Percent Error Calculator
Percent error between a measured and an accepted value, plus absolute and relative error and whether you over- or under-estimated — sign conventions explained.
Percent Error Calculator: with the default inputs, percent error is 3.16%.
What you observed or calculated.
The known or reference value. Can't be zero.
- Absolute error |measured − actual|
- 0.31
- Relative error (fraction)
- 0.0316
- Signed percent error
- -3.16%Negative means you measured low; positive means high.
- Direction
- Underestimate: measured 0.31 below the actual value
Assumptions
- Percent error uses the absolute value (always non-negative) and divides by the actual value.
- The signed version is (measured − actual) ÷ |actual|, so negative means an underestimate.
How this is worked out
The formula
Percent error = |measured − actual| ÷ |actual| × 100% Absolute error = |measured − actual| Relative error = absolute error ÷ |actual| Signed percent error = (measured − actual) ÷ |actual| × 100% (negative = measured low)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Measured (experimental) value
- What you observed or calculated.defaults to 9.5
- Actual (accepted / theoretical) value
- The known or reference value. Can't be zero.defaults to 9.81
What you get back
- Percent errormain answer
- Absolute error |measured − actual|
- Relative error (fraction)
- Signed percent error
- Negative means you measured low; positive means high.
- Direction
What this assumes
- Percent error uses the absolute value (always non-negative) and divides by the actual value.
- The signed version is (measured − actual) ÷ |actual|, so negative means an underestimate.
About this calculator
Percent error tells you how far off a measurement is, as a fraction of the true value. A 0.3 g error is enormous on a 1 g sample and negligible on a 1 kg one; dividing by the accepted value puts both on the same scale. It's the standard way to report accuracy in a lab write-up and to sanity-check an estimate against a known answer.
How to use it
Enter your measured or calculated value and the accepted, theoretical or reference value. The headline number is the conventional unsigned percent error; the signed version and the direction tell you whether you came in high or low, which is usually the more useful thing to know when hunting for a systematic mistake.
Sign conventions
Most textbooks and lab manuals take the absolute value, so percent error is always positive — that's the primary result here. Some fields keep the sign, defining it as (measured − actual) ÷ actual, so that a negative error means an underestimate. The calculator gives both so you can match whatever your course or journal expects. Note the denominator is the actual value, never the measured one; using the measured value gives a different (and wrong) number.
Percent error vs. percent difference vs. percent change
- Percent error compares a measurement to a known correct value.
- Percent difference compares two measurements when neither is "correct", dividing by their average.
- Percent change compares a later value with an earlier one, dividing by the earlier.
Picking the wrong one is the most common mistake in reports — if you don't have an accepted value, you want percent difference (see the Percentage Calculator).
When it breaks down
If the true value is zero — a net force that should vanish, a mean that should be 0 — percent error is undefined because you'd divide by zero. Report the absolute error instead. Values near zero make percent error explode for the same reason, so an enormous percentage isn't always an enormous mistake.
Reading the result
In a school lab, under 5% usually means the method worked; 5–10% suggests a measurable systematic error; above that, look for a units or procedure problem. An error above 100% almost always means a unit mix-up (grams vs kilograms, cm vs m).
Frequently asked questions
▸What is the percent error formula?
Percent error = |measured − actual| ÷ |actual| × 100%. For 9.5 measured against 9.81 that's 0.31 ÷ 9.81 × 100 = 3.16%.
▸Can percent error be negative?
Under the usual definition, no — the absolute value makes it positive. Some disciplines keep the sign so that a negative result means the measurement was too low; the calculator shows that version as 'signed percent error'.
▸Do I divide by the measured value or the actual value?
The actual (accepted) value. The error is expressed relative to the truth, not relative to your guess.
▸What's a good percent error?
It depends on the instrument and field. In introductory labs a few percent is typical; precision measurements aim for a fraction of a percent. Anything over 100% usually signals a units mistake.
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