(x) is (p)% of Which Number? — Reverse Percentage Calculator
Use this calculator to find the original whole when you only know a part of it and what percentage that part represents. This is the reverse of the standard "percent of a number" calculation.
What is a reverse percentage?
A reverse percentage calculation finds the original total from a known portion and its percentage. For example, if you know a discounted price is $60 after a 25% discount, you can work backwards to find the original price was $80.
Formula
Where x is the known part and p is the percentage it represents.
Step-by-step example
Question: 45 is 30% of which number?
- Convert percentage to decimal: 30 ÷ 100 = 0.30
- Divide the known value: 45 ÷ 0.30 = 150
So 45 is 30% of 150.
Common real-world uses
| Scenario | Calculation | Result |
|---|---|---|
| Sale price $60 is 75% of original | 60 ÷ 0.75 | $80 original |
| $40 tip is 20% of the total bill | 40 ÷ 0.20 | $200 total bill |
| 120 voters = 30% of total voters | 120 ÷ 0.30 | 400 total |
| $350 saved = 35% of monthly income | 350 ÷ 0.35 | $1,000 income |
| 18 correct = 90% pass rate | 18 ÷ 0.90 | 20 total questions |
Frequently asked questions
When would I use a reverse percentage?
Any time you know an amount after a percentage has been applied and want to find the original. Common cases: pre-discount prices, pre-tax amounts, or original population sizes.
Why can't p be zero?
If p is 0%, then x represents 0% of the whole, meaning x itself must be 0. Division by zero is undefined, so a 0% input has no valid whole.
How is this different from percent of a number?
Percent of a number goes forward: given p and the whole, find the part. Reverse percentage goes backward: given the part and p, find the whole.