What this calculator does
The absolute error formula is simply the size of the gap between a measured value and the accepted true value: |measured − true|, in the same units as the values themselves. Relative error takes that same gap and divides it by the true value, turning it into a unitless ratio that says how big the error is relative to the size of what was being measured.
The two numbers answer different questions. Absolute error tells you how far off a reading is in real units, which matters when that unit itself is meaningful, such as millimetres on a machined part. Relative error tells you how big that miss is proportionally, which is what lets you compare the accuracy of a measurement of 2 units against one of 2,000.
The formula
Absolute error is the plain difference between the measured and true values, with the sign removed. Relative error divides that absolute error by the size of the true value, giving a decimal ratio rather than a percentage. Multiplying that ratio by 100 gives the more familiar percent error.
| Term | Meaning |
|---|---|
| Absolute error | The size of the gap between measured and true values: |measured − true|, in the original units. |
| Relative error | Absolute error divided by the true value, expressed as a decimal ratio rather than a percentage. |
| Percent error | Relative error multiplied by 100, the same figure expressed as a percentage. |
| Signed error | The error with its sign kept, showing whether the measured value ran high or low rather than just how far off it was. |
The inputs explained
| Field | What to enter |
|---|---|
| Measured value | The value you actually measured, read or calculated. |
| Accepted (true) value | The accepted, reference or true value being compared against. |
When to use it
Reporting the accuracy of a measurement
Lab and workshop reports often ask for both absolute and relative error, since absolute error alone does not say whether a 2 mm miss is trivial on a 2 metre length or serious on a 2 mm one.
Comparing the precision of two different instruments
Two instruments with the same absolute error can have very different relative errors if they are measuring quantities of different sizes, which relative error captures and absolute error does not.
Checking a rounded or estimated figure against an exact one
Working out both the absolute and relative error of a rounded approximation shows exactly how much precision was given up, in both real units and proportionally.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How absolute and relative error change as the measured value moves away from the true value
A fixed true value of 10, against a range of measured values on either side of it.
| Measured value | Absolute error | Relative error (decimal ratio) | Percent error |
|---|---|---|---|
| 8.0 | 2.000 | 0.2000 | 20.0% |
| 9.0 | 1.000 | 0.1000 | 10.0% |
| 9.5 | 0.5000 | 0.0500 | 5.00% |
| 9.8 | 0.2000 | 0.0200 | 2.00% |
| 10.2 | 0.2000 | 0.0200 | 2.00% |
| 11.0 | 1.000 | 0.1000 | 10.0% |
| 12.0 | 2.000 | 0.2000 | 20.0% |
Questions
What is the difference between relative error and percent error?
They carry exactly the same information. Relative error is the ratio expressed as a decimal, such as 0.02; percent error is the same ratio multiplied by 100 and shown with a percent sign, such as 2%.
How do I find absolute error?
Subtract the true value from the measured value and drop the sign: absolute error = |measured − true|. It is in the same units as the two values being compared, unlike relative or percent error, which are unitless.
Why does relative error matter if I already have absolute error?
A 1 cm absolute error is negligible on a 100 metre measurement and severe on a 2 cm one. Relative error puts the absolute figure in proportion to the size of what was measured, which is what makes errors comparable across very different scales.
What does a negative signed error mean?
A negative signed error means the measured value came in below the true value; a positive one means it came in above. Absolute and relative error both report the size of that gap only, with the direction stripped out.
For the same figures reported purely as a percentage, see the percent error calculator.