What to enter
Choose the question first, because the labels on the two number fields change to match it. Every mode takes two numbers, X and Y:
- What is X% of Y?
- X is the percentage and Y is the number you are taking it of. Example: 15% of 80.
- X is what percent of Y?
- X is the part and Y is the whole. Example: 18 out of 72.
- Increase Y by X%
- Y is the starting number and X is the percentage to add. Useful for adding a markup, a raise or a fee.
- Decrease Y by X%
- Y is the starting number and X is the percentage to subtract, such as a discount.
- Percent change from X to Y
- X is the starting value and Y is the ending value. The result shows whether it was an increase or a decrease.
- Percent difference between X and Y
- Compares two values when neither one is the clear starting point, using their average as the base.
You can type numbers with commas, decimals and a leading minus sign. The percent symbol is optional.
How to read your results
The main result is shown large at the top with a plain-language label that repeats your question, such as “15% of 80.” Beneath it, the Working line shows the exact arithmetic so you can check it or copy the method. Where it is useful, extra lines show the amount added or subtracted, the absolute change, or the result as a decimal.
If a question has no valid answer, for example asking what percent a number is of zero, the calculator explains why instead of showing a misleading figure.
The formulas
X is what percent of Y = X ÷ Y × 100
Y increased by X% = Y × (1 + X ÷ 100)
Y decreased by X% = Y × (1 − X ÷ 100)
Percent difference = |X − Y| ÷ ((X + Y) ÷ 2) × 100The change formula divides by the size of the starting value, so it works with negative starting numbers too. Percent difference uses the average of the two values as its base.
Every percentage question comes back to one idea: a percentage is a ratio to a base, times 100. Most mistakes come from using the wrong base, so always ask what the percentage is “of.”
Worked examples
One example for each mode
- 15% of 80. 15 ÷ 100 × 80 = 12.
- 18 is what percent of 72. 18 ÷ 72 × 100 = 25%.
- 250 increased by 8%. The addition is 20, so the new value is 270.
- 90 decreased by 30%. The subtraction is 27, so the new value is 63.
- From 80 to 100. (100 − 80) ÷ 80 × 100 = +25%. Going back from 100 to 80 is -20%, not −25%.
- Between 40 and 60. The difference of 20 divided by the average of 50 gives 40%.
Common percentage mistakes
Percent increases and decreases are not symmetrical. A value that rises 25% from 80 to 100 must fall 20% to get back to 80, because the second percentage is measured against the larger number. The same effect makes a 50% loss require a 100% gain to break even.
Successive percentages do not add. Taking 20% off and then a further 10% off is not 30% off. The second discount applies to the already-reduced price, so the combined saving is 28%. The discount calculator handles this directly.
Percent and percentage points differ. If a rate goes from 4% to 5%, it has risen one percentage point, but the rate itself has risen 25%. News stories and financial statements mix the two often, so check which one is meant.
The base matters. A price that rises 10% and then falls 10% ends below where it started. When you are asked what percent one number is of another, make sure the “whole” goes in the denominator.
Percent change versus percent difference. Use percent change when there is a natural before and after, such as last year’s price and this year’s. Use percent difference when two values are equal partners, such as two competing quotes, where neither is the original.
Where these calculations show up in money decisions
Percentages sit behind most everyday financial decisions. A raise of 3% is a percent increase. A sale is a percent decrease. Comparing how much a stock, an account balance or a price changed is a percent change. Sales tax, tips and markups are percentages of a base amount, and each has its own calculator on this site: the sales tax calculator, tip calculator and markup calculator. For long-term percentage growth compounding year after year, use the compound interest calculator, since a repeated percentage grows faster than a simple one.
Assumptions and limits
The results are exact arithmetic on the numbers you enter, shown to up to four decimal places. Rounding in the display does not change the underlying value. The calculator does not know the meaning of your numbers, so it cannot warn you if you have chosen the wrong base or mixed up the order of X and Y. Read the working line to confirm that it matches your question.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 15% of 80: 15 ÷ 100 × 80 = 12.
How do I find a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%.
Why is a 25% increase followed by a 25% decrease not back to the start?
Because the decrease is applied to the larger, increased number. A 25% increase from 80 gives 100, and 25% of 100 is 25, so the decrease lands at 75.
What is the difference between percent change and percent difference?
Percent change measures movement from a starting value and depends on which number is the start. Percent difference compares two values symmetrically using their average, so the order does not matter.
Can the calculator handle negative numbers?
Yes. Percent change divides by the size of the starting value, so a move from −50 to −25 is reported as a 50% increase. Percent calculations with negative bases can be confusing, so check the working line.
What happens if I divide by zero?
The calculator tells you the question has no answer. For example, no percentage of zero can be found, and percent change from zero is undefined.