Uncertainty Calculator

Author: Henrick Yau
- 31 July 2025
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Uncertainty Calculator

Calculate measurement uncertainty and error propagation for scientific and engineering applications. This calculator helps researchers, students, and professionals determine the precision of their experimental results.

Basic Uncertainty Calculation

Advanced Settings

For Student's t distribution only

Understanding Measurement Uncertainty

Measurement uncertainty quantifies the doubt about the result of a measurement. All measurements include some level of uncertainty, as perfect precision is impossible due to random variations and systematic errors.

Key Concepts in Uncertainty Analysis
  • Standard Uncertainty: Uncertainty expressed as a standard deviation
  • Coverage Factor (k): Multiplier of standard uncertainty for expanded uncertainty
  • Expanded Uncertainty: Standard uncertainty multiplied by coverage factor
  • Confidence Level: Probability that the true value lies within the uncertainty interval
  • Significant Figures: Digits that carry meaningful information about a measurement
  • Propagation of Uncertainty: How uncertainties combine in calculations
Common Uncertainty Propagation Rules
  • Addition/Subtraction: u(A±B) = √(u(A)² + u(B)²)
  • Multiplication/Division: u(A×B)/|A×B| = √((u(A)/A)² + (u(B)/B)²)
  • Power: u(x^n)/|x^n| = |n| × u(x)/|x|
  • General Function: u(f) = √(∑(∂f/∂xi)² × u(xi)²)
Sources of Uncertainty
  • Instrument Resolution: Limitations in reading precision
  • Calibration: Uncertainty in reference standards
  • Random Variations: Natural variability in repeated measurements
  • Environmental Factors: Temperature, humidity, vibration effects
  • Operator Influence: Variations in measurement technique
  • Sample Representativeness: How well the measured sample represents the whole

Disclaimer: This calculator provides estimates based on standard uncertainty propagation methods. Results should be verified using appropriate statistical techniques for critical applications. This tool is for educational and reference purposes only.