LabCalc

Percentage Error Calculator

How far off your measurement is from the accepted value, as a percentage.

Experimental value

Theoretical value

Percentage error (%)

4.082

% error = |exp − theo| / |theo| × 100

Absolute error: 0.4

What you entered

Experimental value: 10.2Theoretical value: 9.8

1
Absolute error = |experimental − theoretical|
|10.2 − 9.8|= 0.4
2
Percentage error = |error| / |theoretical| × 100
0.4 / 9.8 × 100= 4.0816%

Result

Percentage error (%): 4.082

The measurement of 10.2 vs. the accepted value of 9.8 has a percentage error of 4.08%.

Percentage error between measured and accepted values

Percentage error is the absolute difference divided by the theoretical value, times 100.

Experimental	Theoretical	Absolute error	Percentage error
9.8	9.81	0.0100	0.1019
3.14	3.14159	0.0016	0.0506
10.2	10	0.2000	2.0000
98	100	2.0000	2.0000
105	100	5.0000	5.0000

Rows three and four both give 2% from very different absolute errors, which is the point of expressing error relatively - 0.2 out of 10 and 2 out of 100 are equally good measurements. The first row is a typical school pendulum result for g, accurate to about 0.1%. Percentage error uses the accepted value as the denominator, which distinguishes it from percentage difference, where neither value is privileged. The absolute value is taken, so the result never carries a sign and says nothing about whether the measurement was high or low.

Absolute vs. percentage error

Absolute error (|experimental − theoretical|) tells you how far off you are in the same units; percentage error normalizes this by the theoretical value, making it possible to compare accuracy across different scales. Being off by 1 gram matters more when measuring 10 grams than 10 kilograms.

Every lab report needs this

Percentage error is the standard way to report measurement accuracy in science classes and research labs. Values under 5% are generally considered good for student experiments; professional instruments aim for well under 1%. Systematic errors (consistently high or low) are more concerning than random scatter.

Frequently asked questions

My experiment measured the boiling point of water as 99.1 °C — what's my percentage error?

Theoretical value is 100 °C. Absolute error = |99.1 − 100| = 0.9 °C. Percentage error = (0.9 / 100) × 100 = 0.9%. That's well within the acceptable range for most student experiments.

How is percentage error different from percentage change?

Percentage error compares a measurement to a known correct value (the theoretical/accepted value). Percentage change compares two values over time with no 'correct' reference point. Use the percentage change calculator when neither value is the accepted truth.

My percentage error came out negative — is that possible?

The standard formula uses absolute value, so percentage error is always positive (or zero). A negative sign would indicate direction (overestimate vs. underestimate), which some fields call 'relative error.' This calculator reports the unsigned percentage error, which is the most common convention.

What's considered an acceptable percentage error?

It depends on the field. Student physics labs typically accept under 5%. Analytical chemistry expects under 1%. Industrial quality control varies by specification — a machined part might need error below 0.01%. There's no universal threshold; check your course or industry standard.