Percentage Calculator
Work out what X% of a number is, what percent one number is of another, and reverse percentages.
What the Percentage Calculator does
A percentage expresses a number as a fraction of 100. This calculator covers the three questions people actually ask: finding a part of a whole, expressing one number as a percentage of another, and working backwards from a percentage to the original total.
Formula
X% of Y = (X ÷ 100) × YX is what % of Y = (X ÷ Y) × 100X is Y% of what = (X ÷ Y) × 100
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| What do you want to find? | one of 3 options | Yes | — |
| First value (X) | number | Yes | — |
| Second value (Y) | number | Yes | — |
How to use it
- Choose What do you want to find?.
- Enter First value (X) and Second value (Y).
- Select Calculate.
Worked example
A jacket is listed at $80 and you have a 15% off coupon. How much comes off?
- Mode
- What is X% of Y?
- X
- 15
- Y
- 80
15% of 80 = 12, so the coupon saves $12 and you pay $68.
Reading the result
- Percentage of, percentage change and percentage difference answer different questions and give different numbers from the same pair of values. Check which one the situation calls for.
- Percentage change is directional: it depends on which value is the starting point. Percentage difference is symmetric and does not.
- A percentage is meaningless without its base. "Up 40%" describes a very different amount depending on what it grew from.
Assumptions and limitations
- The calculation is pure arithmetic and carries no rounding beyond the displayed precision.
- A percentage change from zero is undefined, because there is no base to compare against.
Common mistakes
- Adding and removing the same percentage and expecting the original value. A 20% fall then a 20% rise leaves you 4% down.
- Confusing percentage points with percent. A rate moving from 5% to 7% has risen 2 percentage points, which is a 40% increase.
- Reversing a discount by adding the percentage back. Removing 20% requires dividing by 0.8, not multiplying by 1.2.
Frequently asked questions
How do I calculate a percentage in my head?
Find 10% by moving the decimal one place left, then scale. For 15% of 80: 10% is 8, half of that is 4, so 15% is 12.
What is the difference between percent and percentage point?
Percent is relative, percentage points are absolute. Moving from 4% to 6% is a rise of 2 percentage points but a 50% increase.
Why does adding then removing the same percentage not return the original number?
Because the second percentage is applied to a different base. 100 raised 10% is 110; dropping 110 by 10% gives 99, not 100.