How to use the Percentage Error Calculator
- Enter your measured (experimental) value.
- Enter the true or accepted value.
- Read the percentage error, the absolute error and the direction.
- A smaller percentage error means a more accurate measurement.
Formula used
Percentage error = |measured − true| ÷ |true| × 100. The signed error is (measured − true) ÷ |true| × 100, positive when the measurement is too high.
Worked example
Here is the Percentage Error Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Measured (experimental) value | 9.6 |
| True (accepted) value | 9.81 |
| Result | |
| Percentage error | 2.14% |
| Absolute error | 0.21 |
| Direction | Measured value is too low |
The formula and an example
Percentage error = |measured − true| ÷ |true| × 100. Suppose you measure the acceleration due to gravity as 9.6 m/s² in an experiment, and the accepted value is 9.81 m/s². The absolute error is |9.6 − 9.81| = 0.21, and the percentage error is 0.21 ÷ 9.81 × 100 = 2.14%. Your measurement was too low.
If you had measured 10.2 instead, the absolute error is 0.39 and the percentage error 3.98%, and the direction is “measured value is too high”.
Absolute error versus percentage error
The absolute error is the plain difference between the two values, in the same units. The percentage error divides it by the true value, so you can compare accuracy across different scales. An error of 1 cm is large when measuring a 10 cm object (10%) and tiny when measuring a 10 m wall (0.1%).
Using the same absolute error of 0.5 on a true value of 5 gives 10%, but on a true value of 500 it gives 0.1%.
Percentage error, percentage difference and percentage change
These are different measures. Percentage error compares a measurement with a known true value. Percentage difference compares two values when neither is the reference, usually dividing by their average. Percentage change compares a new value with an old one. Use the percentage change calculator on this site for increases and decreases over time.
Some textbooks define percentage error with a sign, so a measurement that is too low gives a negative percentage. This calculator shows the size of the error and gives the direction in words.
Reducing error in measurements
Errors come from the instrument, the method and the person doing the measuring. Repeating a measurement and taking the average reduces random errors, calibrating instruments reduces systematic errors, and using a more precise instrument shrinks both.
A small percentage error does not prove a method is right, because a systematic error can be consistent. Compare against several known values when you can.
Frequently asked questions
How do I calculate percentage error?
Subtract the true value from the measured value, take the absolute value, divide by the true value and multiply by 100.
Can percentage error be negative?
The standard formula uses absolute values and is never negative. Some textbooks keep the sign to show direction; this calculator shows the direction separately.
What if the true value is zero?
Percentage error is undefined, because you cannot divide by zero. Use the absolute error instead.
What is a good percentage error?
It depends on the field. In school labs, under 5% is often considered good, while precision work needs far less.
Is percentage error the same as percent change?
No. Percent change compares a new value with an old one. Percentage error compares a measurement with a true value.
Does it matter which value goes in which box?
Yes. The true value is the divisor, so swapping the two gives a different result.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.