Easily find the original amount before a percentage increase or discount was applied with precision, instant step-by-step solutions, and formula breakdowns.
Enter your final amount, select whether it was increased or decreased by a percentage, and get the exact initial starting value instantly.
Calculate starting values, pre-discount prices, or pre-tax totals in four simple steps.
Input the final number after the percentage change (e.g., discounted sale price, final bill after tax, or increased total).
Choose whether the number was Increased (+) or Decreased (-) and enter the percentage rate applied.
Select your desired rounding precision from 0 to 6 decimal places to match your currency or academic requirements.
Click calculate to reveal the original base value along with a complete step-by-step algebraic breakdown.
These two calculations start from opposite ends of the same problem. Knowing which one you need is the first step to getting the right answer.
You know the starting value and the percentage change, and you want to find the final result. For example: "A $100 item increases by 20%. What's the new price?"
Use the Percentage Increase Calculator →You know the final result and the percentage that was applied, and you want to find the original starting value. For example: "An item costs $120 after a 20% increase. What was the original price?"
You're using this calculator right nowReverse percentage problems require working backwards from the final amount using standard algebraic formulas.
The recorded total after an increase or discount has been applied.
The percentage by which the original amount was increased or reduced.
The decimal conversion factor used to scale between original and final amounts.
The calculated base starting amount prior to any adjustments.
See how reverse percentages are calculated in everyday retail, finance, and pricing situations.
A jacket is on sale for $120 after a 20% discount. What was the original retail price?
Final Value = $120, Decrease = 20%
Calculation:Multiplier = 1−(20/100)=0.80Original Price = $120÷0.80=$150
Answer: The original price was $150.00
An electronics invoice totals $460, which includes a 15% sales tax. Find the price before tax.
Final Value = $460, Increase = 15%
Calculation:Multiplier = 1+(15/100)=1.15Pre-Tax Price = $460÷1.15=$400
Answer:The original pre-tax cost was $400.00
An employee's new salary after a 10% performance raise is $5,500/month. What was the starting salary?
Given: Final Value = $5,500, Increase = 10%
Calculation:Multiplier = 1+(10/100)=1.10Base Salary = $5,500÷1.10=$5,000
Answer:The original monthly salary was $5,000.00
A retailer sells a product for $150 after applying a 25% markup. What was the original cost price?
Final Value = $150, Increase = 25%
Calculation: Multiplier = 1 + (25/100) = 1.25 Cost Price = $150 ÷ 1.25 = $120
Answer: The original cost price was $120.00
An investment portfolio dropped 20% in value and is now worth $8,000. What was the original value before the loss?
Final Value = $8,000, Decrease = 20%
Calculation: Multiplier = 1 − (20/100) = 0.80 Original Value = $8,000 ÷ 0.80 = $10,000
Answer: The original investment value was $10,000.00
These are the most frequent errors people make when working backwards from a final value to find the original amount.
Adding the percentage back to a discounted or increased price creates a mathematical error, because the original change was calculated on a different base value. For example, a 20% drop from $100 brings it to $80, but adding 20% back to $80 only gives $96, not $100. You must divide by the multiplier, not multiply or add.
The formula requires the percentage as a decimal (dividing by 100) before it's added to or subtracted from 1. Using the raw percentage number instead of its decimal form will produce a completely incorrect multiplier and result.
Using "Increase" when the value was actually a decrease (or vice versa) will produce a plausible-looking but wrong answer, since both use similar formulas. Always confirm whether the final value is higher or lower than what you're solving for before selecting the calculation type.
Everything you need to know about reverse percentage formulas, pre-tax pricing, and rounding calculations.
A regular percentage calculation finds a fraction or change from a known starting value (e.g., finding 20% of $100). A reverse percentage calculation works backwards to find the unknown starting value when you only know the final amount and the percentage change applied.
Adding the percentage back creates a mathematical error because the discount was calculated on the larger original base, whereas adding it back calculates a percentage of the smaller discounted figure. For example, a 20% drop from $100 brings it to $80, but adding 20% to $80 only gives $96, not $100.
Divide the final gross price by (1+Tax Rate/100). For instance, if your total is $112 with 12% sales tax, divide $112 by 1.12 to get an original pre-tax value of $100.
CalcNova computes all reverse percentages using high-precision floating-point arithmetic. You can configure the output from 0 to 6 decimal places to match exact financial, academic, or accounting standards.
Divide the final value by 1 plus the percentage as a decimal (for an increase), or 1 minus the percentage as a decimal (for a decrease). For example, if a price is $120 after a 20% increase, divide 120 by 1.20 to get the original price of $100. The same approach works for decreases by subtracting instead of adding.
Yes. You can enter decimal percentages like 12.5% or 7.25% and the calculator will handle them the same way it handles whole numbers. You can also choose how many decimal places to show in your result, from 0 to 6, to match your specific needs.
Reverse percentage finds an unknown starting value when you know the final result and the percentage change applied to it. Percent error, on the other hand, compares an estimated or measured value against a known correct value to show how far off it is, usually in scientific or experimental contexts. They solve different problems even though both involve percentages.
The calculator still works correctly. For example, if a value increased by 150% to reach 250, the multiplier becomes 1 plus 1.50, which equals 2.50, and dividing 250 by 2.50 gives an original value of 100. Percentages over 100% are valid for increases, though not for decreases, since a decrease of 100% or more would reduce the original value to zero or below.
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CalcNova was created and is maintained collaboratively by two friends who want to make everyday calculations simpler and more accessible. We build practical online calculators and clear explanations to help people understand results and the methods behind them.
Our focus is on clear formulas, useful examples, and regularly maintaining our tools. Calculator results are intended for guidance; for important financial decisions, confirm figures with the relevant provider or a qualified professional.