Uncertainties Calculation

Notation	Meaning	Unit
$\delta x$	absolute uncertainty, $x\pm\delta x$	Unit of $x$
$\frac{\delta x}{	x	}$

$+$ / $-$

$q=x+y-z$
$\delta q=\sqrt{\delta x^2+\delta y^2+\delta z^2}$

$\times$ / $\div$

$q=x\times y\div z$
$\frac{\delta q}{|q|}=\sqrt{(\frac{\delta x}{x})^2+(\frac{\delta y}{y})^2+(\frac{\delta z}{z})^2}$

$\times$ / $\div$ by a Constant

$a$ is a constant:
$q=ax$
$\delta q=a\delta x$

^

$n$ is known exactly:
$q=x^n$
$\frac{\delta q}{|q|}=|n|\frac{\delta x}{|x|}$

$\sin$ / $\cos$

$q=\sin\theta$
$\delta q=\cos\theta\times\delta\theta$

$q=\cos\theta$
$\delta q=\sin\theta\times\delta\theta$

Exponentials

$q=e^x$
$\delta q=e^x\times\delta x$

$\ln$

Base-10 logarithms must first be converted to base-e via $q=\log_{10}x=0.43\ln x$

$q=\ln x$
$\delta q=\frac{\delta x}{|x|}$

Avg

$\bar{x}$: The average of multiple $x$s
$\sigma$: Standard deviation

// todo

---

Last update: November 6, 2021
Created: September 14, 2021