Mode
Number or expression (e.g. 3.45 * 2.1 + 0.005)
Operators: + − * / ^(power)
Parentheses () supported. Numbers parsed with sig fig rules.
Parentheses () supported. Numbers parsed with sig fig rules.
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Result
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Sig Figs
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Absolute Uncertainty
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Relative Uncertainty (%)
Step-by-Step Explanation
Enter values in the left panel and press Calculate.
Number Line (Uncertainty Visualization)
Run an uncertainty calculation to display
Error Propagation Theory
For independent measurements $a \pm \Delta a$ and $b \pm \Delta b$:
Addition/Subtraction (absolute uncertainty)：$$\Delta(a \pm b) = \sqrt{(\Delta a)^2 + (\Delta b)^2}$$
Multiplication/Division (relative uncertainty)：$$\frac{\Delta(a \cdot b)}{|a \cdot b|} = \sqrt{\left(\frac{\Delta a}{a}\right)^2 + \left(\frac{\Delta b}{b}\right)^2}$$
General form (Gaussian error propagation)：$$\Delta f = \sqrt{\left(\frac{\partial f}{\partial a}\Delta a\right)^2 + \left(\frac{\partial f}{\partial b}\Delta b\right)^2}$$
CAE Note: Used for elastic modulus estimation in material testing (uncertainty of Δσ/Δε), load cell accuracy evaluation, statistical analysis of dimensional tolerances, and FEM result validation. Compliant with GUM (Guide to the Expression of Uncertainty in Measurement).