Reverse percentage calculator (original value)
Find the original value before a discount or increase, or the number a value is a percentage of.
E.g., an item that ended up at $68 after 15% off originally cost $80.
How the calculation works
Reverse percentage answers "what was the value before the change?". It finds the full price from a discounted price, or the pre-tax value from a final value.
Key idea: when a value changes, it becomes the original times a factor. To go back, you divide by that factor.
- After an X% discount:
original = value ÷ (1 − X/100) - After an X% increase:
original = value ÷ (1 + X/100) - "is X% of the original":
original = value ÷ (X/100)
Step-by-step example
An item sold for R$68 at 15% off. What was the full price?
- Discount factor: 1 − 0.15 = 0.85
- Original: 68 ÷ 0.85 = R$80
Why divide, not add 15% back
Because the 15% was taken from the larger value (R$80), not from R$68. Adding 15% of 68 gives R$78.20 — wrong.
Examples
- R$68 at 15% off: 68 ÷ 0.85 = R$80 (full price).
- R$130 after a 30% increase: 130 ÷ 1.30 = R$100 (prior value).
Frequently asked questions
Why not just add the percentage back?
Because the percentage was taken from the larger value (the original), not the smaller. So you divide by the factor instead of adding the same percent back.
How to get the pre-tax value from a final price?
Divide the final price by (1 + tax rate). R$110 with 10% tax came from 110 ÷ 1.10 = R$100.
Can I use it to find the pre-sale price?
Yes — the most common use. With the sale price and the advertised percentage, you can check whether the discount is real.
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Updated on June 30, 2026 · by Rafael Rossi · Methodology & sources