How the three percentage formulas work
A percentage is just a fraction with 100 as the denominator, so every percentage problem reduces to one of three rearrangements of the same relationship: part = percent / 100 × whole. The calculator on this page has one panel for each rearrangement.
- X% of Y:
result = X / 100 × Y. Here X is the rate and Y is the whole. - X is what percent of Y:
percent = X / Y × 100. X is the part, Y is the whole. - Percentage change from A to B:
change = (B − A) / A × 100. A is the starting value and B is the ending value. The panel also shows the plain differenceB − A, and puts a plus sign in front of increases.
Worked examples
15% of 200 is 0.15 × 200 = 30. Reversing the question, 30 is 30 ÷ 200 × 100 = 15% of 200. For change, going from 80 to 100 gives (100 − 80) / 80 × 100 = +25%, with a difference of 20. Going back from 100 to 80 gives (80 − 100) / 100 × 100 = −20%. The same 20-unit gap is a different percentage because the denominator is always the starting value.
Common mistakes
- Percent versus percentage points. If an interest rate moves from 4% to 6%, it rose 2 percentage points, but the percentage change is (6 − 4) / 4 × 100 = +50%. Enter 4 and 6 in the change panel to get the 50%.
- Assuming increases and decreases cancel. A 50% rise followed by a 50% fall takes 100 to 150 and then to 75, not back to 100.
- Working backwards from a final price. If a price is 120 after a 20% increase, the original was 120 ÷ 1.20 = 100, not 120 − 20% of 120 (which is 96). The same logic is used to strip tax out of a tax-inclusive total; see the GST calculator.
- Dividing by zero. A percentage change from 0, or "what percent of 0", is mathematically undefined. This tool shows 0 in those cases rather than an error, so treat a 0 result with a zero starting value as "not defined".
Quick reference
| Question | Inputs | Answer |
|---|---|---|
| What is 20% of 350? | X = 20, Y = 350 | 70 |
| 45 is what % of 60? | X = 45, Y = 60 | 75% |
| Change from 250 to 200 | From 250, To 200 | −20%, difference −50 |
| Change from 40 to 100 | From 40, To 100 | +150%, difference 60 |
When to use it
Typical jobs are checking a markdown (the discount calculator handles final price directly), working out how much a metric grew month over month, converting exam marks to a percentage, and sanity-checking a tip or commission. For tip splitting or sales tax with a fixed rate, the tip calculator and sales tax calculator save a step.