Percentage Calculator

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.

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.