If you ever wondered what's the difference between relative and absolute error, our relative error calculator is right up your alley. Below you'll discover the absolute and relative error formulas, together with easy-to-follow examples. You'll also find a short section on the differences between the two types of error, as well as one on the reason why the relative error is considered to be more useful.
What is the absolute error?
The absolute error — also called the approximation error — is the absolute value of the difference between the actual value and the measured value. The absolute error formula is:
absolute error = |actual value − measured value|
The actual value is otherwise known as the real or true value. On the other hand, the measured value is an approximation.
Very often we talk about absolute error to indicate how inaccurate a measuring device is. For example, imagine that you have a bathroom scale that only displays the result in full pounds — it can't get more accurate than that. Hence, if you weigh e.g. 140 lbs, you can say that your weight is 140 ± 0.5 lbs, with the measured value equal to 140 lbs and the absolute error equal to 0.5 lb. The actual value will be somewhere between 139.5 and 141.5 lbs.
Remember that the absolute error is expressed in the same unit as the measured and real values. For example, if you measured the height of a tree in feet, the absolute error would also be expressed in feet.
What is the relative error?
Relative error (or percent error), on the other hand, expresses the error in terms of a percentage. You can use the following relative error formula:
relative error = |absolute error / actual value| = |(actual value − measured value) / actual value|
We typically express both the absolute and relative errors as positive values, hence the use of absolute values.
The relative error compares the absolute error to the actual value of the property you're measuring. For example, let's say you measure your child's height in a doctor's office to the highest degree of accuracy, so the actual value is equal to 121.2 cm. When you measure your child at home, you find the measured value to be 120.5 cm.
The relative error is:
|(121.2 − 120.5) / 121.2| = 0.00578 = 0.578%
As you can see, the relative error is expressed as a percentage and is unitless. Whether you're analyzing length, weight, or temperature, the unit doesn't influence the result.
How to calculate the absolute error and relative error
- Identify the actual (true) value — the reference figure you trust.
- Identify the measured value — the figure produced by your experiment or instrument.
- Compute the absolute error: subtract the measured value from the actual value and take the absolute value of the difference.
- Compute the relative error: divide the absolute error by the actual value (still as an absolute value).
- Convert to a percentage by multiplying the relative error by 100.
Is my absolute error too high?
There is no universal threshold — the acceptable error depends on the field, the instrument, and what you are measuring. However, the relative error (expressed as a percentage) gives a useful, dimensionless yardstick:
| Percent error | Typical interpretation |
|---|---|
| < 1% | Excellent — research-grade accuracy |
| 1% – 5% | Good — appropriate for most engineering and lab work |
| 5% – 10% | Acceptable — fine for rough estimates, may require improvement |
| > 10% | High — consider re-calibrating, re-measuring, or using a more precise instrument |
FAQs
What is the difference between absolute and relative error?
The absolute error measures the size of the deviation in the same unit as the original measurement (cm, kg, $, etc.). The relative error compares that deviation to the actual value and expresses it as a fraction or percentage. The relative error is dimensionless and lets you compare accuracy across measurements with different units or scales.
Why is the relative error often more useful than the absolute error?
An absolute error of 1 cm is enormous when measuring a coin, but negligible when measuring a football field. The relative error puts the deviation in context with the actual value, so a 1 cm error on a coin of 2 cm diameter becomes 50% (very large), while 1 cm on a 100 m field is 0.001% (very small).
Can the absolute or relative error be negative?
Both formulas use absolute values, so the result is always a non-negative number. Some texts use a signed error to indicate whether the measurement is an overestimate or an underestimate, but the standard absolute / relative error is always reported as a positive value.
Does this calculator support currencies and imperial units?
Yes. You can choose between a pure number, the metric (SI) system, the US / imperial system, or one of 22 world currencies (USD, RUB, EUR, GBP, JPY, CNY, AUD, CAD, CHF, INR, MXN, BRL, KRW, TRY, SEK, NOK, DKK, PLN, CZK, HUF, ILS, ZAR). The absolute error is reported with the unit you choose; the relative error is always a unitless percentage.
What should I do if my actual value is zero?
The relative error is undefined when the actual value is zero, because dividing by zero is not possible. In that case use the absolute error only, or pick a non-zero reference value if your context allows it (for example, a typical or expected value instead of zero).