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Reverse Percentage Calculator

Find the original value before a percentage change.

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Result
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Original Amount

Formula first

Overview

Reverse percentage calculation is a mathematical method used to determine the initial value of a quantity before a specific percentage increase or decrease was applied. It relies on the relationship where the original value is the quotient of the final value and a decimal multiplier representing the total percentage change.

Symbols

Variables

F = Final Amount, M = Multiplier, O = Original Amount

Final Amount
£
Multiplier
Variable
Original Amount
£

Apply it well

When To Use

When to use: This equation is essential when the end result of a change is known, but the starting value is missing. Common scenarios include finding a price before a discount was applied or determining a pre-tax amount from a total receipt. It assumes the percentage of change was calculated relative to the unknown original value.

Why it matters: Understanding reverse percentages is crucial for financial literacy, as it prevents the common mistake of applying percentages to the wrong base value. It allows businesses to calculate markups accurately and helps consumers verify the authenticity of advertised discounts and tax calculations.

Avoid these traps

Common Mistakes

  • Multiplying instead of dividing.
  • Subtracting percentage from final.

One free problem

Practice Problem

Practice Problem 1

A pair of shoes is sold for $72 after a 25% discount. Calculate the original price before the sale.

Final Amount72 £
Multiplier0.75

Solve for:

Hint: A 25% discount means the final price is 75% of the original (1 - 0.25 = 0.75).

Practice Problem 2

An antique vase increased in value by 12% over a year and is now worth $560. What was its value one year ago?

Final Amount560 £
Multiplier1.12

Solve for:

Hint: A 12% increase corresponds to a multiplier of 1.12.

Practice Problem 3

The total bill for a car repair, including a 5% sales tax, came to $315. Determine the cost of the repair before tax was added.

Final Amount315 £
Multiplier1.05

Solve for:

Hint: The total amount represents 105% of the original cost.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Percentage
  2. Britannica: Percentage
  3. Edexcel GCSE (9-1) Mathematics Higher Student Book, Second Edition, Pearson Education Limited, 2015
  4. AQA GCSE Maths — Number