Home › Math › Percent Error Calculator
Percent Error Calculator
Compares a measured or estimated value with the accepted (true) value and reports the absolute error, relative error, percent error and whether the measurement over- or underestimates.
When to use
You have an experimental, estimated or approximated value and a reference value and need the error as a percentage of the reference, e.g. in a physics lab or to judge an approximation.
Do not use when: You want the percentage change between two values over time (use percentage-change) or the symmetric percent difference between two equally valid measurements (also percentage-change).
Formula
absolute_error = |measured − accepted|; relative_error = absolute_error / |accepted|; percent_error = relative_error × 100; signed_percent_error = (measured − accepted) / |accepted| × 100
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
measured | number | yes | The observed, estimated or approximate value. | |
accepted | number | yes | The reference, theoretical or exact value. Must not be 0. |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
absolute_error | number | |measured − accepted|, in the units of the values. | |
relative_error | number | |measured − accepted| / |accepted|, as a plain ratio. | |
percent_error | number | % | Relative error × 100. |
signed_error | number | measured − accepted (negative when the measurement is too low). | |
signed_percent_error | number | % | (measured − accepted) / |accepted| × 100. |
direction | string | 'overestimate', 'underestimate' or 'exact'. | |
accuracy_percent | number | % | 100 − percent error (can be negative for errors above 100%). |
Example
g measured 9.5 vs 9.81 m/s²: {"measured":9.5,"accepted":9.81} → {"absolute_error":0.31,"relative_error":0.0316,"percent_error":3.16,"signed_error":-0.31,"signed_percent_error":-3.16,"direction":"underestimate","accuracy_percent":96.84}
105 vs 100: {"measured":105,"accepted":100} → {"absolute_error":5,"relative_error":0.05,"percent_error":5,"signed_error":5,"direction":"overestimate","accuracy_percent":95}
GET https://tttkmbb.com/api/v1/calculate/percent-error?measured=9.5&accepted=9.81
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/percent-error(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/percent-error · Markdown: https://tttkmbb.com/math/percent-error.md · JSON definition: https://tttkmbb.com/math/percent-error.json
- MCP: server
https://tttkmbb.com/mcp, toolrun_calculator with calculator_id="percent-error" - OpenAPI operationId:
calculate_percent_error - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
- Wikipedia – Approximation error (reference)
- Wolfram MathWorld – Relative Error (reference)
- Wolfram MathWorld – Percentage Error (reference)
FAQ
Is percent error the same as percent difference?
No. Percent error divides by the accepted value (one value is the reference); percent difference divides by the average of two values that are equally valid. Use percentage-change for the latter.
Should percent error be reported with a sign?
Most lab conventions report the absolute (unsigned) value; signed_percent_error is provided when the direction of the bias matters.
Related calculators
- Percentage Change Calculator — Relative change and symmetric percent difference.
- Percentage Calculator — General percent-of and what-percent questions.
- Rounding Calculator — Round the reported error to significant figures.