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Absolute & Relative Uncertainty Conversion

Convert an uncertainty magnitude to a relative percentage, or convert a percentage to uncertainty in the measurement’s units.

Formula & worked example
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Calculator inputs

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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.

Private by default

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

Formula and method

A measured value of −50 with 2% relative uncertainty has uncertainty magnitude 0.02 × |−50| = 1 in the measurement’s units.

Uncertainty magnitude = relative uncertainty fraction × |measured value|

Worked example

Enter these known values and leave the other values blank.

Measured value, nonzero: -50
Relative uncertainty: 2 %

Uncertainty magnitude in measurement units: 1

Assumptions and limitations

The measured value must be nonzero and can be negative. Both uncertainty magnitudes are nonnegative, including zero.
Use the same measurement units for the value and the uncertainty magnitude. Relative uncertainty is entered as a percentage.
This converts an uncertainty already supplied by you. It does not estimate uncertainty from data, establish a coverage probability or measure error against a known true value.
The measured value is an input; the magnitude equation does not uniquely recover its sign and this mode does not solve for it.

Common questions

Can a negative measurement have positive uncertainty?

Yes. Uncertainty magnitude is nonnegative and the conversion uses the absolute value of the measurement.

What happens at a measured value of zero?

Relative uncertainty is undefined because its denominator is zero. An uncertainty in measurement units can still be meaningful, but cannot be converted with this relative formula.

References

Bookify requires a nonzero measured value because relative uncertainty divides by its magnitude.

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