Match the inputs to your percentage question
Choose one of the five calculation modes. For Percent of a number, enter the base in the first box and the percent in the second. For What percent?, the first box is the whole and the second is the part. For Percent change, enter the original then the final value. For Increase or decrease, enter the original and the percent, then select the direction. For Original before change, enter the final value in the first box and the percent in the second, with the direction of the earlier change.
Formulas and worked examples
A percent means per hundred. Percent of a value is base × percent ÷ 100; what percent a part represents is part ÷ whole × 100. With a base of 200 and percent of 15, the part is 200 × 15 ÷ 100 = 30. In What percent? mode, a whole of 200 and part of 30 gives 15%.
An increase or decrease uses original × (1 ± percent ÷ 100). Increasing 200 by 15% gives 230; decreasing it by 15% gives 170. To reverse the increase, select Original before change, enter 230 and 15, and choose Increase. The original is 230 ÷ 1.15 = 200. Subtracting 15% from 230 would give 195.5, because that calculation uses a different base.
Percent change versus percentage points
This tool calculates relative change as (final − original) ÷ |original| × 100. Moving from 40 to 50 gives 10 ÷ 40 × 100 = 25%. If those values are themselves percentages, the difference is also 10 percentage points; the two statements answer different questions. For a negative original, this tool uses its absolute value in the denominator: −40 to −20 gives +50%, indicating an upward numeric change.
Common pitfalls and limits
A zero whole has no defined What percent? result, and relative percent change from zero is undefined. A 100% decrease cannot be reversed to a unique original because every original would become zero. Successive changes multiply: a 20% increase followed by a 20% decrease turns 100 into 120 and then 96. Finite negative values and percentages over 100 are accepted, but you must decide whether they make sense for your question. The tool does arithmetic; it does not assign tax, discount or business rules.
For exact rational arithmetic and conversions, use the fraction calculator.
Method reference
OpenStax: Understanding Percent explains the base, part and percentage relationship.
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