The formula, and why the true value goes on the bottom
Take the absolute difference between your measured and true values, divide by the true value, and multiply by 100 for a percentage. The true (accepted) value is the denominator because it is the fixed reference — that keeps the result comparable no matter what you measured. If the true value is zero, relative error is undefined; report the absolute error instead.
What a percent error actually tells you
The same 5% error is excellent for a rough field estimate and alarming for a calibrated instrument. Judge it against the context, not a single cutoff.
| Percent error | Reading | Typical context |
|---|---|---|
| < 1% | Excellent | Lab calibration, astronomy |
| 1–5% | Very good | Most school and lab experiments |
| 5–10% | Good | Engineering work within tolerance |
| 10–20% | Acceptable | Estimates and approximations |
| > 20% | Poor | Check for a systematic error |
A worked case: measured 45.3 m against a true 45.0 m gives |45.3 − 45.0| ÷ 45.0 = 0.667%, an excellent result.
The things people get wrong
- Dividing by the wrong number. Use the true value on the bottom, not the measured one.
- Dropping the units label. "0.05" is meaningless on its own; say "5%" or "0.05 relative".
- Percent error vs percentage points. Going from 48% to 52% is a 4 percentage-point change, but an 8.3% relative error — different things.
- Rounding too early. Carry full precision through the division and round only the final answer.
Common questions
What is the difference between absolute and relative error?
Absolute error is the plain difference, measured minus true, in whatever units you used, such as 0.3 meters. Relative error divides that by the true value, so it comes out as a fraction or percentage. Relative error lets you compare accuracy across measurements of very different size.
Do you divide by the true value or the measured value?
By the true value. It is the fixed reference, so the same measurement quality always gives the same percentage. Dividing by the measured value would shift the result depending on how far off you were.
Can relative error be more than 100%?
Yes. If the measured value is 5 and the true value is 1, the error is 400%, meaning the reading is five times the real amount. Errors above 100% almost always point to a mistake in units or method.
