Ekuation

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Reverse Percentage Calculator

Calculate the original number when you know the percentage and result. Perfect for working backwards from discounts, taxes, and commissions.

Back to Percentage Calculator

Enter the known percentage

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Enter the known result value

Tips for finding the original number

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Reverse Percentage Calculator | Find Original Number from Percentage

Calculate the original number when you know the percentage and result. Perfect for working backwards from discounts, taxes, and commissions.

Key values: sale price $84 · 30% off · original = $120

Find Pre-Tax Price from Post-Tax Total

A receipt shows $108.90 total including 8.9% tax. What was the pre-tax amount?

Key values: total $108.90 · 8.9% tax · pre-tax = $100

Documentation

Finding the Original Number

Reverse percentage answers: “The price after a 20% discount is $80 — what was the original price?” You work backward from the result to find the starting value.


Formulas

After an Increase

If the value increased by p%p\%, the original was:

Original=Final Value1+p/100\text{Original} = \frac{\text{Final Value}}{1 + p/100}

After a Decrease

If the value decreased by p%p\%, the original was:

Original=Final Value1p/100\text{Original} = \frac{\text{Final Value}}{1 - p/100}

Common mistake: Do not just add the percentage back. If a $80 item is marked as “20% off,” the original is $80 / 0.80 = $100, not $80 + 20% × $80 = $96.


Worked Examples

Sale Price → Original Price

A shirt costs $45 after a 25% discount:

Original=4510.25=450.75=$60\text{Original} = \frac{45}{1 - 0.25} = \frac{45}{0.75} = \$60

Post-Tax → Pre-Tax Price

A receipt shows $108 including 8% sales tax:

Pre-tax=1081+0.08=1081.08=$100\text{Pre-tax} = \frac{108}{1 + 0.08} = \frac{108}{1.08} = \$100

Current Salary → Previous Salary

Your salary after a 12% raise is $67,200:

Previous=672001.12=$60,000\text{Previous} = \frac{67200}{1.12} = \$60{,}000

Frequently Asked Questions

How do I find the original price before a discount?

Divide the sale price by (1discount rate)(1 - \text{discount rate}). For example, if an item costs $80 after a 20% discount: Original = \\$80 / 0.80 = \\$100. Do not add 20% back to $80 — that gives the wrong answer ($96).

How do I find the pre-tax price from a total that includes tax?

Divide the total by (1+tax rate)(1 + \text{tax rate}). For example, if the total is $108 and the tax rate is 8%: Pre-tax = \\$108 / 1.08 = \\$100.

Why can't I just add the percentage back to reverse it?

Because the percentage was applied to the original (unknown) value, not to the result. Adding the percentage to the result uses the wrong base. Division reverses multiplication correctly; addition does not.

How do I find the original salary before a raise?

Divide the current salary by (1+raise rate)(1 + \text{raise rate}). For example, if your salary is $67,200 after a 12% raise: Previous salary = \\$67{,}200 / 1.12 = \\$60{,}000.

What if I know the result is a percentage of the original?

Divide the result by the percentage expressed as a decimal. For example, if $84 represents 70% of the original price: Original = \\$84 / 0.70 = \\$120. This works for any “X is P% of the original” problem.

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