Percent Error Calculator
Compare a measured value with an accepted or theoretical value: percent error, absolute and relative error, the direction of the bias, and a tolerance check — plus percent difference for two measurements — with every step shown.
Written by Suhaib Hassan. Definitions follow the JCGM/GUM measurement vocabulary and standard textbook usage. Our methodology.
It finds the absolute error |measured − accepted|, divides by the accepted value to get the relative error, and multiplies by 100 for percent error.
Most tools return only a positive percentage. This one also shows whether you over- or under-shot, checks a tolerance, and handles percent difference too.
—
—
1 − relative error
—
—
Where your value sits against the accepted value
The green band is the tolerance range around the accepted value; the marker shows your measurement.
Step-by-step working
—
Percent error vs percent difference vs uncertainty
These sound alike but answer different questions. Choose by whether one of your values is a trusted reference.
Percent error
Use when you compare a measurement with a known accepted value. The accepted value is the denominator, so the answer says how far off you were relative to the truth.
Percent difference
Use when comparing two measurements and neither is a reference. The average of the two values is the denominator, so the order does not matter.
Error vs uncertainty
Error is the difference from the true value, which is normally unknown. Uncertainty describes the doubt about a measurement. A percent error smaller than your uncertainty is consistent with the accepted value.
Worked examples
Illustrative measurements, each checked by hand. Use the presets above to reproduce the first, third and fourth.
Pendulum measurement of gravity
A student measures g = 9.62 m/s²; the standard value is 9.80665 m/s².
0.18665 ÷ 9.80665 = 0.019033
percent error = 1.9033% (under)
Titration molarity
A solution prepared as 0.1000 M measures 0.1008 M.
0.0008 ÷ 0.1000 = 0.008
percent error = 0.8000% (over)
Machined shaft
A 50.000 mm shaft measures 50.042 mm against a ±0.050 mm tolerance.
0.042 ÷ 50 = 0.00084
percent error = 0.084%
0.042 ≤ 0.050 → within tolerance
What is percent error?
Percent error expresses how far a measured (experimental) value is from an accepted (theoretical) value, as a percentage of the accepted value. A small percent error means the measurement is close to the reference. It is common in physics, chemistry and engineering labs.
How to calculate percent error
- Subtract: measured − accepted. This is the signed error.
- Take the absolute value to get the absolute error, |Δ|.
- Divide by the absolute value of the accepted value for the relative error.
- Multiply by 100 to get percent error.
Some courses keep the sign (negative = under-measured, positive = over-measured) and others use the absolute value; this page shows both.
By Suhaib Hassan · Reviewed 28 September 2026 · How CalculatePilot verifies formulas →
Sources
- JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM), BIPM.
- Taylor, J. R. (1997). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd ed. University Science Books.
- ASTM E29, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications.
- NIST Special Publication 811, Guide for the Use of the International System of Units (SI) — value of standard gravity, 9.80665 m/s².
Frequently asked questions
Can percent error be negative?
By the strict textbook definition, percent error is the absolute value and so never negative. Many labs keep the sign to show direction: negative means your measurement is below the accepted value, positive means above. Switch the Sign setting to choose.
What is an acceptable percent error?
It depends on the field and the purpose. A teaching lab may accept a few percent, while precision manufacturing or analytical chemistry may require well under 1%. Use the tolerance check with the limit your course, standard or specification sets.
What if the theoretical value is zero?
Percent error is undefined because it divides by the accepted value. Report the absolute error with its units instead, or use an absolute tolerance in the tolerance check.
How do significant figures apply?
Round only the final answer, not the intermediate steps. The significant-figures setting rounds the displayed results; the calculation itself always uses full precision.
What is the difference between percent error and percent difference?
Percent error compares a measurement with an accepted reference value and divides by that value. Percent difference compares two measurements when neither is a reference and divides by their average.
Why is percent error not the same as uncertainty?
Percent error needs a known accepted value, whereas uncertainty describes the doubt in the measurement itself. A percent error smaller than the measurement uncertainty means the result agrees with the accepted value within what the measurement can resolve.
Related calculators
Continue your analysis.