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.
Reverse 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
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.
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