About the Percent Error Calculator
This percent error calculator measures how far an experimental or estimated value is from the accepted (true, theoretical or reference) value. Enter both numbers and it returns the percent error, the absolute error and the relative error, plus a signed version that tells you whether you overshot or undershot.
It is written for chemistry and physics lab reports, where students compare a measured density, acceleration or yield with the textbook value, but it works just as well for checking a forecast against actual sales, a scale against a calibration weight, or an estimate against a final invoice.
Percent error is conventionally reported as a positive number, because it describes the size of the miss rather than its direction. The accepted value must not be zero, since the error is expressed as a fraction of it.
With the default inputs, the percent error is 2.1407%. Change any value above to recalculate instantly.
How to use the percent error calculator
- 1Enter the value you measured or estimated.
- 2Enter the accepted, true or theoretical value.
- 3Read the percent error (always positive).
- 4Use the signed error to see whether you were too high or too low.
Formula and method
First find the absolute error, the size of the difference between your value and the accepted value. Dividing by the accepted value gives the relative error, which puts the miss in proportion — being 1 cm off matters far more on a 10 cm object than on a 10 m one. Multiplying by 100 turns it into a percentage.
The signed percent error keeps the direction: (experimental − accepted) ÷ |accepted| × 100. A positive value means your measurement was too high and a negative value means it was too low, which can hint at systematic errors in an experiment.
- experimental
- The value you measured, estimated or calculated
- accepted
- The true, theoretical or reference value
Worked examples
Measuring gravity in a lab
A pendulum experiment gave g = 9.6 m/s² against the accepted 9.81 m/s². The absolute error is 0.21, and 0.21 ÷ 9.81 × 100 = 2.14% — the measurement was slightly low.
Density of aluminium
A measured density of 2.85 g/cm³ versus the accepted 2.70 g/cm³ is 0.15 too high. 0.15 ÷ 2.70 × 100 = 5.56% error.
Sales forecast vs actual
Forecasting $1.6M when actual sales were $1.5M is an error of 0.1 ÷ 1.5 = 0.0667, or 6.67%.
Frequently asked questions
How do you calculate percent error?+
Subtract the accepted value from the experimental value, take the absolute value, divide by the accepted value and multiply by 100. For example, measuring 52 when the true value is 50 gives |52 − 50| ÷ 50 × 100 = 4%.
Can percent error be negative?+
By the usual definition no — the absolute value makes it positive. Some teachers and fields use the signed form, where a negative result means the measurement was below the accepted value.
What is a good percent error?+
It depends on the field and equipment. In introductory lab work, under 5% is often considered good and under 10% acceptable, while precision engineering or analytical chemistry may require well under 1%.
What is the difference between percent error and percent difference?+
Percent error compares a value with a known correct reference. Percent difference compares two values when neither is the reference, dividing by their average instead.
Why can’t the accepted value be zero?+
Percent error divides by the accepted value, and division by zero is undefined. In that case report the absolute error with units instead.