Reverse Percentage Calculator
Find the original value before a percentage increase or decrease — for example the price before tax or before a discount.
Your inputs
Results
Original value
100
- Size of the change
- 20
✓Exact calculation — rounded only for display
What this calculator does
If a price after 20 % off is 80, the original was not 96. Reverse percentages divide by the multiplier instead of subtracting.
Formula and method
After a decrease: original = final ÷ (1 − p); after an increase: original = final ÷ (1 + p); portion: original = value ÷ p
Worked example
Calculated by this tool with its default inputs:
Inputs
- Value after the change: 80
- The change was: A decrease (e.g. discount)
- Percentage: 20 %
Results
- Original value: 100
- Size of the change: 20
How to read the results
The size of the change is the difference between the original and the final value.
Assumptions and limitations
- A 100 % decrease cannot be reversed.
Questions
Why is 80 ÷ 0.8 correct?
Because the discounted price is 80 % of the original.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy