Error Propagation Calculator
Estimate uncertainty in a calculated result for sums, differences, products, quotients, and powers using standard propagation rules.
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What this calculator teaches
Error propagation estimates how measurement uncertainty affects a calculated quantity. It is essential in labs, engineering, physics, and data analysis.
This calculator assumes independent uncertainties and uses common first-order propagation rules.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Sum/difference | Δz = √(Δx² + Δy²) | Absolute uncertainties combine in quadrature. |
| Product/quotient | Δz/|z| = √((Δx/x)² + (Δy/y)²) | Relative uncertainties combine in quadrature. |
| Power | Δz/|z| = |n| Δx/|x| | Power rule for z=x^n. |
Step-by-Step Examples
- x = 12 ± 0.2 and y = 5 ± 0.1.
- z = 17.
- Δz = √(0.2² + 0.1²).
- For z = xy, first compute relative uncertainty.
- Combine relative uncertainties in quadrature.
- Multiply by |z| to get absolute uncertainty.
Where students use this
Common Mistakes to Avoid
For independent random uncertainties, combine in quadrature, not by simple addition.
Sums and differences use absolute uncertainty.
Products and quotients use relative uncertainty first.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This method approximates a mathematical solution through iteration, discretization, interpolation or numerical quadrature. Assumption: Accuracy depends on step size, initial guesses, smoothness, conditioning and stopping criteria. Compare error and convergence rather than trusting a single approximation.