Percentage Calculator

The formula for percentage change is: ((New Value − Old Value) ÷ Old Value) × 100. If the result is positive, the value has increased. If it is negative, the value has decreased. For example, going from 80 to 100 gives ((100 − 80) ÷ 80) × 100 = 25% increase. This formula works for any two numbers you want to compare over time.

To calculate percentage increase, subtract the original value from the new value, divide by the original value, then multiply by 100. The formula is: ((New Value − Original Value) ÷ Original Value) × 100. For example, if a price goes from £40 to £50, the increase is £10. Dividing £10 by £40 gives 0.25, multiplied by 100 gives a 25% increase. Use the Percentage Change calculator above and it will tell you automatically whether the result is an increase or decrease.

To calculate percentage decrease, subtract the new value from the original value, divide by the original value, then multiply by 100. The formula is: ((Original Value − New Value) ÷ Original Value) × 100. For example, if a price drops from £50 to £40, the decrease is £10. Dividing £10 by £50 gives 0.20, multiplied by 100 gives a 20% decrease. Note that percentage increase and decrease use different denominators, so a 25% increase followed by a 25% decrease does not return to the starting value.

Percentage change measures how much a value has moved from a specific starting point — it has a clear direction (increase or decrease) and the original value is the reference point. Percentage difference, on the other hand, compares two values without implying which came first or which is the reference. It uses the average of the two values as the denominator: (|Value A − Value B| ÷ ((Value A + Value B) ÷ 2)) × 100. Use percentage change when tracking movement over time, and percentage difference when comparing two independent figures side by side.

To find what percentage one number is of another, divide the first number by the second number and multiply by 100. For example, to find what percentage 25 is of 200: divide 25 by 200 to get 0.125, then multiply by 100 to get 12.5%. The formula is: (Part ÷ Whole) × 100. This is useful for calculating test scores, market share, proportions, and many everyday situations.

To add a percentage to a number, multiply the number by (1 + the percentage expressed as a decimal). For example, to add 20% to 150: multiply 150 by 1.20, which gives 180. Alternatively, calculate 20% of 150 (which is 30) and add it to 150 to get 180. This is the calculation used for adding VAT, tips, service charges, and markups to a base price.

To subtract a percentage (such as a discount) from a number, multiply the number by (1 − the percentage as a decimal). For example, a 20% discount on £150 means multiplying 150 by 0.80, which gives £120. Alternatively, calculate 20% of 150 (which is 30) and subtract it from 150. You can also use the 'Subtract a Percentage' calculator above to work this out instantly. This applies to sale prices, commission deductions, and any reduction from a base figure.

A reverse percentage works backwards from a known result to find the original value. If you know that a number is a certain percentage of an unknown whole, you divide the known number by the percentage (expressed as a decimal) to find the original. For example, if 150 is 75% of some number, divide 150 by 0.75 to get 200. This is useful when a price shown already includes a percentage added or removed and you want to find the original figure before that change.

To add VAT or sales tax to a price, use the 'Add a Percentage' calculator and enter the tax rate as the percentage. For example, to add 20% UK VAT to a price of £100, enter 100 as the number and 20 as the percentage — the result is £120. To find the pre-VAT price from a VAT-inclusive price, use the 'Reverse Percentage' calculator: if £120 is the VAT-inclusive price at 20% VAT, then the original price is £120 ÷ 1.20 = £100. The same approach works for any sales tax rate.