Reverse Percentage Calculator

You know a percentage of a number and the result, and want the original number. Example: 32% of a number is 150 — what is the number?

You know a final value after a percentage increase or decrease and want the original value. Example: After a 12% decrease, the price is $15,000 — what was the original price?

<table><tr><th>Final Value</th><th>Percentage Change</th><th>Type</th><th>Original Value</th></tr><tr><td>$120</td><td>20%</td><td>Increase</td><td>$100</td></tr><tr><td>$80</td><td>20%</td><td>Decrease</td><td>$100</td></tr><tr><td>$150</td><td>50%</td><td>Increase</td><td>$100</td></tr><tr><td>$75</td><td>25%</td><td>Decrease</td><td>$100</td></tr></table>

Determine if the change was an increase (final value is more than original), decrease (final value is less than original), or percentage of original.

Convert the percentage to a decimal by dividing by 100. Example: 25% → 0.25

Use the appropriate formula: For increase → divide by (1 + decimal), For decrease → divide by (1 - decimal), For % of original → divide by (P/100)

Perform the division to find the original value. This gives you the value before the percentage change.

<table><tr><th>Scenario</th><th>Formula</th><th>Use Case</th></tr><tr><td>Discount</td><td>Original = Final ÷ (1 − %Discount/100)</td><td>Sales, shopping</td></tr><tr><td>Price Increase</td><td>Original = Final ÷ (1 + %Increase/100)</td><td>Markups, inflation</td></tr><tr><td>Tax Calculation</td><td>Original = Final ÷ (1 + %Tax/100)</td><td>VAT, GST, sales tax</td></tr><tr><td>Reverse Percentage Change</td><td>Original = Final ÷ (1 ± %Change/100)</td><td>Financial analysis</td></tr></table>

Finding original price before a discount or sale. Example: A shirt costs $24 after a 40% discount. What was the original price? Solution: $24 ÷ (1 - 0.40) = $24 ÷ 0.60 = $40

Finding pre-tax amounts when you know the total including tax. Example: Total with 10% tax is $110. What was the pre-tax amount? Solution: $110 ÷ (1 + 0.10) = $110 ÷ 1.10 = $100

Undoing pay raises or reductions to find the original salary. Backtracking original values in financial data analysis.

Calculating original investment amounts, understanding price changes, analyzing percentage-based growth or decline in metrics.

Quick, free, and convenient. Search for 'reverse percentages calculator online' or 'free reverse percentage calculator'. Ideal for one-off calculations and quick checks.

Perfect for bulk calculations, reports, and automated workflows. For increase: =FinalValue/(1+Percentage/100). For decrease: =FinalValue/(1-Percentage/100). Great for handling multiple data points simultaneously.

Best for learning, small calculations, or when a calculator is not available (reverse percentages without a calculator). Helps understand the underlying mathematical principles.