Reverse Percentage Calculator

How it works

When you know the result of applying a percentage to a number but need to find the original number, you use a reverse percentage calculation. This is sometimes called working backwards from a percentage.

The formula

Use the first formula when a percentage was added (e.g. VAT or markup), and the second when a percentage was removed (e.g. a discount). The calculator handles both cases automatically.

Why this works: When a percentage is applied to a number, the result equals the original multiplied by a multiplier (e.g. 1.20 for a 20% increase). To undo this, you divide by the same multiplier. This is why dividing by 1.20 recovers the original pre-VAT price from the gross total.

Worked examples

When to use this

Reverse percentage calculations arise whenever the result of a percentage change is known but the starting value is not:

• VAT and tax calculations: A supplier invoice shows £240 including 20% VAT. Dividing by 1.20 gives the net amount of £200, which is the figure you need for your VAT return input tax claim. This is more accurate than subtracting 20% of the gross (which incorrectly gives £192).
• Sale prices and discounts: An item is on sale for £68 with 20% off. Dividing £68 by 0.80 gives the original price of £85. Useful when the original price is not displayed, or when you want to verify whether a "was" price is consistent with the stated percentage saving.
• Salary history: Your current salary is £44,000 after receiving a 10% rise last year. Dividing by 1.10 gives the pre-rise salary of £40,000. Useful when comparing offers that describe a percentage increase rather than a specific salary.
• Recovering cost from selling price: A wholesaler's price list shows retail prices with 40% markup included. Dividing the retail price by 1.40 gives the trade cost. This helps buyers verify they are receiving the full trade discount on any order.

Understanding the result

The original value will be smaller than the final value when a percentage was added, and larger when a percentage was removed. The most common mistake is subtracting (or adding) the percentage directly to the final value. This is wrong because the percentage was applied to the original, not the final value.

For example: £120 including 20% VAT. Subtracting 20% of £120 gives £96, which is wrong. The correct answer is £100, found by dividing £120 by 1.20. The difference arises because 20% of £100 (the original) is £20, but 20% of £120 (the final) is £24. Always divide by the multiplier, never subtract the percentage from the gross figure.

Related concepts

➡ For the forward calculation where you know the original and the percentage, the percentage of a number calculator finds what any percentage of a known figure gives you directly. ➡ For UK VAT specifically, the VAT calculator adds or removes UK VAT from any price with built-in rate options for standard, reduced, and zero rates. ➡ To find the selling price from a cost price using a markup percentage, the markup calculator applies the markup to arrive at the correct selling price.

How to do this in Excel

Put the final value in A1 and the percentage in B1. Use this formula when the percentage was added (e.g. VAT, markup). For a percentage that was removed (e.g. discount), use =A1/(1-B1/100). To verify, multiply the result by the appropriate multiplier and check it equals the original final value in A1.

How to do this without a calculator

For VAT at 20%, divide by 6 to find the VAT portion and multiply by 5 to find the net (since net = 5/6 of gross at 20%). This shortcut is widely used in UK accounts: a £120 gross invoice divided by 6 gives £20 VAT, and £120 minus £20 = £100 net. For other rates, find 1% of the gross by dividing by the multiplier converted to 100ths, then scale up. For discounts, divide the sale price by the decimal equivalent of the proportion paid (e.g. £85 after 15% off: 85/0.85 = £100).

Common mistakes

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