Free · Percentages
Signed Percent Increase and Decrease with Summary
Use either increase or decrease mode with a consistent signed absolute-magnitude change model and rounded explanations.
- 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
100 increasing to 120 is a 20% rise and difference of 20.
result = start + increase × abs(start) = start − decrease × abs(start)
Worked example
Enter these known values and leave the other values blank.
- Initial value
- 100
- Final value
- 120
- Increase (%)
- 20 %
- Final value − Initial value
- 20
Assumptions and limitations
- The starting value is nonzero; percentages use its absolute magnitude in the denominator. A negative increase represents a decrease.
- Starting-value inverses select a valid positive root before a valid negative root. Boundary cases can be non-unique or impossible; enter a known starting value directly when needed.
- Summary components round to five significant decimal digits. The internal direct calculation retains full precision.
Common questions
How do negative starting values work?
The percentage denominator uses absolute magnitude. For example, a rise from −100 to −80 is a 20% increase.
Does the explanation rounding affect the calculation?
No. The explanatory components use five significant digits; direct results and inverse calculations keep the underlying decimal precision.
References
- Percentage and significant-digit definitions
- Percentage and significant-digit definitions
- Percentage and significant-digit definitions
- Calculation definition and unit reference
Use one consistent absolute-magnitude signed increase identity in both duplicated captured equation groups, with positive-first valid starting-value inverse branches for increase and decrease. Port all four five-significant-digit presentation formulas to exact local decimal rounding rather than binary Number.toPrecision. Preserve both modes, all value/difference inverses and every conditional summary. Evaluate the original nonzero domain through exact sign.