Percentage Calculator
Solve any percentage question — what is X% of Y, X is what percent of Y, X is Y% of what, and percentage increases or decreases.
How to use this calculator
- 1Choose the question that matches what you are trying to find.
- 2Enter the numbers you know.
- 3For increases and decreases, use the direction selector rather than entering a negative percentage.
How the calculation works
Part = % ÷ 100 × Whole % = Part ÷ Whole × 100 Whole = Part ÷ % × 100- Part
- The portion being measured
- Whole
- The total that the percentage refers to
- %
- The percentage — literally "per hundred"
Every percentage question is one of these three rearrangements. Identifying which number is the "whole" is the only difficult part.
For increases and decreases, multiply by (1 + p) or (1 − p) rather than adding or subtracting the percentage of the original.
Worked example
What is 15% of 200?
- 1.Convert 15% to a decimal: 15 ÷ 100 = 0.15.
- 2.Multiply: 0.15 × 200 = 30.
Result: 30
What a percentage actually means
The word "percentage" comes from the Latin "per centum," meaning "per hundred." A percentage is just a fraction with a denominator fixed at 100 — 25% is exactly the same value as 25/100, or 0.25, or one quarter. Writing it as a percentage rather than a fraction makes it easier to compare things that started out as very different sizes: 3 out of 4 and 750 out of 1,000 are hard to compare at a glance, but as percentages they are obviously 75% and 75%.
Because the "hundred" is fixed, a percentage is always relative to some whole. That whole has to be identified before the number means anything — 50% of a small class and 50% of a large stadium are wildly different head counts, even though the percentage itself is identical.
Where percentages turn up every day
Few pieces of math are used as constantly, in as many different settings, as the percentage.
- Shopping — discounts, sales tax and tip calculations all use the same percent-of-a-number logic, just applied to a price instead of an abstract number.
- Money — interest rates on savings, loans and credit cards are quoted as annual percentages, and investment returns are almost always reported the same way.
- Statistics and news — survey results, unemployment figures, election polling and approval ratings are nearly always expressed as percentages so that samples of different sizes can be compared fairly.
- Grades and scores — exam results, batting averages and win rates are converted to percentages to put performance on a common 0–100 scale.
- Nutrition labels — the "% Daily Value" on packaged food shows what share of a full day’s recommended intake one serving provides.
The three questions hiding behind every percentage problem
Nearly every percentage question that comes up in real life is one of three underlying questions, and the confusion people run into is usually about which one they are actually being asked. "What is 20% of 80?" is different from "20 is what percent of 80?", which is different again from "20 is 80% of what number?" — even though all three involve the same three numbers.
Spotting which quantity plays the role of "the whole" is the one skill that makes all three easy: it is whatever the percentage is being taken of, and it always ends up on the bottom of the division.
Mistakes that trip people up
A few errors account for most percentage confusion.
- Percent vs percentage points — if a rate moves from 5% to 8%, that is a rise of 3 percentage points but a 60% increase (3 ÷ 5). The two numbers describe the same change and can differ hugely, so mixing them up can make a shift sound far bigger or smaller than it really is.
- Assuming percentage changes cancel out — a 20% pay cut followed by a 20% raise does not return you to your original salary, because the second 20% is calculated on the smaller, already-reduced number.
- Adding percentages of different wholes — 10% of one number plus 20% of a different number is not 30% of anything meaningful — percentages can only be added directly when they share the same base.
Working percentages out in your head
A handful of shortcuts cover most everyday situations without needing a calculator at all.
- 10% first — move the decimal point one place left to get 10% of any number, then scale that up or down — 10% of 84 is 8.4, so 20% is 16.8 and 5% is 4.2.
- Halve and halve again — 25% is a quarter, so halving a number twice gets you there quickly.
- Flip the numbers — "8% of 50" and "50% of 8" always give the same answer, and one of the two is usually much easier to do in your head.
What this assumes, and where it stops
Assumptions
- Percentages are expressed out of 100, not as decimals. Enter 15, not 0.15.
Limitations
- Percentage-point differences are not the same as percentage changes. Going from 5% to 7% is a rise of 2 percentage points, but a 40% increase — this tool calculates the latter.
Common questions
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. For 45 out of 60: 45 ÷ 60 = 0.75, then × 100 = 75%. The whole always goes on the bottom of the division.
Why is a 50% decrease not undone by a 50% increase?
Because the second percentage is applied to a smaller number. 100 down 50% is 50; 50 up 50% is only 75. To undo a 50% fall you need a 100% rise. This asymmetry catches people out constantly with investment returns.
What is the difference between percent and percentage points?
If an interest rate rises from 4% to 5%, that is a rise of one percentage point but a 25% increase. News reports frequently conflate the two, which can make a change sound five or ten times larger than it is.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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