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Percentage Calculator

Compute percent change, percent of, and ratios instantly.

How it is calculated

The tool has three modes. Of: result = x × y / 100, the value of y percent of x. Change: result = (y − x) / |x| × 100, where x is the starting value and y the new value; a positive result is an increase, a negative one a decrease. Is of: result = x / y × 100, which tells you what percentage x is of y. The "of" mode shows a plain number, the other two show a percent. If the starting value in change mode is 0 the result is shown as 0, because a percent change from zero is undefined, and a zero y in "is of" mode is treated the same way. Percent change divides by the absolute value of x, so the sign always reflects the direction of the move.

Worked example

A product price rises from 80 to 100. Pick the change mode with x = 80 (old value) and y = 100 (new value). The difference is 100 − 80 = 20. Dividing by the starting value gives 20 / 80 = 0.25, and multiplying by 100 gives the final figure: 25.00%. The price went up by a quarter of its original value. Note that going back from 100 to 80 is only a 20.00% drop, because the base is now larger.

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Common mistakes

  • Putting the new value in x and the old value in y in change mode, which flips the base and gives a different percentage (a rise from 80 to 100 is +25%, but 100 to 80 is −20%).
  • Treating a percent change as reversible: a 25% increase followed by a 25% decrease does not return to the start.
  • Mixing up the "of" and "is of" modes: 20% of 50 is 10, but 20 is 40% of 50.
  • Subtracting percentages when the base differs; going from 10% to 15% is a rise of 5 percentage points but a 50% relative increase.

About this calculator

This is a general-purpose tool for the handful of percentage questions that come up constantly: finding what a certain percent of a number is, working out what percentage one number represents of another, and calculating the percentage increase or decrease between two values. Each mode rearranges the same basic part-over-whole relationship to solve for whichever piece is missing.

It gets used for everything from splitting a bill and checking a discount to grading a test, tracking a change in body weight, or comparing this year's numbers to last year's in a small business. Because the underlying math is identical across so many everyday situations, having one calculator that covers all the common variants saves reaching for a different formula each time.

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