Mathematical Foundations

Reverse Percentage Calculator: How to Find the Original Number Before a Percentage

Quick Answer & Key Takeaway (TL;DR)

A reverse percentage calculator finds the original starting amount before a percentage change occurred. If a final price reflects an increase: Original = Final ÷ (1 + rate ÷ 100). If it reflects a decrease: Original = Final ÷ (1 - rate ÷ 100). For example, if an item costs $80 after a 20% discount, the original price was $80 ÷ 0.80 = $100.

Almost everyone encounters reverse percentage problems: seeing a discounted price on a tag and wanting to know the retail price, or looking at an invoice total and needing to deduce the pre-tax amount. A reverse percentage calculator solves this immediately.

What is a Reverse Percentage Problem?

Reverse Percentage Calculation Diagram
Finding the base number before a percentage discount or increase was applied.

Standard percentage math moves forward: Original × Rate = Portion. Reverse percentage problems move backward: you are given the final result and the percentage rate, and you must deduce the original base value.

Formula 1: Original Price After a Discount

Reverse Discount Equation
Original Value = Final Price ÷ (1 - Discount Rate ÷ 100)

If a laptop is on sale for $720 after a 25% discount: $720 ÷ (1 - 0.25) = $720 ÷ 0.75 = $960 original price.

Formula 2: Original Price After an Increase or Tax

Reverse Increase / Tax Equation
Original Value = Final Price ÷ (1 + Tax Rate ÷ 100)

Verify your base calculations on our free Percentage Calculator.

Frequently Asked Questions

Why can’t I just add 20% back to a discounted price?
Because the 20% discount was taken off the larger original price, not the smaller sale price. 20% of $80 is only $16 ($96), whereas the true original was $100.
How do you calculate the original price if a coat costs $120 after a 20% tax?
Original = $120 ÷ 1.20 = $100.

Elena Rostova

Applied Mathematics & Quantitative Analysis Editor

Quantitative math specialist specializing in computational precision, educational math models, and client-side web tools.

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