Percentage Calculator
Work out what percent of a number another is, a percentage of a value, the percentage increase, decrease or difference between two figures, with the working.
Every convention this page applies is named in the result rather than assumed. Your numbers stay in this browser.
Results
How to read this: the verdict describes how much room your numbers leave, not a decision or an offer. Change any input to see how much the result moves.
Assumptions and formula
Every mode rearranges one identity, part = whole × rate. The calculator substitutes your figures into the rearrangement for the question you chose, shows that line as the formula, and lists the intermediate arithmetic as steps.
A percentage change is measured against the size of the starting figure, so a move from −50 to −25 is reported as a 50% increase. A change from zero is rejected as undefined rather than shown as infinity. When both figures are themselves percentages, the change in percentage points is reported alongside the relative change, because the two are different measures.
Worked example
For "what is 20% of 150": 20 ÷ 100 = 0.2, and 150 × 0.2 = 30. For "30 is what percent of 150": 30 ÷ 150 = 0.2, which is 20%. For a change from 150 to 180: the difference is 30, 30 ÷ 150 = 0.2, a 20% increase. Reversing that — 180 back to 150 — is a 16.7% decrease, because the base is now 180.
Frequently asked questions
What is the difference between percentage change and percentage difference?
Percentage change measures movement from a starting value to an ending value: (new − old) ÷ old. Going from 40 to 50 is a 25% increase, and going from 50 to 40 is a 20% decrease, because the base changes. Percentage difference compares two values with no start and no end, dividing the gap by their average: 40 and 50 differ by 10 on an average of 45, so 22.2%, whichever way round you put them. Use change when there is a before and an after; use difference when you are comparing two things side by side.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 150 is 30 ÷ 150 = 0.2, which is 20%. The order matters: 150 out of 30 is 500%. Choose "X is what percent of Y" here and the result names which figure it treated as the whole.
What is the difference between a percentage change and percentage points?
A percentage change compares the move to the starting figure; percentage points are the plain difference between two percentages. An interest rate rising from 4% to 5% has risen by one percentage point, and by 25% (because 1 is a quarter of 4). News reports mix the two constantly. Tick "these figures are percentages" and both are reported.
Why is a percentage decrease not undone by the same percentage increase?
Because the second percentage is taken of a different base. £100 reduced by 20% is £80; £80 increased by 20% is £96, not £100. Recovering the original needs a 25% rise, since 20 is a quarter of 80. Use the "increase or decrease by" mode to see the actual figure rather than assuming symmetry.
How do I find the original price after a percentage was applied?
Use "X is P% of what". If a sale price of £60 is 75% of the original (a 25% discount), the original is 60 ÷ 0.75 = £80. Dividing by the percentage as a decimal reverses the multiplication; subtracting the percentage of the sale price does not, and is the most common way this goes wrong.
What does a percentage change from zero mean?
It is undefined, and this calculator says so rather than showing "Infinity". Going from 0 to any positive number is not a percentage rise, because there is no starting amount to compare against. Report the change as an absolute difference instead, or use the finishing figure as the whole in "X is what percent of Y".
Is a percentage increase calculator different from a percentage change calculator?
No. A percentage increase calculator and a percentage decrease calculator are the percentage change calculator with the direction known in advance: (new − old) ÷ old, positive for an increase, negative for a decrease. From 80 to 100 is a 25% increase; from 100 to 80 is a 20% decrease, because the base is different each way. A percentage difference calculator is the one that is genuinely different: it divides the gap by the average of the two numbers, so 80 and 100 differ by 22.2% in either order. A plain percent calculator, what is 15% of 60, is the first mode on this page.
Which calculator do I need for what is x percent of y, or for percent off?
For what is x percent of y, the first mode on this page: 15% of 60 is 9. A percent off calculator is the same multiplication in reverse, taking the percentage away from a price, and because prices bring tax and stacked discounts with them, that lives on the discount calculator rather than here. This page handles the pure arithmetic: a percentage of a number, one number as a percentage of another, and the change or difference between two.