Error Propagation Calculator
Find out how measurement uncertainty carries through a calculation. Enter two values with their uncertainties and pick an operation to get the propagated uncertainty of the result.
What This Calculator Does
When you combine two measured quantities, each with its own uncertainty, the uncertainty in the result depends on both the operation used and the uncertainties in the original values. This calculator applies the standard error propagation formulas for addition, subtraction, multiplication, and division.
The Formulas
- Addition or Subtraction (A ± B): the uncertainties combine in quadrature — δresult = √(δA² + δB²)
- Multiplication or Division (A × B or A ÷ B): the relative uncertainties combine in quadrature — δresult / |result| = √[(δA/A)² + (δB/B)²]
This quadrature (square-root-of-sum-of-squares) approach assumes the two uncertainties are independent and random, which is the standard assumption in most introductory physics, chemistry, and engineering lab work. It gives a good estimate of the resulting uncertainty even though it isn’t a strict maximum bound. For general educational and lab-reporting use.