Find the original number before a percentage increase or decrease was applied with reverse arithmetic equations.
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A reverse percentage calculator works backward from a final known value to determine the original starting number before a percentage increase or reduction occurred. It is indispensable for calculating pre-sale prices from discount receipts, gross-to-net salary reversals, and pre-tax price points.
V_{\text{orig}} = \frac{V_{\text{final}}}{1 + (P / 100)} \quad (\text{after increase}), \qquad V_{\text{orig}} = \frac{V_{\text{final}}}{1 - (P / 100)} \quad (\text{after decrease})To reverse a 20% increase, divide by 1.20 (not multiply by 0.80). To reverse a 20% decrease, divide by 0.80 (not multiply by 1.20).
Scenario: A pair of shoes is purchased for $84.00 on sale after a 30% discount markdown. What was the original price?
Identify change: 30% decrease -> divisor = 1 - 0.30 = 0.70.
Divide final price by divisor: $84.00 ÷ 0.70 = $120.00.
Verify: $120.00 - (30% of $120 = $36) = $84.00.
Absolute discount was $36.00.
Divide the discounted price by 0.80 (which is 1 - 0.20). For example, if a discounted item costs $80, the original price was $80 ÷ 0.80 = $100.
Because 20% of the discounted price is smaller than 20% of the original baseline. Adding 20% to $80 gives $96, not the true $100 starting price.
Divide the total receipt amount by 1.15. If the total is $115, the original pre-tax price was $115 ÷ 1.15 = $100.
Original = Final ÷ (1 + Percentage / 100).
Quickly calculate percentages, find what percentage one number is of another, and compute percent changes.
Calculate the percentage increase or decrease between two values, along with absolute difference and growth multipliers.
Calculate the percentage drop, markdown, or reduction between two numbers with absolute difference and step-by-step arithmetic.
Net change: +20