Error Propagation

Propagate measurement uncertainty for common operations or a typed formula.

At a glance

Computes
Propagated uncertainty for a sum, difference, product, quotient, power, or a typed formula.
You supply
Each measured value with its uncertainty, and the operation or formula.
Use when
You combined measurements and need the uncertainty of the result reported honestly.
Assumes
First-order linearization; independence assumed because covariance terms are omitted.
Mode

combined standard uncertainty (result units)

1213141516Propag…
Some interval row labels are shortened with an ellipsis; full row labels remain in the table below.

Result value

Enter values

Absolute uncertainty appears below.

Uncertainty details
MetricValue

Value by category

0.000.010.020.030.04Variance contributionAB
Export

uc(y)^2 = sum((df/dxi)^2 * u(xi)^2) How?

How this is calculated

The general method is first-order propagation of uncertainty. Common operations use the same derivative rule as shortcuts, and formula mode estimates partial derivatives with central finite differences.

Formula: uc(y)^2 = sum((df/dxi)^2 * u(xi)^2)

Sources

  1. NIST TN 1297 Appendix A. NIST. Retrieved .
  2. JCGM publications. BIPM. Retrieved .

Method last reviewed