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Percent Error Calculator

Enter your measured (experimental) value and the accepted (theoretical) value to get the percent error, signed error, absolute and relative error, worked out step by step. Ran several trials? Paste them all to get the error of the mean and of each trial.

Measurements
Enter your values to see the result.
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How to use the Percent Error Calculator

  1. Choose one value or several trials.
  2. Enter the experimental value, or paste all trial results separated by commas or new lines.
  3. Enter the theoretical value: the accepted or true value from a textbook or reference.
  4. Read the percent error and whether the result was high or low.
  5. Check the steps, table and chart, or copy the results for your lab report.

How to calculate percent error

Percent error = |experimental − theoretical| ÷ |theoretical| × 100

  1. Subtract the theoretical value from the experimental value.
  2. Take the absolute value (drop any minus sign).
  3. Divide by the absolute theoretical value.
  4. Multiply by 100 to get a percentage.

Example: a student measures the boiling point of water as 98.2 °C at sea level, where the accepted value is 100 °C. |98.2 − 100| ÷ 100 × 100 = 1.8%, and the signed error is −1.8% (too low).

Related error measures

MeasureFormulaExample (9.6 vs 9.81)
Absolute error|E − T|0.21
Relative error|E − T| ÷ |T|0.021407
Percent error|E − T| ÷ |T| × 1002.141%
Signed percent error(E − T) ÷ |T| × 100−2.141%
Percent difference|a − b| ÷ ((a + b) ÷ 2) × 1002.164%

E is the experimental (measured) value and T the theoretical (accepted) value. Sources of error include instrument resolution, calibration, reading technique (parallax), environmental conditions and the approximations built into the method.

Frequently asked questions

What is the percent error formula?

Percent error = |experimental − theoretical| ÷ |theoretical| × 100. Measuring g = 9.6 m/s² when the accepted value is 9.81 m/s² gives |9.6 − 9.81| ÷ 9.81 × 100 ≈ 2.141%.

Can percent error be negative?

The standard percent error uses the absolute value, so it is never negative. Some teachers and fields use the signed version, (experimental − theoretical) ÷ theoretical × 100, where a negative result means the measurement was too low. The calculator shows both.

What is a good percent error?

It depends on the experiment and the equipment. In many school labs under about 5% is considered good and under 10% acceptable, but precise lab work may require far less than 1%. Your instructor or method sets the standard.

What is the difference between percent error and percent difference?

Percent error compares a measurement with a known true value. Percent difference compares two measurements when neither is known to be correct, dividing by their average: |a − b| ÷ ((a + b) ÷ 2) × 100.

Why can't the theoretical value be zero?

The formula divides by the theoretical value, and dividing by zero is undefined. When the true value is 0, report the absolute error |experimental − 0| instead.

How do I find percent error for several trials?

The usual approach is to average the trials first and calculate the percent error of the mean. You can also compute the percent error of each trial; their average is never smaller than the error of the mean, because high and low results do not cancel.

What is the difference between accuracy and precision?

Accuracy is how close results are to the true value, which percent error measures. Precision is how close repeated results are to each other, which the standard deviation and relative standard deviation of your trials measure.

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