Percent Error Calculator
This percent error calculator tells you how far a measured, experimental result deviates from the true, theoretical value, expressed as a percentage. Just enter the value you measured and the accepted true value, and it instantly returns both the percent error and the absolute error. Percent error is one of the most common ways to report accuracy in physics, chemistry and engineering lab work, because it puts the size of a mistake in context: an error of 2 grams matters very differently on a 10-gram sample than on a 10-kilogram one. A smaller percent error means your measurement is closer to the accepted value.
Percent error
Absolute error
Percent error = |measured value − true value| / |true value| × 100. If the true value is 0, the percent error is undefined.
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How it works
Percent error compares your measurement to the accepted true value using the formula: percent error = |measured − true| / |true| × 100. First subtract the true value from the measured value and take the absolute value, so the sign is dropped; this is the absolute error. Then divide by the absolute value of the true value and multiply by 100 to express it as a percentage. For example, if you measure the boiling point of water as 98.2 °C when the accepted value is 100 °C, the absolute error is |98.2 − 100| = 1.8, and the percent error is 1.8 / 100 × 100 = 1.8%. The absolute value is used because we care about the magnitude of the deviation, not its direction.
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Preguntas frecuentes
- What is the difference between percent error and percent difference?
- Percent error compares a measured value against a known, accepted true value — it assumes one value is correct. Percent difference compares two experimental values when neither is considered the reference; it divides the absolute difference by the average of the two values. Use percent error in a lab when you have an accepted or textbook value to compare against.
- Can percent error be negative?
- By the standard formula it cannot, because it uses the absolute value of the difference, so the result is always zero or positive. Some instructors ask for signed error to show whether the measurement was too high or too low; in that case you drop the absolute value in the numerator, and a negative result means your measurement was below the true value.
- Why do we use the absolute value in percent error?
- The absolute value ensures the error reflects the magnitude of the deviation, not its direction. A measurement that is 2 units too high and one that is 2 units too low are equally inaccurate, so both should give the same positive percent error rather than canceling out.
- What is a good percent error?
- It depends on the field and the equipment. In a school physics or chemistry lab, an error under about 5% is often considered acceptable, while precision engineering or analytical chemistry may require well under 1%. A larger percent error suggests measurement mistakes, faulty equipment or an incorrect reference value.
- What if the true value is zero?
- Percent error is undefined when the true value is zero, because the formula divides by the true value and dividing by zero is not possible. In that situation report the absolute error instead, or use percent difference against a nonzero reference.