Percentage Calculator
Work out a percentage of a number, a percent change, a discount or a grade — and see the arithmetic behind every answer.
Find the part
30
15 ÷ 100 × 200
Find the percent
15%
30 ÷ 200 × 100
Find the whole
200
30 ÷ 15 × 100
Find the change
+50%
(75 − 50) ÷ 50 × 100
Answers update as you type — there is no Calculate button anywhere.
Answers
Common percentage questions
Percentages trip people up in the same five places. Here is each one, with the arithmetic written out so you can follow it rather than memorise it.
- How do I calculate a percentage of a number?
- Divide the percentage by 100, then multiply by the number. For 15% of 200: 15 ÷ 100 = 0.15, and 0.15 × 200 = 30.
- How do I work out what percentage one number is of another?
- Divide the part by the whole, then multiply by 100. For 30 out of 200: 30 ÷ 200 = 0.15, and 0.15 × 100 = 15%.
- How do I find the original number from a percentage?
- Divide the part by the percentage, then multiply by 100. If 30 is 15% of a number: 30 ÷ 15 = 2, and 2 × 100 = 200.
- What is the difference between percent and percentage?
- Percent goes with a number, as in 15 percent. Percentage goes without one, as in a large percentage. The arithmetic is identical.
- Why does 10% off then 10% on not return the original price?
- Each percentage applies to a different base. Taking 10% off 100 gives 90. Adding 10% to 90 adds 9, not 10, so you land on 99.
What a percentage is
A percentage is a fraction with 100 on the bottom. "Per cent" is Latin for "by the hundred", so 15% means 15 out of every 100. That single idea is behind all four calculators above.
Because 15% is just another way of writing 0.15, every percentage question turns into an ordinary multiplication or division once you divide by 100.
How to calculate a percentage of a number
A percentage question always involves three numbers: a Part, a Whole, and a Percent. You are given two and asked for the third. Which one is missing decides the formula.
1. Find the Part
Part = Percent ÷ 100 × Whole
Worked example — 15% of 200
15 ÷ 100 = 0.15
0.15 × 200 = 30
So 15% of 200 is 30.
2. Find the Percent
Percent = Part ÷ Whole × 100
Worked example — 30 out of 200
30 ÷ 200 = 0.15
0.15 × 100 = 15
So 30 is 15% of 200.
3. Find the Whole
Whole = Part ÷ Percent × 100
Worked example — 30 is 15% of what?
30 ÷ 15 = 2
2 × 100 = 200
So 30 is 15% of 200.
Doing it in your head
Two shortcuts cover most day-to-day percentages:
- 10% is the decimal point moved one place left. 10% of 84 is 8.4. From there, 20% is double that, and 5% is half of it.
- Percentages can be reversed. 8% of 50 is the same as 50% of 8, which is 4. Swap the numbers whenever one of them is easier.
The mistake almost everyone makes
A percentage always applies to a base, and the base can move. Take 10% off 100 and you get 90. Add 10% back to 90 and you add 9, not 10, so you land on 99. The two percentages were taken from different numbers.
The same trap explains why a 50% loss needs a 100% gain to recover. This is why every calculator on this site prints the working: the formula shows you which number the percentage was taken from.
Every calculator
Fourteen pages, one engine.
Percentage increase
old × (1 + p)
Percent error
|exact − measured| ÷ exact
Percent change
(new − old) ÷ old
Percent difference
|a − b| ÷ mean
Percentile
rank ÷ count
Percent off
price × (1 − off)
Percentage decrease
old × (1 − p)
Percent yield
actual ÷ theoretical
Grade percentage
score ÷ total
Win percentage
wins ÷ games
Weight loss percentage
lost ÷ start
Fraction to percent
a ÷ b × 100
Decimal to percent
x × 100
Average percentage
Σ (p × n) ÷ Σ n