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MasterMath

Percent Error Calculator

How far a measurement is from the true value, as a percentage. The sign tells you whether it overshoots or falls short.

Percent error

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Percent error—
Absolute error—
With sign—
Accuracy—
The measurement—

How this was worked out

    The rule

    percent error = |measured − true| ÷ |true| × 100

    Why it works

    Percent error compares the size of a mistake with the size of what was being measured. A 3-unit error means very different things when measuring 50 and when measuring 50,000, and dividing by the true value is what makes them comparable.

    How to do it by hand

    1. Subtract the true value from the measured one
    2. Take the absolute value if you only want the size
    3. Divide by the true value
    4. Multiply by 100

    What is worth knowing

    The denominator is always the true value, never the measured one — that is what makes the figure meaningful, and swapping them is the usual mistake. Keeping the sign is often worth doing: a consistently positive error points at a systematic bias in the instrument, which is fixable, while errors scattered either side are random noise, which is not. In experimental work a percent error under 5 % is usually considered acceptable, though the threshold depends entirely on the field: analytical chemistry expects far better and field ecology far worse.

    Frequently asked questions

    What do I divide by, the true or the measured value?

    The true value, always. Dividing by the measured one gives a different figure that means nothing standard.

    Should I keep the sign?

    It is often useful. A consistent sign points to systematic bias; scattered signs suggest random error.

    What is an acceptable percent error?

    It depends entirely on the field. Under 5 % is a common rule of thumb, but analytical work demands far tighter.

    What if the true value is zero?

    The calculation is undefined. Only the absolute error means anything in that case.