Error Propagation Calculator
Calculate combined uncertainty from error propagation rules.
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Select the mathematical operation, enter the two values and their uncertainties. The calculator applies standard error propagation rules to compute the combined uncertainty. For addition and subtraction, uncertainties add in quadrature. For multiplication and division, relative uncertainties add in quadrature.
About Error Propagation
Error propagation (uncertainty propagation) determines how measurement uncertainties combine when values are used in calculations. The rules come from partial derivatives and assume independent, random errors. These formulas are fundamental to experimental physics, analytical chemistry, and any field dealing with measurement uncertainty.
Frequently Asked Questions
Why do uncertainties add in quadrature?
When errors are independent and random, they are unlikely to all push in the same direction. Adding in quadrature (square root of the sum of squares) accounts for this statistical cancellation, giving a more realistic combined uncertainty.
What about correlated uncertainties?
This calculator assumes independent (uncorrelated) errors. If your measurements are correlated, you need a covariance term. Correlated errors can make combined uncertainty either larger or smaller than the independent case.
What is the difference between absolute and relative uncertainty?
Absolute uncertainty is in the same units as the measurement (e.g., 5.0 +/- 0.2 meters). Relative uncertainty is the ratio of uncertainty to the value, often expressed as a percentage (e.g., 4%).