Statistics

Error Propagation Calculator

Combine measurement uncertainties through a calculation.

Value A

Uncertainty in A

Value B

Uncertainty in B

Operation

Calculated Output

Result 14

Uncertainty 0.5385

Formula: Add/sub: √(δa²+δb²); Mul/div: relative errors combine

Step-by-Step Breakdown

1. Values used:

2. Value A = 10

3. Uncertainty in A = 0.5

4. Value B = 4

5. Uncertainty in B = 0.2

7. Result = 14

8. Uncertainty = 0.5385

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The math behind it

For addition/subtraction, absolute uncertainties add in quadrature. For multiplication/division, relative uncertainties combine in quadrature.

(10 ± 0.5) + (4 ± 0.2) → 14 ± 0.54.

Why add in quadrature?

Independent random errors partially cancel, so they add as a root-sum-of-squares.