Reverse Percentage Calculator
Find the original number before a percentage increase or decrease was applied with reverse arithmetic equations.
Net change: +20
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What Is a Reverse Percentage Calculator?
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.
How to Use This Calculator
- Select whether the known result followed an increase (+%) or a decrease (-%).
- Enter the final ending value that you currently possess.
- Enter the percentage change that was applied.
- Read the calculated original starting value and verification formula.
Reverse Percentage Formulas
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).
Worked Example
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.
Tips & Key Notes
- Never simply add back the same percentage to reverse a discount; this is the most common math mistake.
- For tax-inclusive prices (such as 20% VAT in the UK), dividing the gross price by 1.20 yields the exact net pre-tax price.
- Check that the multiplier matches your direction: > 1 for reversing increases, < 1 for reversing discounts.
Frequently Asked Questions
How do you reverse a 20% discount to find original price?
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.
Why can’t you just add 20% back onto the discounted price?
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.
How do you find original price before 15% sales tax was added?
Divide the total receipt amount by 1.15. If the total is $115, the original pre-tax price was $115 ÷ 1.15 = $100.
What is the reverse percentage formula for a price increase?
Original = Final ÷ (1 + Percentage / 100).
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