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Error Propagation Calculator

Enter two measurements with their uncertainties and pick an operation to see the propagated uncertainty in the result - the calculation behind every lab report's error-analysis section.

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Propagated uncertainty

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Lab report material is exactly the kind of dense, formula-heavy content spaced repetition was built for - Encodr resurfaces it before the next problem set, not the night before.

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The two formulas this uses

For addition or subtraction, absolute uncertainties add in quadrature: δz = √(δx² + δy²). For multiplication or division, relative uncertainties add in quadrature instead: δz/z = √((δx/x)² + (δy/y)²), then that relative uncertainty is scaled back up by the result to get an absolute uncertainty again. Both formulas assume the uncertainties in x and y are independent and random, which is the standard assumption for a single-trial measurement uncertainty (not a full statistical treatment of repeated trials, which uses standard error instead). This is the same method behind the propagated-uncertainty section of a typical physics or chemistry lab report.

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