Reverse Percentage Calculator

Know the final value and the percentage applied? Work backwards to find the original value instantly. Perfect for discounts, tax, markup, and any percentage change.

e.g. $80 sale price
e.g. 20 for a 20% discount
e.g. $120 including tax
e.g. 20 for 20% VAT
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Click any record to fill it back into the calculator

What Is Reverse Percentage Calculation?

A reverse percentage calculation works backwards from a final value to find the original value before a percentage was applied. Instead of asking "what is 20% off $100?" — a forward calculation — you ask "if $80 is the price after 20% off, what was the original price?" That is a reverse percentage problem.

This comes up constantly in real life. You see a sale price but want to know what the item cost before. You receive a pay slip showing take-home pay but want to calculate gross income before tax. You see a total including VAT but need the pre-tax amount. In all of these cases, you are reverse calculating a percentage — working from the result back to the starting point.

The key insight is that you cannot simply apply the percentage in reverse. If something dropped 20% to reach $80, the original is not $80 + 20% = $96. That is wrong because 20% of $80 is different from 20% of $100. The correct reverse percentage formula divides by the multiplier, not adds back the percentage. This reverse percentage calculator handles that automatically. Whether you need to calculate a reverse percentage for shopping, tax, or salary, or want to know how do you calculate reverse percentages step by step, the tool above and formulas below cover every scenario. A percentage reverse calculator like this one is especially useful when you encounter a final price and need to trace it back to the starting point.

How to Reverse Calculate a Percentage

There are two versions of the reverse percentage calculation formula depending on whether the original value was increased or decreased.

Formula 1: After a Percentage Decrease (discount, reduction)

Use this when you know the value after it was reduced by a percentage — for example, a sale price after a discount.

Original Value = Final Value ÷ (1 − Rate ÷ 100)

Example: A jacket costs $80 after a 20% discount. What was the original price?
Original = 80 ÷ (1 − 0.20) = 80 ÷ 0.80 = $100

Common mistake: Many people add the percentage back — $80 + 20% = $96. This is wrong because 20% of $80 ($16) is not the same as 20% of $100 ($20). Always divide by the multiplier, never add the percentage directly back. This is the most important thing to understand about reverse calculating percentages.

Formula 2: After a Percentage Increase (tax, markup)

Use this when you know the value after it was increased by a percentage — for example, a price including VAT or sales tax.

Original Value = Final Value ÷ (1 + Rate ÷ 100)

Example: A hotel bill is $132 including 10% service charge. What was the pre-charge amount?
Original = 132 ÷ (1 + 0.10) = 132 ÷ 1.10 = $120

How to Do Reverse Percentage Calculation in Excel

To calculate reverse percentage in Excel, put the final value in column A and the percentage rate in column B. Then use one of these formulas in column C:

After a discount (decrease):
=A1/(1-B1/100)

After tax or markup (increase):
=A1/(1+B1/100)

Amount of tax / discount added or removed:
=A1 - A1/(1+B1/100)

These reverse percentage calculation formulas in Excel work identically in Google Sheets and LibreOffice Calc. Format column C as currency to display the result cleanly. Drag the formula down to apply it to an entire column of values — useful for processing invoices or price lists in bulk.

How to Calculate Reverse Percentage Increase

A reverse percentage increase calculator answers: "if a value is now X after increasing by Y%, what was it before?" Use Formula 2 above: divide the current value by (1 + rate/100). For example, if a salary is now $55,000 after a 10% raise: original salary = 55,000 ÷ 1.10 = $50,000.

How to Calculate Reverse Percentage for Tax (GST/VAT)

To extract the pre-tax price from a total that includes GST, VAT, or sales tax, divide the total by (1 + tax rate/100). For example, with 15% GST: if the total is $115, the pre-GST price is 115 ÷ 1.15 = $100. The GST amount itself is $115 − $100 = $15. Use the "After Tax / Increase" tab in the calculator above for this calculation.

Reverse Percentage Examples — Click to Calculate

Click any example to see the full calculation in the calculator above. These cover the most common reverse percentage calculation scenarios.

$80 after 20% discount
$100.00
Original price before discount
$120 including 20% VAT
$100.00
Pre-tax price
$75 after 25% off
$100.00
Original price
$55,000 after 10% raise
$50,000
Salary before the raise
$63 after 30% discount
$90.00
Original price
$115 including 15% GST
$100.00
Pre-GST price

Real-World Reverse Percentage Scenarios

Retail shopping: A coat is priced at $119 in a 30% off sale. To reverse calculate the percentage and find the original price: 119 ÷ (1 − 0.30) = 119 ÷ 0.70 = $170. Knowing the original price lets you judge whether the sale is genuine.

Invoice processing: A supplier sends an invoice for $2,360 including 18% tax. The pre-tax amount for your accounts is: 2,360 ÷ 1.18 = $2,000. The tax portion is $360. This is the standard reverse percentage calculation used in bookkeeping.

Salary negotiation: A job offer of $65,000 represents a 30% increase on your current salary. To find your current salary: 65,000 ÷ 1.30 = $50,000. This lets you verify the percentage claim made by the employer.

Property prices: A house is listed at $420,000 after rising 40% in value. The price five years ago was: 420,000 ÷ 1.40 = $300,000. Useful for understanding how much values have truly changed.

Who Uses Reverse Percentage Calculations

Shoppers

Find the original price before a discount to judge whether the sale is real. Compare pre-sale prices across different retailers offering different percentage reductions.

Accountants & Bookkeepers

Extract pre-tax amounts from VAT-inclusive invoices. Separate tax from total amounts when processing purchase records and expense claims.

HR & Payroll

Calculate gross salary from take-home pay after knowing the tax rate. Verify that a stated percentage raise matches the actual salary figures.

Students

Solve reverse percentage problems in GCSE, A-Level, and university maths. Reverse percentages are a standard topic in UK secondary school maths curricula.

Retail & Pricing

Work out the cost price of a product from its retail price and known markup percentage. Essential for margin analysis and pricing strategy.

Property & Investment

Find the original value of an asset before a known percentage gain or loss. Useful for valuation, tax reporting, and investment return analysis.

Frequently Asked Questions

How do you reverse calculate a percentage?
For a percentage decrease: divide the final value by (1 − rate/100). For a percentage increase: divide by (1 + rate/100). For example, $80 after a 20% discount: 80 ÷ 0.80 = $100 original. Never simply add the percentage back — that gives the wrong answer because the percentage applies to the original, not the final value.
Why can't I just add the percentage back?
Because the percentage was applied to the original value, not the final value. If something dropped 20% to reach $80, adding 20% of $80 ($16) gives $96 — not $100. The correct answer is $80 ÷ 0.80 = $100, because the 20% discount was taken off $100, not off $80. This is the core concept behind reverse calculating percentages.
How do I find the original price before a discount?
Divide the sale price by (1 − discount%/100). Example: $60 after a 25% discount → 60 ÷ (1 − 0.25) = 60 ÷ 0.75 = $80. The original price was $80. Use the "After Discount" tab in the calculator above for instant results.
How do I extract the pre-tax price from a VAT-inclusive total?
Divide the total by (1 + tax rate/100). Example: $230 including 15% VAT → 230 ÷ 1.15 = $200 pre-tax. The VAT amount is $230 − $200 = $30. Use the "After Tax / Increase" tab in the calculator above. This works for GST, VAT, sales tax, and any other percentage-based tax.
What is the reverse percentage formula in Excel?
For a discount: =A1/(1-B1/100) where A1 is the final price and B1 is the discount rate. For tax: =A1/(1+B1/100). To find just the tax or discount amount: =A1-A1/(1+B1/100). These reverse percentage calculation formulas work identically in Google Sheets.
How do you calculate reverse percentage increase?
Divide the increased value by (1 + rate/100). Example: a value is now 650 after a 30% increase → 650 ÷ 1.30 = 500. The original value was 500. This is the standard reverse percentage increase calculator formula used in finance and HR to back-calculate pre-raise or pre-growth values.
How do you do reverse percentages without a calculator?
Write the final value as a fraction of the original. If something is 80% of the original (after a 20% drop), then: original = final ÷ 0.80. To do this mentally, think of the multiplier: 80% → divide by 0.8 (same as multiplying by 1.25). 75% → divide by 0.75 (multiply by 4/3). 50% → divide by 0.5 (multiply by 2). Practise these common cases and you can reverse calculate percentages quickly in your head.
Is reverse percentage the same as inverse percentage?
Yes, they refer to the same concept — working backwards from a final value to find the original. Some textbooks and teachers use "inverse percentage" while others say "reverse percentage." The formula and method are identical regardless of which term is used.

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