Free · Percentages
Signed Percent Error and Inverse
Calculate signed percent error for positive measurements, or solve for the observed or true value with a retained step-by-step explanation.
- 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
An observed value of90 against a true value of100 gives−10% signed error; its absolute percent error is10%.
e=(observed−true)/true; percent error=100e; observed=true(1+e).
Worked example
Enter these known values and leave the other values blank.
- True value
- 100
- Observed value
- 90
- Percent error
- -10 %
Assumptions and limitations
- This retained model uses strictly positive true and observed values; zero and negative measurements lie outside its captured input domain.
- Percent error is signed here. A negative value is an underestimate; absolute percent error is its magnitude. Do not confuse signed error with symmetric percentage difference.
- All three numeric controls remain editable. Clear the unknown before solving an inverse. The working text follows actual supplied-versus-derived state, including locks and clears.
- Finite nonzero values beyond fixed-decimal display resolution retain their computed precision in scientific notation.
Common questions
Why can percent error be negative?
The signed definition preserves the sign of observed minus true. An underestimate has negative signed error; taking its absolute value gives absolute percent error.
How do I recover the true value?
Divide observed by one plus the relative signed error. In this positive-value model the relative error must exceed−1.
References
Retain signed relative error and all captured inverse/working branches for strictly positive true and observed values, comparing positivity exactly. Input provenance for explanatory steps uses actual manual input state, not value presence.