Uncertainty & Error Propagation Calculator
In empirical science, no measurement is perfectly exact. Every lab observation carries an inherent degree of uncertainty. The Error Propagation Calculator simplifies the rigorous mathematical process of determining how errors compound when you use measurements to calculate derived quantities.
This tool seamlessly applies partial derivative calculus rules—supporting addition, subtraction, multiplication, division, and exponents. Input your measurement values alongside their absolute uncertainties to accurately track percentage relative error and absolute ranges of your final result.
The Math of Error Propagation
Why use this calculator instead of just adding errors directly? Statistical independence! When independent random errors combine, they often partially cancel out rather than stacking directly. We use Quadrature combinations:
- Addition & Subtraction (A ± B): The absolute uncertainties add in quadrature:
δR = √(δa² + δb²) - Multiplication & Division (A × B, A ÷ B): The relative (percentage) uncertainties add in quadrature:
δR / R = √((δa/A)² + (δb/B)²) - Exponents (A^n): The exponent multiplies the relative uncertainty:
δR / R = |n| × (δa/A)