Free · Percentages
Signed Percentage Decrease and Value Inverses
Compare nonzero signed starting values and final values with an absolute-magnitude percentage change.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
From 100 to 80 is a 20% decrease and a difference of −20.
final = initial − decrease × abs(initial); difference = final − initial
Worked example
Enter these known values and leave the other values blank.
- Initial value
- 100
- Final value
- 80
- Decrease (%)
- 20 %
- Final value − Initial value
- -20
Assumptions and limitations
- The starting value is nonzero. Decrease uses the absolute magnitude of that starting value in the denominator, so signed values remain meaningful.
- The starting-value inverse selects a positive valid solution when available, then a negative valid solution. Some decrease percentages admit two solutions; the calculator reports the documented selected branch. A zero final value at a ±100% boundary can be non-unique and is left unresolved.
Common questions
Can the decrease be negative?
Yes. A negative percentage decrease represents a rise under the same signed starting-value convention.
What happens when there is more than one starting value?
The inverse prefers a valid positive starting value, otherwise a valid negative one. Enter a known starting value directly to select its actual branch.
References
Remove the unused captured precision JavaScript helper and correct the starting-value inverse for the full signed absolute-magnitude decrease identity. Select a positive valid root when available, otherwise a negative valid root; leave ambiguous zero-final and impossible inverse states unresolved. Preserve direct signed calculations and every difference inverse. Test nonzero starting values through exact sign so the same domain also accepts tiny nonzero decimals.