Reverse Percentage Calculator
Work backwards from a value to the original amount before a percentage increase, decrease, or "is X% of what number".
How it works
After increase: original = value ÷ (1 + P/100) · After decrease: original = value ÷ (1 − P/100) · Is P% of: original = value ÷ (P/100)
A reverse percentage undoes a percentage that has already been applied. Because a 20% rise multiplies the original by 1.20, you recover the original by dividing by 1.20 — not by subtracting 20%, which is the classic mistake. The same logic runs a discount backwards to a pre-sale price, or turns "45 is 30% of what" into the whole.
Worked example
A price is $120 after a 20% markup. The original is 120 ÷ 1.20 = $100 — not 120 − 20% = $96, because the 20% was taken on the smaller original, not on the final $120.
Sources: Percentage — Wikipedia
Frequently asked questions
Why can’t I just subtract the percentage?
Because the percentage was applied to the original, not to the final value. A 20% increase multiplies by 1.2, so you must divide the result by 1.2 to get back. Subtracting 20% of the larger final number removes too much.
How do I find the price before tax or a discount?
Use the decrease or increase mode. For a price that includes a 25% tax, choose "after a % increase" with P = 25; for a 30%-off sale price, choose "after a % decrease" with P = 30 to recover the sticker price.
What does "is P% of the original" mean?
It answers questions like "45 is 30% of what number?". Dividing 45 by 0.30 gives 150, the whole that 45 represents 30% of.
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This calculator is for educational purposes. Double-check important results before acting on them.