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.
combined standard uncertainty (result units)
Result value
Enter values
Absolute uncertainty appears below.
| Metric | Value |
|---|
Value by category
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
- NIST TN 1297 Appendix A. NIST. Retrieved .
- JCGM publications. BIPM. Retrieved .
Method last reviewed