Percentage Error Calculator
Compare a measured or calculated value with a true or reference value. Gives the error, the absolute error, the relative error and the percentage error
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates percentage error, absolute percentage error, error and 2 more results from measured value and true value. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Use the absolute percentage error when only the size of the error matters, such as checking a meter against a tolerance. Percentage error is not the same as percentage difference, which compares two values with neither one a reference. For the uncertainty of a measurement chain see the measurement uncertainty guide.
Cross-check: 32 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Pure mathematics or statistics; no electrical standard governs the method |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 32 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Measured value | 98.5 |
| True (reference) value | 100 |
- Error = measured − true = 98.5 − 100 = -1.5
- Absolute error = |-1.5| = 1.5
- Relative error = error / |true| = -1.5 / 100 = -0.015
- Percentage error = -0.015 × 100 = -1.5%
Assumptions
- Percentage error is taken relative to the true (reference) value, not the measured one
- A negative percentage error means the measured value is below the true value; a positive one means it is above
- Both values are plain numbers in one consistent unit; the percentage does not depend on the unit
- The true value must not be zero
Use the absolute percentage error when only the size of the error matters, such as checking a meter against a tolerance. Percentage error is not the same as percentage difference, which compares two values with neither one a reference. For the uncertainty of a measurement chain see the measurement uncertainty guide.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Measured value | (number) | any number | The reading or calculated value you are checking. Use the same unit as the true value. |
| True (reference) value | (number) | any number | The accepted, rated or reference value. It cannot be zero, because the error is expressed as a share of it. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Percentage error (signed, %) | (number) | Shown to 4 decimal places | |
| Absolute percentage error (%) | (number) | Shown to 4 decimal places | |
| Error (measured − true) | (number) | Shown to 6 decimal places | |
| Absolute error | (number) | Shown to 6 decimal places | |
| Relative error (fraction) | (number) | Shown to 6 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with measured value
| Measured value | Percentage error | Absolute percentage error | Error |
|---|---|---|---|
| 9.85 | -90.15 | 90.15 | -90.15 |
| 24.6 | -75.4 | 75.4 | -75.4 |
| 49.3 | -50.7 | 50.7 | -50.7 |
| 98.5 | -1.5 | 1.5 | -1.5 |
| 197 | 97 | 97 | 97 |
| 394 | 294 | 294 | 294 |
| 985 | 885 | 885 | 885 |
Other inputs are the same as in the worked example above.
Standards and further reading
Complex numbers, rectangular and polar form and angle conversion are standard mathematics, not the subject of a standard. Standards apply when the result feeds an electrical design, and they set the method there.
Frequently asked questions
What do I need to enter?
Enter measured value and true (reference) value. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Percentage error is taken relative to the true (reference) value, not the measured one. A negative percentage error means the measured value is below the true value; a positive one means it is above. Both values are plain numbers in one consistent unit; the percentage does not depend on the unit. The true value must not be zero.
Which calculators should I use next?
Common next steps are Complex Numbers (Rectangular and Polar), Phasor Sum and Difference (Polar Inputs), Ohm's Law and RMS, Peak and Peak-to-Peak. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 32 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Percentage Error Formulas for Measurements: Percentage error formulas for engineers: absolute, relative and percentage error of a meter reading
- Measurement Uncertainty Formulas: Measurement uncertainty formulas: the standard uncertainty of a rectangular limit
- Ohm’s Law Formulas and Power Wheel: all twelve V, I, R and P formulas
More Engineering Mathematics calculatorsAll engineering calculatorsPercentage Error in Elecmetric