Percent error calculator
Enter what you measured and the accepted (true) value. You get the percent error |measured − true| / |true| × 100, the absolute error, and the signed version that tells you whether the measurement came out too high or too low.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Type the value you measured in the first box.
- Type the accepted or theoretical value in the second box.
- Read the percent error at the top. The rows below give the absolute error, the signed error and a plain-words direction.
How it works
The tool subtracts the true value from the measured one, takes the absolute value, divides by the absolute value of the true value and multiplies by 100. Dividing by |true| rather than true keeps the answer positive when the true value is negative. The signed version skips the absolute value on the top, so it shows whether you overshot or undershot.
Worked example
A student measures the boiling point of water as 98.5 °C; the accepted value at sea level is 100 °C.
- Error: 98.5 − 100 = −1.5
- Percent error: 1.5 / 100 × 100 = 1.5%
- Signed percent error: −1.5%, so the measurement is lower than the true value.
Tips
- Use the same units for both values. Mixing grams and kilograms gives a meaningless percentage.
- Do not round the inputs first. Round only the final answer.
- A tiny true value makes percent error huge even for a small absolute miss. In that case also report the absolute error.
Frequently asked questions
What is the percent error formula?
Percent error = |measured − true| / |true| × 100. The vertical bars mean absolute value, so the result is never negative. A measured 9.5 against a true 10 gives |−0.5| / 10 × 100 = 5%.
Can percent error be negative?
In the standard definition it cannot, because of the absolute value. Some courses keep the sign to show the direction of the miss. That is the signed percent error row here, where negative means you measured below the true value.
What is a good percent error?
It depends on the field and the instrument. In school labs under 5% is often counted as good and under 1% as excellent, but a physics experiment may demand far less and a rough field estimate may accept more. Your instructor or method sets the standard.
Why can the true value not be 0?
The formula divides by the true value, and division by zero has no answer. When the true value is 0 you can still report the absolute error, but a percentage of zero has no meaning.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known true value, dividing by that value. Percent difference compares two values that are both measurements and divides by their average, so neither is treated as the reference.