Percentage Calculator and Percentage Difference Calculator, Percentage Increase and Percentage Change Calculator

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. It also finds percentage increase and decrease: enter the old and new values and it gives the percentage change with the formula shown.

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.

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.

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.

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.

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".

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.

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.

Choose "Percentage change from A to B", enter the old value as A and the new value as B, and it gives the percent increase or decrease. A rise from 80 to 100 is a 25% increase; a fall from 100 to 80 is a 20% decrease.

Multiply the number by the percentage and divide by 100: 15% of 80 is 80 × 15 ÷ 100 = 12. Choose "What is P% of a value?" above to do it for any numbers.

Divide the part by the whole and multiply by 100: 30 out of 120 is 30 ÷ 120 × 100 = 25%. Choose "X is what percent of Y?" above.

Subtract the new value from the old one, divide by the old value and multiply by 100. A price that falls from 50 to 40 has decreased by (50 − 40) ÷ 50 × 100 = 20%. The "Percentage change from A to B" mode works out decreases as well as increases.

Only average percentages directly when they are out of the same total. Otherwise add up the parts and the totals first: 8 out of 10 (80%) and 30 out of 50 (60%) together are 38 out of 60, which is 63.3%, not 70%.

Percentage = part ÷ whole × 100. Rearranged, the same formula gives the other two figures: part = percentage × whole ÷ 100, and whole = part × 100 ÷ percentage. 12 out of 48 is 12 ÷ 48 × 100 = 25%; 25% of 48 is 25 × 48 ÷ 100 = 12; and 12 is 25% of 12 × 100 ÷ 25 = 48. The first, second and fourth modes on this page are those three rearrangements.

Percentage increase = (new value − original value) ÷ original value × 100. From 60 to 75 is (75 − 60) ÷ 60 × 100 = 25%. Divide by the original value, not the new one: dividing by 75 gives 20%, which is the most common mistake. A negative result means the value fell, and its size is the percentage decrease.

Subtract the first number from the second, divide by the first and multiply by 100. From 250 to 200 is (200 − 250) ÷ 250 × 100 = −20%, a 20% fall. The order matters because the first number is the base: from 200 to 250 is a 25% rise. If neither number is a starting point, such as two prices from different shops, use the percentage difference instead, which divides by their average: 200 and 250 differ by 22.2% in either order.

Profit percentage = (selling price − cost price) ÷ cost price × 100, and loss percentage = (cost price − selling price) ÷ cost price × 100. Both are measured on the cost price. Bought for 400 and sold for 500 is a profit of 100, which is 25%; sold for 340 it is a loss of 60, which is 15%. Here that is "Percentage change from A to B" with the cost price as A and the selling price as B: a positive result is the profit percentage, a negative one the loss. Profit as a share of the selling price is the margin, a different figure: 100 ÷ 500 = 20%.