Reverse percentage calculator

120 after a 20% increase originally was 100. Enter the value after the change and its signed percentage rate to recover the original: use a positive rate for an increase and a negative rate for a decrease.

What this calculator does

A reverse percentage calculation works backwards from a final amount. You know what something costs, weighs or pays now, together with the percentage change that produced it, and want to find the earlier amount. The final value is not the base that the original percentage was calculated from.

This tool reverses one change at a known rate. It does not work out an unknown rate from two amounts, and it cannot recover an exact original price from a rounded receipt without some uncertainty. Keep the full precision of the final amount when it is available, then round according to the purpose of your calculation.

Formula

Original = final value ÷ (1 + percentage change ÷ 100)

Or in one step: Final value × 100 ÷ (100 + percentage change)

In plain English, divide the final value by the fraction of the original that remains after the change. A 20% increase leaves 120% of the original, so divide by 1.2. A 20% decrease leaves 80%, so enter −20 and divide by 0.8. The percentage change must be greater than −100%.

Worked example

A value is 120 after a 20% increase. The multiplier is 1 + 20 ÷ 100 = 1.2. Divide 120 by 1.2 to get the original value of 100. Check it forwards: 100 × 1.2 = 120.

Worked example: recover a price before a sale

A jacket costs 80 after a 20% discount. The shopper pays 100% − 20% = 80% of the original price. Write this as a decimal multiplier of 0.8, then divide: 80 ÷ 0.8 = 100. The original price was 100, and the discount amount was 20.

Check the answer against the actual sale rule rather than applying the same rate in reverse. Starting at 100, taking off 20% leaves 80. Adding 20% to 80 would give only 96. The increase from 80 back to 100 is 25%, even though the original discount was 20%.

Worked example: a salary before a pay rise

A salary is 33,000 after a 10% rise. The new salary is 110% of the old salary, so the multiplier is 1.1. Divide 33,000 by 1.1 to get 30,000. Checking forwards, 10% of 30,000 is 3,000 and the new total is 33,000.

The same arithmetic can remove a known tax that was added to the whole base price. It does not determine which tax rules apply, distinguish exempt items on a mixed receipt, or reconstruct a bill containing separate fixed fees. Identify the amount and rate that belong together before reversing the percentage.

Reverse percentages in Excel and Google Sheets

Put the final value in A1 and the signed rate as an ordinary number in B1, such as 20 or −20. Use =A1/(1+B1/100). With 120 in A1 and 20 in B1 the result is 100. Both Excel and Google Sheets use the same formula.

If B1 instead contains a percentage-formatted value such as 20%, use =A1/(1+B1), without dividing B1 by 100 again. Keep the result numeric and apply currency formatting only if appropriate. Validate that the rate is above −100%, and preserve enough decimal places before using the answer in another calculation.

Everyday examples

Example	Answer	Try it
VAT-inclusive price 120 at 20%	100
Sale price 80 after a 20% discount	100
Salary 33,000 after a 10% rise	30,000
Mass 45 kg after a 10% reduction	50

Common mistakes

Subtracting 20% from a final amount to reverse a 20% increase. The percentage was originally applied to a different, smaller base.
Entering a discount as a positive rate. For a 20% reduction, enter −20 so that the multiplier is 0.8 rather than 1.2.
Treating a 100% reduction as reversible. Nothing remains, so the final zero does not identify a unique original value.
Combining consecutive changes by adding their rates. Undo each multiplier separately, ideally starting with the last change.

Common questions

How do I reverse a 20% increase?

Divide the final amount by 1.2. For example, 120 ÷ 1.2 = 100. Subtracting 20% from 120 gives 96, which does not recover the original because that subtraction uses 120 as its base.

How do I find a price before a 20% discount?

Divide the sale price by 0.8. A sale price of 80 therefore came from an original price of 100. In this calculator enter 80 as the value after the change and −20 as the percentage change.

How do I remove VAT from an inclusive price?

If the entire price includes VAT at 20%, divide it by 1.2 to find the price before VAT. An inclusive price of 120 becomes 100 before VAT, with 20 of VAT. Use the actual applicable rate, which may differ.

What if the percentage change is zero?

The multiplier is one, so the original and final values are identical. For example, 75 after a 0% change originally was 75. This is a valid calculation and does not involve division by zero.

Why are rates of −100% or less rejected?

At −100% the multiplier is zero, so division cannot recover an original. Below −100% the multiplier is negative and no longer describes an ordinary remaining share. This calculator deliberately excludes those rates rather than presenting a misleading price reversal.

Can I undo two percentage changes?

Yes, but reverse them one at a time using their actual rates. If a price rose 10% and then fell 20%, divide the final price by 0.8 and then by 1.1. Do not treat that sequence as a single 10% fall.

Does the answer include rounding?

Plain-number answers display up to six decimal places, while money displays two. Repeating divisions may need rounding. The check uses the unrounded calculation internally, so a displayed original rounded to pennies may not reproduce every digit of the final amount.

Last reviewed 8 November 2026. Results use exact decimal arithmetic and are rounded once for display.