SuperCalX

Error Propagation Calculator

Calculate the uncertainty propagation for basic arithmetic operations.
Calculator
Enter your values
Analysis
Interpretation of the current calculator output

Enter values to see detailed analysis and insights.

How to Use

Step-by-step instructions
  1. 1Enter value A and its uncertainty.
  2. 2Enter value B and its uncertainty.
  3. 3Select the operation (Add, Subtract, Multiply, Divide).
  4. 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 values
dA, dBAbsolute uncertainties

Example

Addition: (10 +/- 1) + (20 +/- 2)

Inputs:

A:10 +/- 1
B:20 +/- 2
Op:Add

Steps:

  1. 1.Value: 10 + 20 = 30
  2. 2.Error: sqrt(1^2 + 2^2) = sqrt(5) = 2.236
Result:
30 +/- 2.236

Frequently Asked Questions

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.