Percent Error Calculator

How to use the percent error calculator

Enter the experimental value (what you measured or calculated) and the theoretical value (the accepted, true or textbook value). The calculator shows:

• Percent error, the headline figure most lab reports ask for.
• Absolute error, the size of the difference in the original units.
• Relative error, the same comparison as a decimal fraction rather than a percentage.
• Signed percent error, which tells you whether you measured too high or too low.

Use the rounding menu to report the answer to 2, 3 or 4 significant figures. The working shows the unrounded value too, so you can round at the end, as you should.

Percent error formula

Percent error = |E − T| ÷ |T| × 100

• E = experimental (measured) value
• T = theoretical (accepted) value
• | | = absolute value, which drops any minus sign

The two building blocks are the absolute error, |E − T|, and the relative error, |E − T| ÷ |T|. Multiplying the relative error by 100 turns it into a percentage. The signed version, (E − T) ÷ |T| × 100, keeps the direction: positive when the measurement is too high, negative when it is too low.

Worked examples

Physics: acceleration due to gravity. A pendulum experiment gives g = 9.6 m/s². The accepted value is 9.81 m/s².

1. Difference: 9.6 − 9.81 = −0.21
2. Absolute error: |−0.21| = 0.21 m/s²
3. Relative error: 0.21 ÷ 9.81 = 0.021407
4. Percent error: 0.021407 × 100 = 2.1407%, or 2.14% to three significant figures. The signed error is −2.14%, so the measurement was low.

Chemistry: density of aluminum. You measure 2.6 g/cm³; the accepted value is 2.70 g/cm³. The absolute error is 0.1 and the percent error is 0.1 ÷ 2.70 × 100 = 3.7037%, which is 3.70% to three significant figures.

Percent error vs percent difference vs percent change

These three formulas look alike but answer different questions:

• Use percent error when one value is known to be correct, such as a textbook constant.
• Use percent difference when comparing two measurements and neither is the “true” one, such as two students’ results.
• Use percent change when a value moved from a starting point, such as a price or a population over time.

Percent error and percent change share the same arithmetic when the accepted value plays the role of the old value. The difference is the meaning, and percent error normally drops the sign. The percentage calculator handles percent change and percent difference with worked steps.

Significant figures in percent error

Keep every digit while you calculate and round only the final answer. Rounding the relative error 0.021407 to 0.02 before multiplying by 100 would turn a 2.14% error into 2%, hiding a real difference. Most lab reports quote percent error to two or three significant figures, which matches the precision of typical school equipment. Note that trailing zeros count: 3.70% (three significant figures) claims more precision than 3.7% (two).

Common mistakes

• Dividing by the wrong value. Always divide by the theoretical value. Dividing by your measurement gives 0.21 ÷ 9.6 = 2.19% in the gravity example, which is a different (and wrong) answer.
• Forgetting the absolute value, then reporting a negative percent error when the formula calls for a positive one.
• Mixing units. Convert both values to the same unit first. Temperature is a special case: percent error depends on the scale. Measuring water’s boiling point as 98.6 °C gives a 1.4% error in Celsius, but the same reading in kelvin (371.75 K vs 373.15 K) is only a 0.375% error. Kelvin is the safer choice for temperature, since it starts at absolute zero.
• Confusing accuracy with precision. Percent error measures accuracy (closeness to the true value). Repeated measurements that agree closely with each other are precise, which you can check with the standard deviation calculator.

If you took several readings, average them first with the average calculator, then compare the mean with the accepted value.