What is the Measurement Uncertainty Calculator?
Combine and propagate measurement uncertainty with this free measurement uncertainty calculator. Use root-sum-of-squares (RSS) to merge independent standard uncertainties, propagate error through addition, subtraction, multiplication, and division, convert percent uncertainty to absolute values, and compute expanded uncertainty U = k·u. Step-by-step work for physics and chemistry lab reports. Runs instantly in your browser.
How to use the Measurement Uncertainty Calculator
- Choose Combine (RSS), an arithmetic propagation mode, From %, or Expanded U.
- Enter measured values and their standard uncertainties (±), or comma-separated uncertainties to combine.
- Set the coverage factor k (default 2 for ~95% confidence).
- Review combined standard uncertainty, expanded uncertainty, and relative percent.
- Copy the full summary with formulas and steps for your lab report.
Common use cases
- Combining instrument, calibration, and random uncertainties in lab work
- Propagating uncertainty through calculated quantities (density, speed, etc.)
- Converting manufacturer percent tolerance to absolute uncertainty
- Computing expanded uncertainty for formal lab report conclusions
- Teaching error analysis in introductory physics and chemistry
Frequently asked questions
- What is measurement uncertainty?
- Measurement uncertainty quantifies doubt about a measured value. It is often reported as value ± uncertainty, where the uncertainty reflects limitations of instruments, methods, and assumptions.
- How do you combine independent uncertainties?
- Independent standard uncertainties combine in quadrature (RSS): u_c = √(u₁² + u₂² + …). This is the standard approach in the GUM (Guide to the Expression of Uncertainty in Measurement).
- How does error propagation work for multiplication?
- For f = A × B, relative uncertainties combine in quadrature: u_f/|f| = √((u_A/A)² + (u_B/B)²). The absolute uncertainty is u_f = |f| × (u_f/|f|).
- What is expanded uncertainty?
- Expanded uncertainty U = k × u, where u is the combined standard uncertainty and k is a coverage factor. k = 2 is commonly used for approximately 95% confidence under normal assumptions.
- What is the difference between standard and expanded uncertainty?
- Standard uncertainty (u) is the estimated standard deviation of the measurement. Expanded uncertainty (U) widens the interval by factor k to achieve a desired confidence level for reporting.
