Error Propagation Calculator
Error Propagation Calculator
Calculate the uncertainty of a result when there are errors in the input data. The calculator automatically applies error propagation rules for different mathematical operations.
What is Error Propagation?
Error propagation is a method for calculating the uncertainty of a result based on the uncertainties of input quantities. It's a key tool in scientific measurements and experiments.
Supported Operations:
- Addition/Subtraction: δ(A±B) = √(δA² + δB²)
- Multiplication/Division: δ(A×B)/|A×B| = √((δA/A)² + (δB/B)²)
- Power Function: δ(A^n)/|A^n| = |n| × δA/|A|
- Square Root: δ(√A) = δA/(2√A)
- Logarithm: δ(ln A) = δA/A
- Exponential: δ(e^A) = |e^A| × δA
Applications:
- Physics experiments
- Chemical analysis
- Engineering calculations
- Scientific research
- Laboratory measurements
- Quality control
- Calibration procedures
How to Use:
- Select the type of operation (basic, functions, or linear combination)
- Enter the values and their uncertainties
- Click "Calculate Error" to get the result
- Review the detailed breakdown and relative error
Understanding Results:
Results are presented in the format: value ± uncertainty. The calculator also provides relative error as a percentage and shows the step-by-step calculation process.
Frequently Asked Questions
What is measurement uncertainty?
Uncertainty is a parameter that characterizes the range of values within which the true value of a measured quantity may lie.
How should I report a result with error?
Results should be written as: value ± error, for example: 9.81 ± 0.02 m/s². The error is usually rounded to 1-2 significant figures.
What is relative error?
Relative error is the ratio of absolute error to the value, expressed as a percentage: (δA/A) × 100%.
When should I use linear error propagation?
Linear propagation is used for complex functions through partial derivatives. For simple operations, there are specific formulas.
How do I handle correlated errors?
This calculator assumes uncorrelated errors. For correlated errors, additional covariance terms must be considered in the propagation formula.
What's the difference between precision and accuracy?
Precision refers to the reproducibility of measurements (random error), while accuracy refers to how close measurements are to the true value (systematic error).