Percentage Calculator
Find a percent of a number, what percent one number is of another, or the base from a part and percent; also percentage difference, percent change, increasing or decreasing by a percent, and a percent of a percent, with working shown.
Change the values and press Calculate to work out your own figures.
P% of X = Y (enter any two)
Enter any two values and press Calculate to find the third.
Show the working
- 20 ÷ 100 = 0.2
- 0.2 × 150 = 30
What is P% of X?
Find a percentage of a number, such as 15% of 80.
Show the working
- 15 ÷ 100 = 0.15
- 0.15 × 80 = 12
Y is what percent of X?
Find what percent one number is of another.
Show the working
- 12 ÷ 80 = 0.15
- 0.15 × 100 = 15%
Y is P% of what?
Find the whole when you know a part and its percentage.
Show the working
- 40 ÷ 100 = 0.4
- 12 ÷ 0.4 = 30
Percentage difference between two values
Compare two values without treating either as the starting point.
Show the working
- Difference: |10 − 20| = 10
- Average of the sizes: (|10| + |20|) ÷ 2 = 15
- 10 ÷ 15 × 100 = 66.6666666667%
Percent change from X to Y
Find how much a value went up or down, as a percentage of where it started.
Show the working
- Change: 60 − 80 = -20
- -20 ÷ |80| × 100 = -25%
Increase or decrease by a percent
Increase or decrease a number by a percentage, or work backwards to the original.
Show the working
- Multiplier: 1 − 20/100 = 0.8
- 100 × 0.8 = 80
A% of B%
Take a percentage of a percentage, such as 50% of 20%.
Show the working
- 50 × 20 ÷ 100 = 10
What a percentage is
Per cent means per hundred, so a percentage is a fraction with 100 on the bottom: 25% is 25/100, or 0.25. To use a percentage in a calculation, divide it by 100 first. Every calculator on this page shows its working, so you can follow each step.
P% of X = Y Y = P ÷ 100 × X P = Y ÷ X × 100 X = Y ÷ (P ÷ 100)
The three basic questions
- What is 15% of 80? Multiply: 15 ÷ 100 × 80 = 12.
- 30 is what percent of 120? Divide the part by the whole: 30 ÷ 120 = 0.25, which is 25%.
- 12 is 15% of what number? Divide the part by the percentage: 12 ÷ 0.15 = 80.
The first calculator answers all three: enter any two of the values and it finds the third. The next three each answer one question, if you prefer a form that says it in words.
Percent change and percentage difference
Percent change compares a new value with an old one and measures the change against where you started. A price that goes from 50 to 65 rose by 15, which is 15 ÷ 50 = 30%. The order matters: going back from 65 to 50 is a fall of 15 ÷ 65, about 23.1%.
Percentage difference compares two values when neither one is the starting point, such as two measurements or two shops' prices. It divides the difference by the average of the two, so the answer is the same whichever way round you enter them: 10 and 15 differ by 5, their average is 12.5, and 5 ÷ 12.5 = 40%. The calculator also shows the percent change from the first value to the second, for comparison.
Percent change = (new − old) ÷ |old| × 100 Percentage difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100
A change from 0 has no percentage, because there is nothing to compare it with, and the calculator says so instead of showing a number.
Increasing or decreasing by a percent
To increase a number by a percentage, multiply by 1 plus the percentage: 80 increased by 25% is 80 × 1.25 = 100. To decrease, multiply by 1 minus it: 80 decreased by 25% is 80 × 0.75 = 60.
Working backwards is a common trap. If a price including 20% tax is 96, the price before tax is 96 ÷ 1.2 = 80, not 96 minus 20% (76.80). Enter the new value and the percentage, and the calculator finds the original.
A percentage of a percentage multiplies the two: 50% of 20% is 0.5 × 20% = 10%.
Percent or percentage points?
When a rate that is already a percentage changes, say whether you mean percentage points or percent. An interest rate rising from 4% to 5% has gone up by 1 percentage point, but by 25% of its old value (1 ÷ 4). Subtracting two percentages gives percentage points; use percent change for the relative rise.
Questions
How do I work out a percentage of a number in my head?
Find 10% by moving the decimal point one place left, then scale it. For 15% of 80: 10% is 8, 5% is half of that, 4, so 15% is 12.
Is a 50% increase undone by a 50% decrease?
No. 100 increased by 50% is 150, and 150 decreased by 50% is 75. The decrease is taken from the larger number, so it removes more than the increase added. To get back to 100 from 150 you need a decrease of one third, about 33.3%.
Can a percentage be more than 100%?
Yes. 150 is 150% of 100, and a value that triples has increased by 200%. Only a part of a whole, such as a share of a class, can't go above 100%.
Sources
Limitations
- Percentages are treated as pure ratios; percentage points (differences between two percentages) are not a separate mode — subtracting two percents gives percentage points, not a percent change.
- Percentage difference uses the mean of absolute values as its reference; other references (e.g. the larger value) are not offered.
- Compound or repeated percent changes over several periods are out of scope (see the percent growth and compound interest tools).