Work backwards to the original value

What This Calculator Does

A reverse percentage calculator answers the backwards question: you know the result, and you want the number you started with. It covers the two cases that come up most often.

X is Y% of what: a part and its percentage give you the whole.

Undo a change: a value that already went up or down by a percentage gives you the original before the change.

Both modes show the reverse formula and the steps, so you can follow the logic rather than trust a black box. For a discount specifically, the shopping-first percent off calculator finds the original price too. This page handles every other reverse case as well. The forward math lives on our percentage calculator.

The Reverse Percentage Formula

Reversing a percentage means dividing, not subtracting. That single idea prevents most mistakes.

X is Y% of what

Whole = Part ÷ (Percent ÷ 100)

Example: 15 is 30% of what number? 15 ÷ 0.30 = 50.

Undo an increase or decrease

Original = Result ÷ (1 ± Percent ÷ 100)

Use plus for something that grew and minus for something that shrank.

Example: a salary is $52,000 after a 4% raise. Before the raise it was $52,000 ÷ 1.04 = $50,000.

Back Out Tax or VAT

Prices that already include tax are a classic reverse-percentage problem. To find the amount before tax, divide by 1 plus the tax rate.

Sales tax: a receipt total of $106 that includes 6% tax started at $106 ÷ 1.06 = $100 before tax.

VAT: a £120 price that includes 20% VAT is £120 ÷ 1.20 = £100 before VAT.

The tax itself is then the difference, $6 and £20 in these examples. For a gentler walk-through of the underlying steps, read the easy way to calculate percentages.

Find the Original Price Before a Discount

Reverse discounting is the everyday version of this calculator. You see a sale price and want to know what the item cost before the markdown.

Example: a shirt rings up at $60 after 25% off. The original price was $60 ÷ (1 − 0.25) = $60 ÷ 0.75 = $80.

That confirms the deal: a real $80 item, genuinely $20 off. To run the sale in the other direction, or to check the savings on a marked price, use the percent off calculator or the general discount calculator.

Reverse Percentage Questions

What is a reverse percentage?

It is working backwards from a result to the value you started with, after a percentage was added, subtracted, or taken of a whole. You divide instead of multiply.

How do I find the original price before a discount?

Divide the sale price by (1 minus the discount as a decimal). A $60 price after 25% off is $60 divided by 0.75 = $80 original.

15 is 30% of what number?

Divide the part by the percentage as a decimal: 15 divided by 0.30 = 50.

How do I reverse a percentage increase?

Divide the higher value by (1 plus the increase as a decimal). A total of $52,000 after a 4% raise is $52,000 divided by 1.04 = $50,000.

Why can't I just add the percentage back?

Because the percentage was a share of the original, not of the result. Adding it to the smaller result undershoots the true starting value. Dividing recovers it exactly.

Related Tools

• Percent off calculator - sale price, savings, and reverse discount
• Discount calculator - forward and reverse discounts in one place
• Percentage change calculator - solve for the original, new value, or percent

For more worked examples, browse our percentage guides.