Why quadrature?
Adding errors directly (linear sum) assumes the worst-case scenario where errors always reinforce each other. Quadrature (square root of sum of squares) assumes errors are independent and random.
Calculator
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Analysis
Interpretation of the current calculator output
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How to Use
Step-by-step instructions
- 1Enter value A and its uncertainty.
- 2Enter value B and its uncertainty.
- 3Select the operation (Add, Subtract, Multiply, Divide).
- 4The calculator will show the result with propagated error.
Quadrature Sum
When combining measurements with uncertainties, errors propagate. For addition/subtraction, absolute errors add in quadrature. For multiplication/division, relative errors add in quadrature.
Addition: sqrt((dA)^2 + (dB)^2), Multiplication: |R|sqrt((dA/A)^2 + (dB/B)^2)Variables:
A, BMeasured valuesdA, dBAbsolute uncertaintiesExample
Addition: (10 +/- 1) + (20 +/- 2)
Inputs:
A:10 +/- 1
B:20 +/- 2
Op:Add
Steps:
- 1.Value: 10 + 20 = 30
- 2.Error: sqrt(1^2 + 2^2) = sqrt(5) = 2.236
Result:
30 +/- 2.236