What this calculator does
Find out how far off a measurement is, as a percent of the value it should have been. Say a lab group measures 52.3 g for a sample known to weigh 50 g. They're 2.3 g off, which is a 4.6% error. Putting the gap as a percent lets you compare experiments of very different sizes.
Enter the measured (experimental) value and the true (theoretical or accepted) value. Choose absolute to get the usual figure, which is always positive. Or choose signed to see whether the measurement came out high or low.
Where it's used
Why this math matters outside the classroom:
- Lab experiments. A student who measures g as 9.6 m/s² against the accepted 9.81 m/s² has a percent error of about 2.1%.
- Kitchen scales. A kitchen scale that reads 510 g for a 500 g test weight has a 2% error.
- Estimation games. A student who guessed 80 jelly beans in a jar holding 100 was off by 20%.
- Machined parts. A machinist finds that a part measured at 25.1 mm against a 25.0 mm spec is off by 0.4%.
- Rain forecasts. A forecaster who predicted 2.2 inches of rain when 2.0 inches fell had a 10% error.
Grade level and standards: Grade 7; Common Core State Standards for Mathematics 7.RP.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter your measured or experimental value — the number you observed.
- Enter the true value: the theoretical, accepted or reference value you're comparing against. It can't be zero.
- Choose absolute (the size of the error only) or signed (positive when the measurement is too high, negative when it's too low).
- Read the percent error, the raw error and the relative error. Each step of the calculation is shown underneath.
What the inputs mean
- Measured (experimental) value
- The value you obtained by experiment, estimate or calculation. It may be zero or negative.
- True (theoretical) value
- The value treated as correct: a textbook constant, a manufacturer's specification, or a carefully measured reference. The formula divides by it, so it can't be zero.
- Report as
- Most lab reports give the absolute percent error. The signed version keeps the direction. That helps you spot a steady lean one way, such as an instrument that always reads high.
Formula and method
percent error = |measured − true| ÷ |true| × 100 signed percent error = (measured − true) ÷ |true| × 100
The bars | | mean absolute value: the size of a number with any minus sign dropped. The top of the fraction is the error itself, the gap between what you measured and what was expected. Dividing by the size of the true value turns it into a relative error, a fraction of the true value. Multiplying by 100 makes it a percent.
The signed form keeps the sign of measured − true. So +3% means the measurement was 3% too high, and −3% means 3% too low. The calculator divides by the absolute value of the true value. That way the sign always shows the direction of the measurement, even when the true value is negative.
Worked example
A sample with an accepted mass of 50 g is weighed on a classroom scale at 52.3 g.
- Find the error: 52.3 − 50 = 2.3 g.
- Take the absolute value: |2.3| = 2.3.
- Divide by the true value: 2.3 ÷ 50 = 0.046.
- Multiply by 100: 0.046 × 100 = 4.6%.
Result: The percent error is 4.6%. In signed form it's +4.6%, meaning the scale read high.
Understanding the result
Smaller is better, but what counts as good enough depends on the setting. A few percent is often fine in an intro lab. Precision manufacturing or analytical chemistry may need well under 1%.
Percent error can go over 100%. Measuring 30 when the true value is 10 is a 200% error: the gap is twice the size of the true value.
If the sign stays the same across repeated trials, that points to a systematic error, like a badly calibrated instrument. Random scatter would land on both sides.
Assumptions and limitations
- The true value is known and treated as exact. All of the error is blamed on the measurement.
- The difference is worked out on the decimals you typed. So 52.3 − 50 is exactly 2.3, without the tiny rounding noise computers can add.
- Percent error has no answer when the true value is zero. It gets very large and jumpy when the true value is close to zero. In those cases, report the absolute error with its unit instead.
- For temperatures and other scales where zero doesn't mean "none at all", the result depends on the scale used. An error of 1 degree is a different percent in °C than in K. Use a scale that starts at true zero, such as kelvin, if you need a meaningful ratio.
- To compare two measurements when neither is the accepted value, use percentage change or percentage difference instead.
Frequently asked questions
Can percent error be negative?
The usual percent error uses an absolute value, so it's never negative. The signed version can be. A negative result means the measured value is below the true value. Pick whichever your course or report asks for.
What is the difference between percent error and percent change?
Percent error compares a measurement against a value known to be correct. Percent change compares a new value against an old one, with no idea of which is right. The arithmetic is similar, but the value you compare against plays a different role.
Why can't the true value be zero?
The formula divides by the true value. Dividing by zero has no defined result, so there is no meaningful percent. Report the raw difference, with its unit, instead.
What is relative error?
Relative error is the same comparison as a plain fraction instead of a percent: 2.3 ÷ 50 = 0.046. Percent error is just the relative error multiplied by 100.
How this calculator is checked
Method: Standard definition of percent error: |measured − true| ÷ |true| × 100. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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