Reverse Percentage Calculator
Fill in the blanks and press Calculate. A fall of 50% needs a rise of 100% to undo, not another 50% — the page works that out for you.
A reverse percentage calculator works backwards. You know what something costs now, after a discount or a tax, and you want the figure it started from.
A jacket is $255 in a sale marked 15% off. The original price was $300 — and if you reached for $293.25 by adding 15% back on, you have company. Almost everybody does that first, and it is wrong for a reason worth understanding once.
Why Adding the Percentage Back Does Not Work
The discount was 15% of the original price — and the original price is the thing you do not have yet.
Adding 15% to $255 takes 15% of $255, which is a smaller number, so it gives back less than was taken away. You land at $293.25 — sixty-seven and a half rupees short, and nowhere near $300.
On a jacket the gap is sixty-seven rupees; on a laptop it is thousands. Reverse percentages are also called inverse percentages, and a price before discount question is the commonest form they take.
Every wrong answer to a reverse percentage question comes from one substitution: using the figure you have in place of the figure you want.
How to Do a Reverse Percentage
Three steps, and the first is the whole difficulty.
Step 1 — work out what percentage the figure you have represents. After 15% comes off, what is left is 85% of the original. So $255 is 85%.
Step 2 — turn that into a multiplier. 85 ÷ 100 = 0.85. The original was multiplied by 0.85 to become $255.
Step 3 — divide. 2,550 ÷ 0.85 = 3,000. Undoing a multiplication means dividing, and that is the entire calculation.
Check it forwards before you write it down: 15% of 3,000 is 450, and 3,000 − 450 = 2,550. The figure you were given comes back, so the answer holds. Do that check every time — in an exam it costs ten seconds and catches the one mistake this topic produces.
Backing Sales Tax Out of a Total
Reverse percentages run in the other direction just as often, and tax is where most people meet them.
A receipt totals $107.50 and the sales tax was 7.5%. The tax was charged on the pre-tax price, so the total is 107.5% of it. Divide: 107.50 ÷ 1.075 = $100, and the tax itself was $7.50.
Taking 7.5% off $107.50 would have given $99.44, a little over fifty cents short — the same substitution as before, running the other way. Outside the United States the tax has other names and the arithmetic is identical: a UK price including 20% VAT is 120% of the net figure, so you divide by 1.2, and a total including 18% GST is 118% of the amount before it. A salary of $55,000 after a 10% raise was $50,000 before it, because 55,000 is 110% of what it used to be.
The One Line to Remember
original = final ÷ (the percentage it represents ÷ 100)
| What happened | The figure you have is | Divide by |
|---|---|---|
| 20% off | 80% of the original | 0.8 |
| 40% off | 60% | 0.6 |
| 7.5% sales tax added | 107.5% | 1.075 |
| 20% VAT added (UK) | 120% | 1.2 |
| it simply is 32% of it | 32% | 0.32 |
Discounts always give a divisor below one, so the answer comes out bigger than the figure you had. Additions give a divisor above one and the answer comes out smaller. That single sanity check will catch a misplaced calculation faster than re-reading the question will.
Doing It Without a Calculator
Worth knowing, because numerical reasoning tests and non-calculator exam papers both love this topic.
Find 1% first. If $255 is 85%, then 1% is 2,550 ÷ 85 = 30, and 100% is 30 × 100 = $300. Dividing by 85 is unpleasant but dividing by 85 once beats fumbling a decimal three times.
For friendlier numbers the fractions are quicker still. A quarter off means the price you see is three quarters of the original, so divide by 3 and multiply by 4. Half off means double it. A fifth off — 20% — means divide by 4 and multiply by 5.
Where This Gets Money Wrong in Real Life
Two situations catch people out repeatedly, and both are the same error wearing different clothes.
Backing tax out of an invoice. An invoice for $44,250 including 7.5% sales tax has a pre-tax value of $41,162.79, not the $40,931.25 you get by taking 7.5% off the total. On one invoice the gap is small; across a year of them it is a line item.
Judging a sale. A shop shows $1,049.30 marked "30% off". Was the original $1,499 or was the tag inflated first? Divide by 0.7 and you get exactly $1,499, which tells you the discount is real against the list price. Doing the arithmetic in the aisle takes five seconds and is the only way to tell.
Which Percentage Tool You Actually Want
This page is for when you know the percentage that was applied and want the figure before it.
If you want a straightforward percentage of a number, or one number as a percentage of another, the percentage calculator covers those. If you have two figures and want the movement between them named as a rise, that is the percentage increase calculator. If the value fell instead, the percentage decrease calculator is written around discounts and depreciation, and will tell you what rise it would take to recover.
For the plain signed movement with no word attached, use the percent change calculator. And two sit further off: when neither of your numbers is a baseline the percent difference calculator divides by their average, and when one is a known accepted value the percent error calculator divides by the truth.
How to Use This Reverse Percentage Calculator
Pick what happened to the number: a discount came off, tax or a mark-up went on, or the figure simply is a known percentage of something. The sentence in the form changes to match, so you read the question before you answer it.
Then type the percentage you were told — 15 for "15% off", not the 85 that survives it. Working out that 85 is the step this page exists to do for you, and it appears in the working so you can follow it rather than take it on trust. This is also the one place a reverse percentage question is usually lost.
Prices go in as they are written: $255 and 2,550 both read cleanly, and so does a percentage typed with its sign. Every answer arrives with the multiplier, the amount that came off or went on, a check running the sum forwards, and the wrong figure the obvious method would have produced.
Reverse Percentage Calculator FAQ
How do you do a reverse percentage?
A jacket costs $255 after 15% off. What was the original price?
Why can't I just add the percentage back on?
How do I find the price before sales tax?
What is the reverse percentage formula?
If 32% of a number is 150, what is the number?
How do I work out a reverse percentage without a calculator?
Is a reverse percentage the same as a percentage decrease?
Why does a 100% discount have no answer?
Is this reverse percentage calculator free?
Work out what fraction of the original you are holding, divide by it, and check the answer forwards before you trust it. Those three habits turn the hardest percentage topic on the syllabus into a single division — and the reason the obvious method fails is worth carrying with you long after the arithmetic has become automatic.
