Relative error calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- Absolute error = |measured − true| = 0.01.
- Relative error = absolute error ÷ |true value| = 0.01 ÷ 9.81 = 0.001019.
- Multiply by 100 for percent: 0.101937%.
| Inputs | Answer |
|---|---|
| Measured or approximate value: 9.8; True or accepted value: 9.81 | The relative error is |9.8 − 9.81| ÷ |9.81| = 0.001019, or 0.101937%. |
| Measured or approximate value: 102; True or accepted value: 100 | The relative error is |102 − 100| ÷ |100| = 0.02, or 2%. |
| Measured or approximate value: 48; True or accepted value: 50 | The relative error is |48 − 50| ÷ |50| = 0.04, or 4%. |
How to use it
Absolute error is the size of the difference between a measured value and the true value. Relative error divides that by the true value, so it tells you how large the error is compared with what you were measuring: relative error = |measured − true| ÷ |true|.
Multiply by 100 to get the percent error. Relative error is undefined if the true value is 0. The calculator also says whether the measurement was an overestimate or an underestimate.
Frequently asked questions
What is the formula for relative error?
|measured − true| ÷ |true|.
Is relative error the same as percent error?
Percent error is the relative error times 100.
Can relative error be negative?
With the absolute value it cannot; some books keep the sign to show over- or underestimates.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.