Percentage calculator
Work out a percent of a number, percentage change, percent difference, or a number increased or decreased by a percentage.
- Formula and assumptions shown
- Table and CSV export
- Runs in your browser
How it works
Pick what you want to work out and enter the numbers. The calculator shows the answer, the formula written out with your numbers and a short table of related results, such as the same number increased and decreased by the percentage.
X% of Y = (X ÷ 100) × Y. X as a percent of Y = X ÷ Y × 100. Percentage change = (B − A) ÷ |A| × 100. Percent difference = |A − B| ÷ ((A + B) ÷ 2) × 100. Y increased by X% = Y × (1 + X ÷ 100); decreased = Y × (1 − X ÷ 100). The whole when X is P% of it = X ÷ (P ÷ 100).
Percentage change measures a move from a starting value to a new one: (new − old) ÷ old × 100. It is not symmetric: going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease, because each change is measured from its own starting point. Percent difference compares two values without choosing a start, dividing the gap by their average.
Percent and percentage points are not the same. When an interest rate goes from 4% to 5%, it rises by 1 percentage point, which is a 25% increase in the rate. The calculator works with any numbers, including values above 100% and negative numbers where the formula allows them.
Assumptions
- A total of 0 or a starting value of 0 has no percentage, so those inputs show an error instead of a number.
- Percentage change from a negative starting value divides by its absolute value, so the sign shows the direction of the move.
- Percent difference is defined here for values of 0 or more.
- Results are exact; the page shows them to 2 decimals and the formula line to 4.
Worked example
Worked examples on this page use US dollars.
15% of 80, and a change from 80 to 100
15% of 80 is 0.15 × 80 = 12, and 30 is 25% of 120. Going from 80 to 100 is a 25% increase, while going back from 100 to 80 is a 20% decrease; the percent difference between them is 22.22%. 80 increased by 15% is 92, and it takes a 13.04% decrease to return to 80. If 12 is 15% of a number, that number is 80.
Step by step
- Turn the percentage into a decimal. 15% ÷ 100 = 0.15. Every percentage calculation starts from this decimal.
- Take the percentage of the number. 0.15 × 80 = 12, so 15% of 80 is 12. Adding it gives 92 (80 increased by 15%); taking it off gives 68.
- Measure a change from a starting value. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%. From 100 back to 80: (80 − 100) ÷ 100 × 100 = −20%.
- Compare two values without a starting point. Percent difference: |80 − 100| ÷ ((80 + 100) ÷ 2) × 100 = 20 ÷ 90 × 100 = 22.22%.
- Work back to the whole. If 12 is 15% of a number, the number is 12 ÷ 0.15 = 80.
How to read your result
The headline is the answer for the mode you picked: a number (X% of Y, a number increased or decreased, or the whole), or a percentage (what percent, percentage change or percent difference). The line under it writes the formula out with your numbers.
The table lists related results for the same inputs, such as the change back to the start or the same number decreased instead of increased. A positive percentage change is an increase and a negative one a decrease.
When both values are themselves percentages, such as two interest rates, the difference between them is in percentage points, while the percentage change is relative to the first rate.
What changes the result most
- The starting value
- The same gap of 20 is a 25% increase from 80 but a 20% decrease from 100, because each change is divided by its own starting value.
- Increasing and then decreasing
- 80 increased by 15% is 92, but 92 decreased by 15% is 78.2, not 80; getting back to 80 takes a 13.04% decrease.
- Percent or percentage points
- A rate that goes from 4% to 5% rises by 1 percentage point, which is a 25% increase in the rate.
Questions
How do I calculate a percentage of a number?
Turn the percentage into a decimal by dividing by 100, then multiply. 15% of 80 is 0.15 × 80 = 12, and 20 percent of 50 is 0.2 × 50 = 10.
How do I calculate percentage increase or decrease?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%, an increase. From 100 to 80 is (80 − 100) ÷ 100 × 100 = −20%, a decrease.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 120 is 30 ÷ 120 × 100 = 25%, and 17 out of 20 is 85%.
What is the difference between percent change and percent difference?
Percent change has a direction and a starting point: 80 to 100 is +25%. Percent difference treats both values the same and divides the gap by their average: |80 − 100| ÷ 90 × 100 = 22.22%, whichever order you enter them in.
What is a percentage point?
The plain difference between two percentages. A rate that goes from 4% to 5% rises by 1 percentage point, which is a 25% increase in the rate itself.
How do I calculate percentage decrease?
Subtract the new value from the old one, divide by the old value and multiply by 100. From 100 to 80 is (100 − 80) ÷ 100 × 100 = a 20% decrease.
How do I find the original number from a percentage?
Divide the part by the percentage as a decimal. If 6 is 30% of a number, the number is 6 ÷ 0.3 = 20; if 12 is 15%, it is 80.
More in Everyday & business
Sources
These references explain the concepts behind the calculation. They do not endorse this site. Estimates leave out any cost or condition you did not enter.
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