Reverse Percentage Calculator

Most people get this wrong. When a price has already had a percentage taken off or added on, working backwards to the original figure is not as simple as reversing the maths. The trap is that adding a percentage back on gives the wrong answer. It feels logical, but the maths does not work that way. This calculator does it correctly: find the original price before a discount, remove VAT from a total, or recover any figure before a percentage was applied.

Common mistake: You cannot reverse a percentage by adding it back on, as this gives the wrong answer. The calculator uses the correct formula.

Use when you know the final price after a discount.

The price or amount after the percentage was removed

The percentage that was taken off

How to use this calculator

1
A percentage was removed: choose this mode when working back from a discounted price, a post-cut salary, or any figure where a percentage has been taken away. Enter the final value and the percentage that was removed.
2
A percentage was added: choose this mode when removing VAT, a service charge, or any figure where a percentage has been added on top. Enter the VAT-inclusive or surcharge-inclusive total and the percentage rate.

Still unsure? Ask: "Did the percentage make the number smaller or larger?" Smaller means it was removed; larger means it was added.

Formula

When a percentage was removed (discount, pay cut):

Original = Final ÷ (1 − Percentage ÷ 100)

Example: £80 after 20% off → 80 ÷ 0.80 = £100

When a percentage was added (VAT, surcharge):

Original = Final ÷ (1 + Percentage ÷ 100)

Example: £120 including 20% VAT → 120 ÷ 1.20 = £100

Worked examples

Percentage removed

A coat is £67.50 after a 25% discount

67.50 ÷ (1 − 0.25) = 67.50 ÷ 0.75 = £90

Check: 25% of £90 = £22.50; £90 − £22.50 = £67.50 ✓

A salary is £36,000 after a 10% pay cut

36,000 ÷ (1 − 0.10) = 36,000 ÷ 0.90 = £40,000

Check: 10% of £40,000 = £4,000; £40,000 − £4,000 = £36,000 ✓

A car is £17,000 after a 15% reduction

17,000 ÷ (1 − 0.15) = 17,000 ÷ 0.85 = £20,000

Percentage added

A product is £120 including 20% VAT

120 ÷ (1 + 0.20) = 120 ÷ 1.20 = £100

Check: 20% of £100 = £20; £100 + £20 = £120 ✓

A restaurant bill is £94.50 with a 5% service charge

94.50 ÷ (1 + 0.05) = 94.50 ÷ 1.05 = £90

How it works

Here is the situation that trips people up: a coat costs £80 after a 20% discount. The natural instinct is to add 20% back on. But 20% of £80 is only £16, so that gives £96, which is wrong.

The correct original price is £100. The discount was 20% of the original price, not 20% of the sale price. If the original price was £100, then 20% of £100 is £20, and £100 minus £20 is £80. That checks out. But adding 20% of £80 back on gives £96, and 20% of £96 is £19.20, which means £96 minus £19.20 is £76.80, not £80.

The numbers do not add up because you are taking a percentage of the wrong starting figure. The correct method divides by the complement of the percentage:

Step 1: convert 20% to a decimal

20 ÷ 100 = 0.20

Step 2: subtract from 1

1 − 0.20 = 0.80

Step 3: divide the final price

£80 ÷ 0.80 = £100

The same logic applies in reverse when a percentage has been added. To remove 20% VAT from a VAT-inclusive price, divide by 1.20, not by 1 minus 0.20. The direction of the percentage determines whether you use (1 − pct) or (1 + pct).

Common uses

  • Removing VAT: finding the ex-VAT cost of a product or service from a VAT-inclusive price
  • Sale prices: finding the original price of an item after a discount has been applied
  • Service charges: recovering the pre-surcharge total from a bill that includes a booking fee or service charge
  • Pay cuts: working out a pre-cut salary after a percentage pay reduction has been applied
  • Checking discounts: verifying that an advertised discount is accurate by confirming the original price a retailer claims
  • Supplier pricing: calculating the ex-tax price of goods when a supplier shows only the VAT-inclusive total
  • Markup reversal: finding the cost price of an item a business prices at a fixed percentage above cost
  • Inflation adjustments: finding the pre-inflation value of an amount to understand real-terms changes over time

Frequently asked questions

Divide the final value by (1 minus the percentage as a decimal) if a percentage was removed, or by (1 plus the percentage as a decimal) if a percentage was added. For example, to find the original price before a 20% discount: divide the sale price by 0.80. To find the pre-VAT price on a 20% VAT-inclusive total: divide the VAT-inclusive price by 1.20.

Because the percentage applies to the original price, not the final price. A 20% discount on £100 removes £20, leaving £80. But 20% of £80 is only £16, so adding it back gives £96, not £100. Both percentages use different base figures, which is why the shortcut fails.

Divide the VAT-inclusive price by 1.20 for the standard UK VAT rate of 20%. For the reduced rate of 5%, divide by 1.05. This formula works for any VAT rate: divide the VAT-inclusive price by (1 + VAT rate ÷ 100). For example, £240 including 20% VAT: £240 ÷ 1.20 = £200 ex-VAT.

There are two versions. If a percentage was removed: Original = Final ÷ (1 − Percentage ÷ 100). If a percentage was added: Original = Final ÷ (1 + Percentage ÷ 100). Choose the version based on whether the percentage made the final figure smaller (removed) or larger (added).

Divide £68 by 0.85 (which is 1 minus 0.15). £68 ÷ 0.85 = £80. The original price was £80. To check: 15% of £80 is £12, and £80 minus £12 is £68.

Related calculators

Percent Off Calculator → Calculate the sale price and saving when you know the original price and the discount percentage. Percentage Increase Calculator → Find the percentage increase between two numbers, with the full working shown. Percentage Decrease Calculator → Find the percentage decrease between two numbers, including the recovery paradox explained.

Last reviewed: May 2026