How to Compute Uncertainty?

Identify the measured quantity and its units

Determine the measurement method and instrument

Find the instrument resolution or least count

Estimate random uncertainty from repeated measurements

Compute the mean of repeated measurements

Compute the standard deviation of repeated measurements

Compute the standard error if using the mean

Determine systematic uncertainty from calibration or bias

Combine independent uncertainties using root-sum-square

Propagate uncertainty through calculations using partial derivatives

For addition or subtraction, add absolute uncertainties in quadrature

For multiplication or division, add relative uncertainties in quadrature

For powers, multiply relative uncertainty by the exponent

Report the final value with its uncertainty

Round the uncertainty to one or two significant figures

Round the measured value to the same decimal place as the uncertainty

State the confidence level if required

Verify units are consistent throughout the calculation

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