That is this page: 30 ÷ 0.4 = 75.
The giveaway is that the total is never stated. Phrases like "which represents", "which is", "accounts for" and "of the total" almost always introduce a part whose whole you are being asked to find.
Worked examples
| Question | Calculation | Whole |
|---|---|---|
| 12 is 25% of what? | 12 ÷ 0.25 | 48 |
| 30 is 40% of what? | 30 ÷ 0.40 | 75 |
| 45 is 60% of what? | 45 ÷ 0.60 | 75 |
| 51 is 68% of what? | 51 ÷ 0.68 | 75 |
| 90 is 150% of what? | 90 ÷ 1.50 | 60 |
| 7 is 5% of what? | 7 ÷ 0.05 | 140 |
Frequently asked questions
If 30 is 40% of a number, what is the number?
75. Divide the part by the percentage as a decimal: 30 ÷ 0.40 = 75.
What is the formula for finding the whole from a part?
Whole = part × 100 ÷ percentage. Equivalently, divide the part by the percentage written as a decimal.
Can the percentage be more than 100?
Yes. If 30 is 150% of a number, that number is 30 ÷ 1.5 = 20. The part is larger than the whole because the figure has grown past its baseline.
Why does 0% have no answer?
0% of any number is zero, so if the part is zero every possible whole fits and the information is genuinely gone. The calculator explains this rather than showing an error.
How do I do this without a calculator?
Use the unitary method. Divide the part by its percentage to get 1%, then multiply by 100. If 40% is 30, then 1% is 0.75 and 100% is 75.