Percent Error Calculator
Calculate percentage error between observed experimental data and true theoretical values.
Measuring how wrong a measurement is
Percent error compares a measured value against an accepted one:|measured − actual| / actual × 100. Dividing by the actual value is what makes it comparable across scales — being 2 cm out on a 10 cm object is a far worse measurement than being 2 cm out on a 10 m one, and the raw difference cannot tell you that.
The absolute value is conventional but not universal. Dropping it gives a signederror, where a positive figure means the measurement overshot and a negative one means it undershot. That is often more useful in practice, because a consistent sign across repeated measurements points at a systematic problem — a miscalibrated instrument — rather than random noise.
Distinguish it from two neighbours. Percent difference compares two measurements where neither is authoritative, and divides by their average rather than by one of them.Percent change measures movement over time in a single quantity. And percent error speaks only to accuracy, how close you are to the truth — not precision, how tightly repeated measurements cluster. A instrument can be highly precise and consistently wrong.
Frequently Asked Questions
What is the percent error formula?
Percent Error = (|Experimental Value - Theoretical Value| / |Theoretical Value|) × 100.
How is percent error calculated?
|experimental - theoretical| / |theoretical| x 100. The absolute value keeps the result positive, and the theoretical or accepted value is always the denominator - dividing by the measured value instead is the most common mistake and gives a different answer.
What is the difference between percent error and percent difference?
Percent error compares a measurement to a known accepted value. Percent difference compares two measurements when neither is authoritative, dividing by their mean rather than by one of them. Using percent error when there is no accepted value implies a precision you do not have.
What counts as an acceptable percent error?
It depends entirely on the field. Analytical chemistry might demand under 1%, introductory physics labs often accept under 10%, and some biological measurements tolerate far more. The honest comparison is against the known precision of your instrument and method.