Quick answer
To undo a percentage change: original = final ÷ (1 ± percent ÷ 100), plus for an increase and minus for a decrease. A final amount of 120 after a 20% increase means the original was 100.
Enter the final amount, the percentage and whether it was an increase or decrease. The calculator returns the original. Use this reverse percentage calculator to check your own figures.
Related tools: Percent Decrease Calculator: Percentage decrease between two values. Percent Increase Calculator: Percentage increase between two values. Percent Difference Calculator: Symmetric percent difference between two values.
How to use the Reverse Percentage Calculator
- Enter final amount.
- Enter percentage applied (%).
- Choose it was: Increased and Decreased.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Final amount | A number | — |
| Percentage applied | A number, in % | — |
| It was | Choose one: Increased; Decreased | Starts at Increased |
Formula and method
Formula
original = final ÷ (1 ± percent ÷ 100)
IEEE-754 double precision; shown to at most 6 decimal places.
Increasing by p% multiplies by (1 + p/100); decreasing multiplies by (1 − p/100). Divide the final amount by that factor.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Final amount = 120; Percentage applied = 20; It was = Increased.
| Result | Value |
|---|---|
| Original amount | 100 |
The first line is the headline result (original amount). IEEE-754 double precision; shown to at most 6 decimal places.
Why not subtract 20%
20% of 120 is 24, giving 96, which is wrong. The 20% was taken of the original, so divide: 120 ÷ 1.2 = 100. After a 20% decrease, 80 ÷ 0.8 = 100.
Typical uses
Find the price before VAT or sales tax, or before a discount. A price including 20% VAT of 120 has a net price of 100. A 100% decrease makes the original undefined.
How the result changes with final amount
Holding every other input at the first worked example, this table changes only final amount. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Final amount | Original amount |
|---|---|
| 60 | 50 |
| 120 | 100 |
| 240 | 200 |
| 480 | 400 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Percentage applied: entering "100" shows "A 100% decrease has no defined original value." beside that field and no result.
Choosing between the Reverse Percentage Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Percent Decrease Calculator](/math/percent-decrease-calculator/) | original value and new value | Percentage decrease |
| [Percent Increase Calculator](/math/percent-increase-calculator/) | original value and new value | Percentage increase |
| [Percent Difference Calculator](/math/percent-difference-calculator/) | value 1 and value 2 | Percent difference |
| [Percentage Change Calculator](/math/percentage-change-calculator/) | old value and new value | Percentage change |
| [Percentage Calculator](/math/percentage-calculator/) | what do you want to find?, a and b | 15% of 200 |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- A 100% decrease makes the original undefined
- Percent below −100 is rejected for increases
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for percentage applied to confirm this.
Frequently asked questions
What was the price before a 25% discount if now $60?
If $60 is after a 25% discount, the original was 60 ÷ 0.75 = $80.
How do I remove 10% tax?
A price with 10% tax included is 1.10 times the net price, so divide by 1.10: $110 becomes $100.
Is reverse percentage the same as percent decrease?
No, it starts from the final value.
What does the Reverse Percentage Calculator calculate?
Work backwards from a final amount to the original value before a percentage increase or decrease. It returns Original amount.
What formula does the Reverse Percentage Calculator use?
original = final ÷ (1 ± percent ÷ 100). Increasing by p% multiplies by (1 + p/100); decreasing multiplies by (1 − p/100).
What do I need to enter in the reverse Percentage Calculator?
You enter Final amount, Percentage applied (%) and It was.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. A 100% decrease makes the original undefined.
What are the limits of this calculator?
A 100% decrease makes the original undefined. Percent below −100 is rejected for increases.
What does the “It was” option change?
It sets how the reverse Percentage is worked out. The choices are Increased and Decreased.
What is an example of a reverse Percentage result?
With final amount 120, percentage applied 20 and it was Increased, the original amount is 100.
Related calculators
- Percent Decrease Calculator — Percentage decrease between two values.
- Percent Increase Calculator — Percentage increase between two values.
- Percent Difference Calculator — Symmetric percent difference between two values.
- Percentage Change Calculator — Find the percentage increase or decrease from an old value to a new value.
- Percentage Calculator — Calculate a percentage of a number, what percent one number is of another, or the whole from a part.
- Percentage of a Percentage Calculator — Find X% of Y%, optionally applied to a base amount.
- Ratio Percentage Calculator — Percentage share of each part of a ratio.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.