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How to Work Out the Original Price Before a Discount or Tax
If you only know the price after a discount or after tax was added, you can recover the original figure — but not by adding the same percentage back. Here is the correct method.
To find an original price from a final price, divide rather than subtract. If 20% was taken off, the price you see is 80% of the original, so you divide by 0.80. If 15% tax was added, the price you see is 115% of the original, so you divide by 1.15. Adding or subtracting the same percentage back gives the wrong answer every time, because the percentage was applied to a base you no longer have.
The two formulas
Both are the same idea. Work out what fraction of the original the final price represents, then divide by that fraction. Express the rate as a decimal: 20% becomes 0.20, 7.5% becomes 0.075.
After a discount: Original = Final price / (1 - discount rate) After tax was added: Original = Final price / (1 + tax rate)
Worked example: removing a discount
A jacket is on the rack at 68 with a sign saying 15% off. What was it before?
The 68 represents 85% of the original, so 68 divided by 0.85 gives 80. The original price was 80, and the discount was worth 12.
The tempting shortcut is to add 15% to 68, which gives 78.20 — nearly two units short. It is wrong because 15% of 68 is smaller than 15% of 80, and the discount was calculated on the larger number.
Worked example: stripping out sales tax
A receipt shows 129.99 including 8% sales tax, and you need the pre-tax figure for an expense claim.
Divide 129.99 by 1.08 to get 120.36. The tax portion is 129.99 - 120.36 = 9.63.
Check it: 120.36 x 1.08 = 129.99. If your reversed figure multiplied back by the rate does not return the amount you started with, the calculation went wrong somewhere.
Worked example: a rate you have to find
Sometimes you know both prices and want the rate. A laptop was 900 and is now 693. The final price divided by the original is 693 / 900 = 0.77, so the price is 77% of what it was, meaning a 23% discount.
That framing — final divided by original — is worth learning on its own. Whatever multiplier it produces, subtract it from 1 for a fall or from it subtract 1 for a rise.
Quick reference
| What was applied | Final price is this share of original | Divide the final price by |
|---|---|---|
| 10% off | 90% | 0.90 |
| 25% off | 75% | 0.75 |
| 33% off | 67% | 0.67 |
| 5% tax added | 105% | 1.05 |
| 15% tax added | 115% | 1.15 |
| 20% tax added | 120% | 1.20 |
When this is genuinely useful
The bookkeeping case is the most common. Many expense systems want the net amount and the tax separately, and a receipt that only prints a gross total leaves you to reverse it. Building the division into a spreadsheet column once saves redoing it by hand every month.
- Separating a pre-tax amount for bookkeeping or a tax return when you only have a gross receipt.
- Checking whether an advertised 'was' price is real by reversing the stated discount and seeing if it matches.
- Working out a supplier's list price when you have been quoted a net figure after a trade discount.
- Reconstructing a base salary from a take-home figure when a single fixed-percentage deduction applies.
- Comparing two offers where one is quoted inclusive of tax and the other exclusive.
Why adding the percentage back gives the wrong price
- Adding the percentage back instead of dividing. This is the central error and it always understates the original price.
- Reversing two discounts by adding them together. A 20% then 10% discount is not 30% off; see the note below.
- Using the wrong tax rate for the item. Many jurisdictions apply different rates to food, books or services, so a single blanket rate across a whole receipt can be wrong.
- Forgetting that the displayed price may already have been rounded. Reversing a rounded figure gives an original that is close but not exact.
- Assuming the discount applied to the whole basket when it only applied to one line.
Reversing more than one change
When two percentages were applied in sequence, reverse them in sequence too, in the opposite order. If an item had 20% taken off and then tax of 10% added, the final price is Original x 0.80 x 1.10. To recover the original, divide by 1.10 first, then by 0.80.
Because the multipliers can be applied in any order without changing the product, you can also just divide by the combined multiplier 0.88 in one step. The important thing is that you never add 20% and 10% together into a single 30% adjustment.
Assumptions and limits
This method assumes the percentage was applied to the full amount you are working with, and that nothing else was added or removed along the way. Shipping, a fixed handling fee, a loyalty credit or a rounding rule all break the clean relationship between the two numbers.
It also assumes the rate you are dividing by is the rate that was actually used. A receipt that shows a blended rate across mixed-rate items cannot be reversed with one division.
Where the stakes are meaningful — a tax filing, a contract price, a reclaim — treat a reversed figure as a check on someone else's number rather than as the authoritative one. Ask for a breakdown that states the net amount directly.
Reverse the percentage with division
When a final price already includes a discount or tax, the percentage was applied to the original amount. To recover the original, divide by the remaining multiplier rather than simply adding the percentage back. For example, after a 20% discount the final price is 80% of the original, so the original is final ÷ 0.80.
Frequently asked questions
Why can't I just add the discount percentage back?
Because the discount was calculated from the original, larger price, and adding it back calculates it from the smaller discounted price. The result is always too low.
How do I remove tax from a total that includes several tax rates?
You cannot do it with a single division. Split the total by item or line, apply the correct rate to each group, then add the net amounts back together.
Does this work for compound interest too?
The same structure works for one period: divide by (1 + rate). For several periods you divide by (1 + rate) raised to the number of periods, which is the present-value calculation.
What if I get a long decimal?
Keep the full figure through the calculation and round only the final answer, normally to two decimal places for currency. Rounding early can shift the result by a few units on larger amounts.
Why can't I add the discount percentage back?
Because the percentage was calculated from the original price, while the amount you have is the discounted price. The two bases are different.
Can I reverse two discounts separately?
You can reverse them by undoing each multiplier in the correct sequence. Do not combine the percentages by simple addition unless the pricing rule explicitly makes them additive.
Conclusion
Reversing a percentage is division, not subtraction. Work out what share of the original the price in front of you represents, divide by that share as a decimal, and verify by multiplying back. The habit of checking the reversal is what catches the errors, particularly when more than one adjustment was applied and the temptation is to collapse them into a single number.
Figures in this article are illustrative. Results depend on your own rates, fees, taxes and circumstances, and are for educational and planning purposes rather than financial advice.