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Percent error tells you how close an experimental measurement is to the accepted, true value — a staple of every science lab report. It expresses the gap as a percentage of the accepted value, so a small error on a large quantity and a large error on a small one can be compared fairly.
Enter your measured value and the accepted value; the tool returns the percent error, the signed error and the absolute difference.
Percent Error Calculator: step-by-step worked example
- Measured (experimental) value
- 9.6
- Accepted (theoretical) value
- 9.81
- 1
Difference
Difference = Experimental − Theoretical
9.6 − 9.81 = -0.21
- 2
Signed relative error
Relative = Difference ÷ |Theoretical| × 100
-0.21 ÷ 9.81 × 100 = -2.1407%
- 3
Percent error
% Error = |Experimental − Theoretical| ÷ |Theoretical| × 100
0.21 ÷ 9.81 × 100 = 2.1407%
- Excellent
- Good
- Acceptable
- High
Good to know: Percent error uses the absolute value, so it is always positive; the signed relative error tells you whether you measured high or low. Example: measuring g = 9.6 m/s² with a pendulum vs the accepted 9.81 gives ≈ 2.14% (low).
Percent Error Calculator — how it works
The percent error formula
percent error = |measured − accepted| ÷ |accepted| × 100
| Result | Meaning |
|---|---|
| Percent error | The magnitude of the error, always positive |
| Signed error | Same value with a sign: positive if you over-measured, negative if under |
| Absolute difference | measured − accepted, without dividing |
Why divide by the accepted value
Dividing by the accepted (true) value turns the raw difference into a *relative* error, so it's comparable across scales. Being 1 cm off on a 1 m length (1%) is far better than being 1 cm off on a 5 cm length (20%), and the percentage captures that where the raw 1 cm doesn't.
Sign tells you the direction
The standard percent error uses absolute value, so it's always positive. But the *signed* error is often more useful: a positive sign means your measurement was too high, a negative sign too low. A consistent sign across repeats points to a systematic error (a mis-calibrated instrument) rather than random scatter.
Where it helps
Chemistry and physics lab reports, calibration checks, and comparing an estimate against a known figure. Percent error compares against a known true value; when there's no accepted value and you're comparing two measurements to each other, percent *difference* is used instead.
Worked example
You measure the density of aluminium as 2.60 g/cm³; the accepted value is 2.70 g/cm³. The percent error is |2.60 − 2.70| ÷ |2.70| × 100 = 0.10 ÷ 2.70 × 100 = 3.70%. The signed error is −3.70%, the minus sign showing you under-measured, and the absolute difference is 0.10 g/cm³.
Frequently asked questions
How do I calculate percent error?+
Take the absolute difference between the measured and accepted values, divide by the accepted value, and multiply by 100: |measured − accepted| ÷ |accepted| × 100.
Why divide by the accepted value?+
Dividing by the true value makes the error relative, so measurements on different scales can be compared. A 1 cm error is 1% on a metre but 20% on 5 cm.
Can percent error be negative?+
The standard percent error uses absolute value and is always positive. This tool also shows the signed error: positive means you measured too high, negative too low.
What is a good percent error?+
It depends on the experiment, but in a school lab under about 5% is usually considered good. Consistently large errors in one direction suggest a systematic problem with the method or instrument.
What is the difference between percent error and percent difference?+
Percent error compares a measurement to a known accepted value. Percent difference compares two measured values to each other when neither is the accepted truth.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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