Percent Error Calculator

Percent error formula

• Percent error = |Measured − Accepted| ÷ |Accepted| × 100
• Signed percent error = (Measured − Accepted) ÷ |Accepted| × 100 (positive = too high, negative = too low)

The vertical bars mean absolute value, so standard percent error is never negative. Many lab teachers also want to know the direction of the error, which the signed version shows.

How to calculate percent error: step by step

1. Subtract the accepted value from the measured value.
2. Take the absolute value of the difference.
3. Divide by the absolute value of the accepted value.
4. Multiply by 100 to get a percentage.

Example: a student measures gravitational acceleration as 9.6 m/s²; the accepted value is 9.81 m/s². Difference = 9.6 − 9.81 = −0.21; absolute error 0.21; 0.21 ÷ 9.81 = 0.0214; × 100 = 2.14%. The signed error is −2.14%, meaning the measurement was too low.

More worked examples

Percent error vs percent difference vs percent change

For 9.6 and 9.81 the percent difference is 0.21 ÷ 9.705 × 100 = 2.16% – close to the percent error, but based on the average of the two values instead of the accepted value.

Percent error, margin of error and standard error

Percent error compares one result with a known value. Margin of error and standard error come from statistics: they describe the uncertainty of an estimate based on a sample, without knowing the true value. A survey's ±3% margin of error is not a percent error.

What is a good percent error?

It depends on the experiment and the instruments. In many school labs a percent error under about 5% is treated as good agreement, but precise lab work may require less than 1%. A large error usually points to a systematic problem – an uncalibrated instrument, heat loss, parallax – rather than random variation.

How to reduce percent error

• Calibrate instruments against a known standard before you start.
• Repeat the measurement and use the average to reduce random error.
• Use the most precise instrument available and record all its digits.
• Control conditions such as temperature and draughts.
• Report results with sensible rounding – see our rounding calculator.

Percent yield in chemistry is a related but different measure: actual yield ÷ theoretical yield × 100. A 92% yield means 8% of the possible product was lost, not that the measurement was 8% wrong.

Sources

1. Systematic errors push every result the same way – an uncalibrated balance, a thermometer that reads 1 °C high, reading a scale at an angle (parallax).
2. Random errors scatter results above and below the true value – small fluctuations in timing, temperature or reading the last digit.
3. Method errors – heat lost to the surroundings, incomplete reactions, or an assumption in the formula that doesn't hold.
4. NIST/SEMATECH e-Handbook of Statistical Methods – Measurement process characterization — itl.nist.gov/div898/handbook/mpc/mpc.htm