Measurement Uncertainty Calculator
Calculate mean, sample standard deviation, standard uncertainty, and combined uncertainty from repeated measurements.
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What this calculator teaches
Measurement uncertainty tells how much confidence to place in a measured value. Repeated measurements estimate random variation, while instrument uncertainty represents resolution or calibration limits.
This calculator combines statistical uncertainty with instrument uncertainty and gives an expanded uncertainty using a coverage factor.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Mean | x̄ = Σx/n | Best estimate from repeated measurements. |
| Sample standard deviation | s = √(Σ(x-x̄)²/(n-1)) | Spread of repeated measurements. |
| Standard uncertainty | u = s/√n | Uncertainty of the mean. |
| Combined uncertainty | u_c = √(u² + u_inst²) | Combines independent uncertainty sources. |
Step-by-Step Examples
- Measurements: 10.2, 10.1, 10.3, 10.2, 10.4.
- Compute the mean.
- Compute sample standard deviation and standard uncertainty.
- Combine with instrument uncertainty.
Where students use this
Common Mistakes to Avoid
For repeated lab samples, use sample standard deviation with n − 1.
Repeated measurements do not remove instrument resolution limits.
Report uncertainty with sensible significant figures.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.