Measurement Uncertainty Calculator

What Is Measurement Uncertainty?

Measurement uncertainty quantifies the doubt about a measurement result. Following the GUM (Guide to the Expression of Uncertainty in Measurement), this tool helps you identify all sources of uncertainty, compute their individual contributions, and combine them into an expanded uncertainty with a stated confidence level.

1Setup

Enter a title for your budget, describe the measurand (what is being measured), select the unit, and choose a coverage factor (k=2 for approximately 95% confidence). Optionally enter the measurement result for the uncertainty statement.

2Type A Sources

Type A sources are evaluated by statistical analysis of repeated measurements. Enter your readings and the tool computes the standard uncertainty as s/sqrt(n), where s is the standard deviation and n is the number of readings.

3Type B Sources

Type B sources come from specifications, calibration certificates, and engineering judgment. Common examples: gauge resolution (rectangular distribution), reference standard uncertainty (normal from certificate), and temperature effects (rectangular). Enter the half-width and distribution type for each source.

4Uncertainty Budget

The budget combines all sources. Each source's standard uncertainty is multiplied by its sensitivity coefficient, squared, and summed. The combined standard uncertainty is the square root of this sum. The expanded uncertainty is k times the combined uncertainty.

5View and Export

Review the complete uncertainty statement, download a PDF report, or start a new budget. The uncertainty statement follows the format: "X +/- U unit (k=2, ~95% confidence)".

Key Terms

Type A Uncertainty

Evaluated by statistical analysis of repeated observations. Standard uncertainty = s/sqrt(n).

Type B Uncertainty

Evaluated from other information: manufacturer specs, calibration certificates, handbooks, or experience.

Combined Uncertainty (u_c)

Root sum of squares of all individual standard uncertainties weighted by sensitivity coefficients.

Expanded Uncertainty (U)

U = k * u_c. Defines an interval with a stated confidence level (k=2 gives approximately 95%).

Coverage Factor (k)

Multiplier for confidence level. k=1 (~68%), k=2 (~95%), k=3 (~99.7%).