Reverse Percentage Calculator
When you only have the final figure, you cannot recover the original by subtracting the same percentage — you have to divide by the multiplier. This calculator does that for increases, decreases, taxes and discounts.
Formula
- Final
- = the amount you already have
- p
- = the percentage that was applied
- Original
- = the value before the percentage was applied
Every case is a division by the multiplier that produced the final figure. Subtracting the percentage instead is the single most common error in reverse percentage problems.
How to use this calculator
- Choose what produced your final figure: something was added to it, something was taken off it, or it represents a stated share of a larger whole.
- Enter the final amount you already have.
- Enter the percentage that was applied — 20 for 20%, not 0.2.
- Press Calculate. The result includes a check line multiplying the original back up, so you can confirm it reproduces your final figure.
Worked example
Removing 20% tax from a $120 invoice
An invoice total of $120 includes 20% tax. The instinct is to take 20% off $120, giving $96 — but that is wrong, because the 20% was calculated on the pre-tax figure, not the total.
The pre-tax price was multiplied by 1.20 to reach $120, so recovering it means dividing by 1.20.
- Multiplier: 1 + 20% = 1.20
- 120 ÷ 1.20 = 100
- Check: 100 × 1.20 = 120 ✓
Answer: The pre-tax price is $100 and the tax is $20 — not the $24 that subtracting 20% would suggest.
Why subtracting the percentage fails
A percentage is always applied to a base. When 20% tax is added to a $100 item, the 20% is 20% of $100, giving $20 and a total of $120. If you then take 20% off $120, you are taking 20% of a different, larger base — $24 — and you land at $96 instead of back at $100.
The reliable mental model is multipliers. Adding 20% multiplies by 1.2. The inverse of multiplying by 1.2 is dividing by 1.2, not multiplying by 0.8. Once you think in multipliers, reverse percentage problems stop being a special case and become ordinary division.
The three situations this covers
Removing an addition. Sales tax, VAT, GST, service charges, markups and any "price includes" figure. Divide by 1 + rate.
Removing a reduction. Finding the ticket price behind a sale price, the list price behind a negotiated discount, or the gross figure behind a net-of-commission payment. Divide by 1 − rate.
Scaling up from a share. When your figure is stated as a percentage of something larger — "we have reached 35% of target, which is 8,750 units" — divide by the rate as a decimal to recover the whole.
Discount reversal in practice
A jacket is marked at $63 after a 30% discount. The multiplier for a 30% reduction is 0.70, so the original price is 63 ÷ 0.70 = $90, and the saving was $27. Subtracting 30% from $63 would have given $44.10, which is not a price that ever existed.
For stacked discounts, divide by each multiplier in turn or by their product. An item at $56 after "30% off then a further 20% off" started at 56 ÷ (0.70 × 0.80) = 56 ÷ 0.56 = $100.
| Final | Applied | Multiplier | Original | Wrong answer (subtracting) |
|---|---|---|---|---|
| $120 | +20% | 1.20 | $100.00 | $96.00 |
| $63 | −30% | 0.70 | $90.00 | $81.90 |
| $220 | +10% | 1.10 | $200.00 | $198.00 |
| $75 | −25% | 0.75 | $100.00 | $93.75 |
Sanity-checking the answer
Direction is the quickest check. Reversing an increase must give an original smaller than the final figure. Reversing a discount must give an original larger than the final figure. If your answer moves the wrong way, the mode is wrong.
The result panel above always shows the round-trip multiplication so you can confirm the original reproduces the final amount exactly. If that check line does not match your figure, something in the inputs is wrong.
Important considerations
- A decrease of 100% or more cannot be reversed — nothing remains to work back from.
- Tax-inclusive pricing conventions vary by jurisdiction; confirm whether the stated rate applies to the net or gross figure.
- Rounding in the original transaction may mean the recovered figure is a cent or two off the true original.
- Stacked percentages must be reversed by dividing by the product of their multipliers, not by their sum.
- For compound interest over multiple periods, use present value rather than a single reverse percentage.
Common mistakes to avoid
- Subtracting the percentage from the final figure. This is the defining error of reverse percentage problems.
- Using the wrong mode. Reversing an increase and reversing a decrease move the answer in opposite directions.
- Entering the rate as a decimal. Type 20 for 20%, not 0.2.
- Reversing stacked discounts by adding them. 30% then 20% is a 0.56 multiplier, not 0.50.
- Forgetting that the answer must move the right way. An original recovered from a discount is always higher than the sale price.
Frequently asked questions
How do I find the original price before a discount?
Divide the sale price by (1 − discount ÷ 100). A $63 item after 30% off was originally 63 ÷ 0.70 = $90. Subtracting 30% from $63 gives the wrong answer because the discount was calculated on the higher original price.
How do I remove VAT or sales tax from a total?
Divide the tax-inclusive total by (1 + rate ÷ 100). At 20%, divide by 1.20; at 7.5%, divide by 1.075. The tax itself is then the difference between the total and that result.
Why can I not just subtract the percentage?
Because the percentage was calculated on the original amount, not on the final one. Those are different bases, so subtracting produces a number that never existed in the transaction. Always divide by the multiplier instead.
How do I reverse two stacked discounts?
Multiply the two multipliers and divide by the product. For 30% then 20% off, the combined multiplier is 0.70 × 0.80 = 0.56, so an item at $56 started at $100.
What if the final amount came from a percentage increase over several years?
That is compound growth, not a single percentage. Divide by (1 + rate)ⁿ where n is the number of periods, or use the present value calculator, which handles the compounding directly.
Does the calculator work for negative percentages?
Yes. A negative value in "increase" mode behaves as a decrease and vice versa. The multiplier line in the working shows exactly what was applied, so the interpretation is always visible.
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