Percentage Calculator

How do you calculate a percentage?

A percentage expresses a number in hundredths. Twenty percent means 20 out of 100, or 0.20. This calculator answers the five questions people ask most.

• Percent of a number: p percent of x is x × p / 100.
• What percent: a as a percentage of b is a / b × 100.
• Increase or decrease: x raised by p percent is x × (1 + p / 100), and x lowered by p percent is x × (1 − p / 100).
• Percent change: going from an old value to a new one, (new − old) / old × 100.
• Reverse percentage: divide a value that already includes the percentage by (1 + p / 100), or by (1 − p / 100) if the percentage was taken off.

Examples

Twenty percent of 250 is 250 × 20 / 100 = 50. The number 45 is 45 / 180 = 0.25, or 25 percent, of 180. A material whose price went from 80 to 100 rose by (100 − 80) / 80 = 25 percent. An amount of 1200 that includes 20 percent tax is 1200 / 1.20 = 1000 before tax.

A common mistake

Taking 20 percent of a tax inclusive amount does not give the tax: 20 percent of 1200 is 240, while the tax is 200. The percentage was applied to the original value, so you divide to go back. For the same reason a 10 percent rise followed by a 10 percent cut does not return the starting price.

Limits

A percentage is undefined when the whole or the old value is zero, and the calculator shows a warning in that case. Per mille (‰) can be selected instead of percent.