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Absolute & Relative Error from a Reference Value

Measure the magnitude of a value’s deviation from a nonzero reference, including negative reference values.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A measurement of −95 compared with reference −100 has absolute error 5 and relative error 5%.

Absolute error = |measurement − reference|; relative error = absolute error / |reference| × 100%

Worked example

Enter these known values and leave the other values blank.

Reference value, nonzero: -100
Measured or approximate value: -95

Absolute error magnitude: 5
Relative error magnitude: 5 %

Assumptions and limitations

The reference value is nonzero, while either value can be negative. Absolute and relative error magnitudes are nonnegative.
These are unsigned magnitudes. They do not report whether the measurement is above or below the reference and do not estimate measurement uncertainty.
Inverse branches are not unique. Given a reference and absolute error, the measurement inverse adds the error; given a measurement and absolute error, the reference inverse adds the error.
Recovering reference from absolute and relative error selects the positive magnitude. Use known values to choose the intended sign; not every pair of fields determines a unique solution.

Common questions

Can relative error exceed 100%?

Yes. The absolute deviation can be larger than the magnitude of the reference value.

Why can an inverse result differ from my original measurement?

Absolute values discard direction. A reference of 100 and error 5 allow measurements 95 and 105; the retained measurement inverse selects 105.

References

Bookify uses the absolute reference magnitude when recovering absolute error from relative error, including negative reference values. Bookify requires a nonzero reference value and nonnegative error magnitudes.

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