Percent Error Calculator

Percent error, absolute error, and relative error between a measured and an accepted value.

What it does

Percent error answers the lab report question: how far off was the measurement, relative to the value it was aiming at? One subtraction, one division, one conversion to a percentage, and a result that reads well in a conclusion paragraph.

The tool above takes the measured value and the accepted value and returns all three common ways of stating the gap: the percent error, the plain absolute difference, and the decimal relative error for further calculations.

The defaults compare a 2.45 g measurement against a 2.70 g accepted value: an absolute error of 0.25, a relative error of 0.0926, and a percent error of 9.26 %. Slide the measured value up to 2.65 and the error falls to 1.85 %, which is often the difference between a good and a great result in a student lab.

The formula and its distinction from percent difference and uncertainty follow standard lab references: the measurement and error appendices from Maricopa and Bates, and NIST's Technical Note 1297 on expressing uncertainty, the international reference for doing this rigorously.

How to use

1. Enter the value you measured, with its sign if it has one.
2. Enter the accepted or true value as the reference.
3. Read the percent error first for reporting.
4. Use the absolute error when units matter more than ratios.
5. Use the relative error when it feeds into further calculations.

Formula

measured

The experimental value you are checking.

accepted

The reference value the measurement is compared against.

percent error

The relative gap expressed as a percentage.

relative error

The same gap as a decimal fraction.

Taking absolute values in numerator and denominator means a negative accepted value, like a heat of reaction or a freezing-point depression, produces a sensible positive error instead of a sign puzzle. Only one case genuinely breaks the formula: an accepted value of exactly zero, because the division has no answer, which is why the tool suggests absolute error there. Keep the vocabulary straight: percent error points at a reference value, percent difference compares two measurements with each other, and percent uncertainty describes the spread of repeated measurements of the same thing.

Worked example

Reference table

Limits

• The accepted value must be nonzero for percent error to exist.
• Assumes the accepted value is a legitimate reference.
• Does not judge whether the error is statistically significant.
• Reports magnitudes only; it will not tell you which way you missed.

Common mistakes

• Dividing by the measured value instead of the accepted value.
• Calling it percent difference when a reference value exists.
• Averaging signed errors until they cancel to zero.
• Reporting more decimal places than the measurement supports.
• Forcing the formula when the accepted value is zero.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• Maricopa Community Colleges: Measurements and Error Analysis
• Bates College laboratory guide: Error and uncertainty
• NIST Technical Note 1297: Guidelines for Evaluating and Expressing Uncertainty

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