Percent Error Calculator

Calculate percent error between a measured and accepted value. See absolute error and accuracy analysis for labs, experiments, and quality checks.

Error Analysis

Experimental Value

Measured or observed value

Theoretical Value

Expected or true value

Common Examples

Error Types

Absolute Error: |Experimental - Theoretical|

Relative Error: Absolute Error / |Theoretical|

Percent Error: Relative Error × 100%

Percent Error

0.102%

Excellent accuracy

Absolute Error

0.01

Difference magnitude

Accuracy

99.9%

100% - % Error

Relative Error

0.001019

Fractional error

Status

Accurate

< 5% error

Error Analysis

Experimental Value:9.8

Theoretical Value:9.81

Difference:-0.01

Calculation

Formula: % Error = |Experimental - Theoretical| / |Theoretical| × 100%

Calculation:
|9.8 - 9.81| / |9.81| × 100%
= 0.01 / 9.81 × 100%
= 0.102%

Interpretation: Experimental value is 0.10% lower than theoretical value

Accuracy Scale

< 1%Excellent

1% - 3%Very Good

3% - 5%Good

5% - 10%Fair

> 10%Poor

How it works

Percent error measures how far a measured or estimated value is from the true value, as a percentage. You take the absolute difference, divide by the true value, and multiply by 100. Smaller is better — it's a standard accuracy check in science and engineering.

Percent error

Percent error = |measured − actual| ÷ |actual| × 100

measured: your experimental/estimated value
actual: the true or accepted value

Worked example

Measured = 9.7
Actual (accepted) = 10

|9.7 − 10| = 0.3
0.3 ÷ 10 × 100

Percent error = 3%.

Good to know

The absolute value keeps the error positive whether you over- or under-shot.
Divide by the accepted (true) value, not your measurement.
Lower percent error means higher accuracy; it pairs with precision (repeatability) for a full picture.

Related Calculators

Frequently Asked Questions

What is percent error?

Percent error measures how far a measured or experimental value is from the true (accepted) value: |measured - true| / |true| x 100. It expresses accuracy as a percentage so results from different scales can be compared.

Can percent error be negative?

By convention percent error uses an absolute value, so it's reported as positive. Some fields keep the sign to show direction — negative means you underestimated, positive means you overestimated.

What is the difference between percent error and percent difference?

Percent error compares a measurement to a known true value. Percent difference compares two equally valid measurements to each other, dividing by their average instead of an accepted reference.

What is an acceptable percent error?

It depends on context: precision instruments may demand under 1%, typical chemistry or physics lab work aims for under 5%, and rough engineering estimates may tolerate 10% or more.

What if the true value is zero?

Percent error divides by the true value, so it is undefined when the accepted value is zero. In that case report the absolute error instead, or compare against a different reference quantity.