Error Propagation Calculator
Enter measured values with their uncertainties and choose an operation to compute the propagated uncertainty.
Result
8.1000
Uncertainty
0.2236
How to Use This Calculator
- Select the operation that combines your measurements.
- Enter each measurement’s value and its standard uncertainty.
- Review the propagated uncertainty shown beneath the inputs.
- Add or remove measurements to model the experiment more accurately.
Formula
Addition/Subtraction: σresult = √(σ₁² + σ₂² + …)
Multiplication/Division: σresult = |result| · √[(σ₁/x₁)² + (σ₂/x₂)² + …]
These formulas assume independent random errors expressed as standard uncertainties (one standard deviation).
Full Description
Error propagation quantifies how measurement uncertainties combine when calculating derived quantities. Engineers, scientists, and analysts use these formulas to ensure reported results include realistic uncertainty bounds.
Always verify that measurements are independent and uncertainties are random. Systematic errors require separate analysis.
Frequently Asked Questions
Can I use percentages?
Convert percentage uncertainties to absolute (σ = % × value) before entry.
What if measurements are correlated?
These formulas assume independence. Correlated errors require covariance terms not included here.
Does ordering matter?
No. Addition/subtraction and multiplication/division handle any order, though subtraction/division interpret left-to-right.
Why is the uncertainty zero?
If all input uncertainties are zero or a measurement value is zero in multiplication/division, propagation may produce zero uncertainty.