Percentage Calculator

Most percentage questions are one of three: what is p percent of a value, what does the value become after adding or removing it, and how big is the gap between two numbers. This tool answers all three at once, because they usually come up together — a discount, the price after it and how that compares with last month.

How it is calculated

p% of x = x × p ÷ 100 · change = (b − a) ÷ a × 100

Percent means "per hundred", so the first form is a plain multiplication. Percentage change is always measured against the starting value, which is why it is undefined when that value is zero: there is nothing to compare against.

Source: A percentage is a ratio expressed as a fraction of 100: p% of x = x × p / 100, and the change from a to b is (b − a) / a × 100

Questions people ask

Why is a 25% rise not cancelled by a 25% fall?

Because each percentage applies to a different base. 200 raised by 25% is 250, and 250 cut by 25% is 187.5, not 200. To undo a 25% rise you need a 20% fall.

What is the difference between percent and percentage points?

If a rate moves from 4% to 5%, that is a rise of one percentage point but a 25% increase. Financial and political reporting mixes the two constantly, usually in whichever direction sounds better.

Why does change show as undefined?

Percentage change divides by the starting value, so a start of zero has no defined answer — any increase from nothing is infinite in relative terms. The tool says so rather than printing a misleading number.

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