Calculation desk / percentages
Reverse Percentage Calculator
Find the original value when you know a percentage result.
Reverse Percentage Calculator: Recover a whole amount from a known portion and the percentage that portion represents. It also finds a pre-discount or pre-tax amount when you enter the final amount's percentage of the original, such as 80% after a 20% discount. Runs 100% locally in your browser with zero server file uploads.
- Category
- Calculators
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Original value
240
Original = result ÷ (percentage ÷ 100)- The percentage must be greater than zero.
- The known result is assumed to be a percentage of the original value.
Formula and worked example
Original = result ÷ (percentage ÷ 100)
A worked example with sample values:
| Inputs | |
|---|---|
| Known result | 36 |
| Percentage | 15% |
| Results | |
|---|---|
| Original value | 240 |
Undo multiplication by a percentage
Let R be the known result, p the percentage it represents and O the unknown original. The forward relationship is R = O × p ÷ 100. Divide both sides by p ÷ 100 to obtain O = R ÷ (p ÷ 100). The denominator is a decimal share or multiplier, not a subtraction from the known result.
If 36 represents 15% of an unknown whole, enter Known result 36 and Percentage 15. Convert 15% to 0.15, then divide: O = 36 ÷ 0.15 = 240. The calculator shows Original value = 240. Checking forward, 240 × 0.15 = 36, so the recovered whole is consistent with the portion.
OpenStax's basic percent equations (https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent) solve an unknown base by division. The same algebra works for a percentage smaller or larger than 100.
Translate the wording before entering a rate
For a reduction of d%, the final amount is (100 − d)% of the original. For an uplift of t%, it is (100 + t)%. This translation is the key to reversing a discount, markup or a tax added to a net amount; the widget has one generic percentage field rather than separate discount and VAT modes. Several successive adjustments combine as multipliers. For example, a 10% discount followed by another 10% discount leaves 90% × 90% = 81% of the original, so use 81 in the percentage field. A non-negative zero result with a positive percentage recovers zero.
How to use it
- Enter the values for the selected percentage relationship.
- Calculate to update the result sheet.
- Review the formula and assumptions before using the result.
Privacy & limitations
Every value and calculation stays in your browser. This is a planning utility, not financial, tax, legal, or investment advice.
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Frequently asked questions
Which percentage do I enter to reverse a discount?
Enter what remains, not what was removed. After a 20% discount, the paid price represents 80% of the original. A known result of 160 with percentage 80 gives original 200. Entering 20 would mistakenly treat 160 as the discount amount.
How do I remove VAT from an inclusive price?
For a hypothetical 20% VAT added to the net price, the gross amount is 120% of net. Enter gross 120 and percentage 120 to recover net 100. Do not subtract 20% of gross: that would give 96. Supply the applicable rate yourself.
Why is a percentage of zero rejected in the reverse calculation?
Zero per cent of every original is zero, so knowing a zero result does not identify the original. A positive result cannot be zero per cent of a finite original. Division by that zero percentage therefore has no usable answer.
Embed this tool
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