You know the result after a percentage was applied — now you need to work backward to the number it started from. Here's the exact formula, with worked examples for prices, salaries, and taxes.
Published August 24, 2026 · Reviewed by the Ihsabha Editorial Team
Most percentage questions start with an original number and ask you to move forward: what is 20% of 150? Reverse percentage questions run the opposite direction. You're handed the number that's left after a percentage was already applied — a discounted price, a post-raise salary, a tax-inclusive total — and asked to find the number it started from. It's one of the most commonly mis-calculated types of percentage problem, because the instinctive shortcut most people reach for is mathematically wrong. This guide walks through the correct reverse percentage formula, why the obvious shortcut fails, and how to apply it to the situations where it comes up most often.
A reverse percentage calculation (sometimes called "working backward from a percentage" or finding the "original value") starts from a final number and a percentage that was applied to reach it, and solves for the number that existed before the percentage was applied. This is different from the standard percentage formulas covered in Ihsabha's guide to the core percentage formulas, which assume you already know the original number and are solving for a part, a whole, or a percent from numbers you already have going in. In a reverse percentage problem, the "before" number is exactly what's missing. For a deeper look, our guide on How to Calculate a Tip: The Complete Tip Percentage Guide covers this in more detail. To save time, enter your values into the Percentage Calculator and get an instant result.
There are two versions of the formula, depending on whether the percentage that was applied was an increase or a decrease. Both follow the same underlying logic: you divide the new value by an adjustment factor, rather than adding or subtracting the percentage directly.
In both cases, the denominator represents the new value as a fraction of the original — a 25% discount leaves 75% of the original price (0.75), while an 8% increase leaves 108% of the original amount (1.08). Dividing the new value by that fraction undoes the operation and returns you to the starting number.
The most common mistake in reverse percentage problems is assuming you can simply calculate the percentage of the new number and add or subtract it, the same way you'd apply a percentage moving forward. This fails because a percentage discount or increase is always calculated against the original number, not the number left over afterward — and once the value has changed, that original base is gone from the new number.
Consider a $100 item marked down 20% to $80. If you tried to reverse this by adding 20% of $80 (which is $16) back onto $80, you'd land on $96 — not the correct original price of $100. The error happens because 20% of $80 is a smaller amount than 20% of $100 was. The only way to recover the original $100 correctly is to divide $80 by 0.80 (which is 1 − 0.20), giving exactly $100.
This is the single most common reverse percentage scenario: an item is on sale, you know the discounted price and the discount percentage, and you want to know what it cost before the sale.
So an item on sale for $60 after a 25% discount originally cost $80. You can sanity-check this the forward way: 25% of $80 is $20, and $80 − $20 = $60, which matches.
The same logic applies to increases — a salary after a raise, a population after growth, or a price after tax was added.
So a salary of $5,400 after an 8% raise started at $5,000. Checking it forward: 8% of $5,000 is $400, and $5,000 + $400 = $5,400, which confirms the answer. This naturally leads to a related question, answered in How to Calculate Percentage Error: Formula, Steps & Worked Examples.
Finding the pre-tax price from a tax-inclusive total is mathematically identical to reversing a percentage increase, and it trips people up constantly on receipts and invoices. If a receipt shows a final total of $212 and you know a 6% sales tax was included, the pre-tax price is $212 ÷ 1.06 = $200. It's tempting to instead calculate 6% of $212 (which is $12.72) and subtract that from $212 to get $199.28 — but that's incorrect, for the same reason subtracting a discount from the new price is incorrect: the tax was calculated on the pre-tax price, not on the tax-inclusive total. Try the Percentage Calculator to run these numbers with your own figures.
| You want to find... | What you already know | Formula |
|---|---|---|
| The result after a percentage change (forward) | Original value and the percent | New = Original × (1 ± Percent ÷ 100) |
| The original value before a percentage change (reverse) | New value and the percent | Original = New ÷ (1 ± Percent ÷ 100) |
Recognizing which of these two directions a question is asking for — before doing any arithmetic — is the fastest way to avoid the subtraction/addition mistake covered earlier in this guide.
For discounts you calculate often, it helps to have the divisor memorized rather than working it out from scratch each time.
| Discount | Divide sale price by... |
|---|---|
| 10% | 0.90 |
| 20% | 0.80 |
| 25% | 0.75 |
| 30% | 0.70 |
| 50% | 0.50 |
| 75% | 0.25 |
Reverse percentage problems show up far more often in daily life than most people realize, precisely because businesses and institutions usually publish the "after" number rather than the "before" one. A restaurant bill shows a total that already includes a service charge. A payslip shows take-home pay after deductions. A property listing shows a price that already reflects an agent's commission built in. A weight-loss tracker shows a current weight after a percentage of body weight was lost. In every one of these cases, if you only have the final number and the percentage that produced it, the reverse formula — not the forward one — is the tool you need. You may also find it useful to check Percentage Increase and Decrease: How to Calculate Percentage Change, which covers a related angle.
Suppose a restaurant receipt shows a final total of $138 that already includes a 15% automatic service charge on the food total. To find the pre-service-charge food total:
So the food total before the service charge was added came to $120. This is the same calculation restaurants and diners alike use to work out how much of a bill is the service charge itself: $138 − $120 = $18.
A property sells for a net amount to the seller of $282,000 after a 6% commission was deducted from the sale price. To find the original sale price the commission was calculated against:
The full sale price was $300,000, of which $18,000 (6%) went to commission, leaving the seller with $282,000 — which matches the number given. For an instant, practical check, the Percentage Calculator is ready to go.
Reverse percentage logic also comes up in halal financial planning. If someone knows their remaining eligible wealth after a Zakat payment was deducted and wants to reconstruct what their Nisab-eligible total was before paying, the same reverse formula applies: Original Wealth = Remaining Wealth ÷ (1 − 0.025), since Zakat is calculated at a flat 2.5% rate. For example, if $19,500 remains after Zakat was paid, the pre-Zakat eligible total was $19,500 ÷ 0.975 ≈ $20,000, meaning $500 was paid in Zakat. Ihsabha's dedicated Zakat calculation guide covers the forward version of this calculation — working out what's owed from a known total — in full detail.
Because reverse percentage mistakes tend to produce numbers that look plausible rather than obviously wrong, it's worth building a verification step into the process every time: If you want to go further, Markup vs. Margin: How to Calculate Each Percentage Correctly explains this point in more depth.
Some real situations involve more than one percentage change stacked together — for example, a price that includes both a service charge and a tax, or a salary that went through two separate raises. In these cases, you must reverse each step separately, in the opposite order from how they were applied, rather than combining the percentages into a single number first. If a $100 base price had a 10% service charge added, then a 5% tax added on top of that new total, the final price is $100 × 1.10 × 1.05 = $115.50. To reverse it, divide by the factors in reverse order: $115.50 ÷ 1.05 = $110, then $110 ÷ 1.10 = $100. Dividing by a single combined 15% factor instead ($115.50 ÷ 1.15 = $100.43) gives a close but technically incorrect answer, because the two percentages were never meant to be summed in the first place.
Skip the manual division. Ihsabha's Percentage Calculator includes the "find the whole" mode used throughout this guide — enter the result and the percentage, and it works backward to the original number instantly, with no rounding errors.
Reverse percentage problems are closely related to two other topics on Ihsabha. If you're calculating the discounted price forward, rather than working backward from it, the guide to calculating a percentage off a price covers that direction step by step. And for the three foundational percentage formulas this guide builds on, the core percentage formula guide is the place to start.
To undo a percentage increase, divide the new value by (1 + Percent ÷ 100). To undo a percentage decrease, divide the new value by (1 − Percent ÷ 100). Either way, you are dividing, never multiplying, by a percentage to get back to the original number.
Divide the sale price by (1 − Discount ÷ 100). For example, if an item now costs $60 after a 25% discount, the original price was 60 ÷ 0.75 = $80.
Divide the new amount by (1 + Increase ÷ 100). For example, if a salary is now $5,400 after a 8% raise, the original salary was 5,400 ÷ 1.08 = $5,000.
Because the percentage was originally applied to the old number, not the new one. Subtracting 25% of the new (already reduced) price undoes the wrong base amount and gives an incorrect result — you must divide by the adjusted factor instead.
Reverse percentage calculations are exact, just like forward ones — there's no inherent estimation involved once the correct formula is applied to the correct numbers. The only real risk is falling back on the intuitive but incorrect shortcut of adding or subtracting a percentage of the new value instead of dividing by the adjustment factor. Once that distinction is clear, reverse percentages become just as mechanical as any other percentage calculation, whether you're pricing a sale item, checking a tax receipt, or working out what a salary looked like before a raise.
Work it out instantly with Ihsabha's Percentage Change Calculator and Percentage Error Calculator. For related reading on Ihsabha's blog, see How to Use a Scientific Calculator: Every Function Explained, Degrees vs. Radians: The Complete Guide to Angle Units and Significant Figures: Rules, Examples & How to Round Correctly.