Percentage calculators for everyday questions
A percentage writes a number as parts per hundred, and most everyday questions about percentages follow one of a few patterns, such as a share of a whole, a change from an old value, a comparison of two peers, or a percentage added or removed. The explainer below sets out the terms and the formulas these calculators use.
All percentage calculators
Percentage calculator
Find P% of X, what percent A is of B, or the whole when you know a part and its percent.
Open A percent is a count of parts per hundred, so 15% of 80 is 0.15 × 80 = 12. Each row of the calculator answers one version of that same equation and updates as you type.Percent change calculator
Percent increase or decrease from an old value to a new one, plus raising or lowering a number by a percent.
OpenPercent difference calculator
Compare two values by the gap relative to their average, with percent change in both directions alongside.
OpenDiscount calculator
Final price, savings and the effective discount for one or two stacked percentages, or the percent off from two prices.
OpenReverse percentage calculator
Recover a net price, an earlier salary or a regular price from the value after a percentage was added or removed.
OpenPercent, percentage points and basis points
A percent is a number divided by 100: 7% is 0.07, and 7% of something is that thing multiplied by 0.07. On its own a percentage is meaningless until you know what it is a percentage of, and most confusion with percentages comes from losing track of that base.
When the quantity being discussed is already a percentage, such as an interest rate, a tax rate or a share of the vote, there are two ways to describe how it moved. A percentage point is the plain difference between two percentages: a rate going from 4% to 5% has risen by 1 percentage point. The same move is a 25% increase in the rate, because 1 is a quarter of 4. Both statements are true, so careful writing says which one is meant. The UK Office for National Statistics makes the distinction explicit in its style guide.
Finance uses an even smaller step, the basis point, which the US Securities and Exchange Commission’s investor glossary defines as one hundredth of a percentage point. A central bank rate cut of 0.25 points is 25 basis points; a rate of 8% is 800 basis points.
Percent of a number versus percent change
“Percent of” describes a part of one whole at one moment: 30 is 12% of 250. “Percent change” compares two values of the same thing at different times or states, and its base is always the earlier value. Going from 250 to 280 is a 12% rise, but going from 280 back to 250 is a fall of only 10.71%, because the base has moved. When two values have no before and after, such as the same product in two shops, a percent difference measured against their average avoids picking a side.
Percent changes also chain by multiplying, not by adding. A 50% rise followed by a 50% fall ends 25% below the start, and discounts of 20% and then 10% combine to 28% off. Undoing a percentage works the same way: divide by the multiplier rather than subtracting the percentage of the final value.
| Question | Formula |
|---|---|
| What is P% of X? | X × P ÷ 100 |
| A is what percent of B? | A ÷ B × 100 |
| A is P% of what? | A ÷ (P ÷ 100) |
| Percent change from old to new | (new − old) ÷ |old| × 100 |
| Percent difference of A and B | |A − B| ÷ ((|A| + |B|) ÷ 2) × 100 |
| Value after adding P% | X × (1 + P ÷ 100) |
| Original before P% was added | final ÷ (1 + P ÷ 100) |
| Percentage point change | new rate − old rate |
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