Percentage Calculator
Find a percent of a number, what percent one number is of another, percent change, or the original number behind a percentage.
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A percentage is just a ratio expressed out of 100, and most everyday percentage questions fall into one of four shapes: finding a percent of a number, finding what percent one number is of another, finding the percent change between two numbers, or working backward to find the original number a percentage came from.
This calculator covers all four, each in its own tab, with the exact numbers plugged into a plain-English sentence so the answer is easy to double-check by hand.
How does this calculator work?
Pick the tab that matches your question, then enter the two numbers it asks for. All four tabs run independently, so switching tabs doesn't affect the others.
"% of a Number" answers questions like "what is 18% of 250?" by computing number × (percent ÷ 100). This is the most common shape: discounts, tips, and "take X% of Y" questions.
"What % is X of Y" answers questions like "45 is what percent of 250?" by computing (X ÷ Y) × 100, the reverse of the first tab: you have both numbers and want the percentage that relates them.
"% Change" answers questions like "what's the percent change from 50 to 65?" by computing ((new − old) ÷ old) × 100, then labeling the result as an increase or decrease based on its sign. Notice the denominator is always the starting ("from") value, which is why this calculation isn't symmetric, see the FAQ below.
"X is % of What" answers questions like "45 is 18% of what number?" by computing X ÷ (percent ÷ 100), solving algebraically for the base number rather than a percentage or a portion.
For a refresher on the underlying math with more worked examples, see Math Is Fun's introduction to percents or Cuemath's percentage guide.
Worked example
A $250 jacket is marked 18% off.
- Discount amount
- 18% of $250 = $45
- Sale price
- $250 - $45 = $205
How the numbers work
The "% of a Number" tab answers the discount amount directly: 18% of 250 is 45.
From there, subtracting the discount from the original price gives the sale price, a step outside the calculator but simple arithmetic once you have the discount amount.
The same four calculations show up everywhere: discounts, tips, sales tax, interest rates, growth rates, and commission splits. Recognizing which of the four shapes a question fits is usually the hardest part; the arithmetic itself is simple once you know which one applies.
Percentage Calculator glossary
- Percent Of
- Multiplying a number by a percentage expressed as a decimal (percent divided by 100) to find a portion of it.
- Percent Change
- The difference between a starting and ending value, divided by the starting value, expressed as a percentage. Positive means an increase, negative means a decrease.
- Base Number
- The original total that a percentage is calculated from, sometimes the unknown you're solving for rather than a given input.
Percentage Calculator FAQs
Why is percent change from 50 to 65 not the same size as from 65 to 50?+
Percent change always divides by the starting value. Going from 50 to 65 is a 15-point gain on a base of 50, or 30%. Going from 65 to 50 is the same 15-point loss but on a larger base of 65, so it works out to about 23.08%. The direction you're moving changes the denominator.
How is a percentage point different from a percent?+
A percentage point is a plain difference between two percentages, for example going from 10% to 15% is a 5 percentage point increase. Expressed as a percent change, though, that's a 50% increase (5 divided by 10). The two describe the same move in different units, and mixing them up is a common source of confusion in news headlines, and in comparing a marginal versus effective tax rate.
See marginal vs. effective rate in the Tax Bracket CalculatorCan percentages go above 100%?+
Yes. Anything where the part is larger than the base produces a result over 100%, for example 300 is 150% of 200. Percent change can also exceed 100% for a large enough increase. A percent decrease, though, can never go below -100%, since a value can't drop by more than its full starting amount.
If something drops 50% and then rises 50%, does it end up back where it started?+
No, it ends up lower. A $100 item that drops 50% becomes $50; a 50% rise from there is only $25, landing at $75, not back at $100. Each percent change applies to whatever the current value is, not the original one, so stacked percent changes never simply cancel out or add together. Run each step through the "% of a Number" or "% Change" tab separately to see the real result.