Editing Conversion of units (section)

== Calculation involving non-SI Units ==
In the cases where non-[[SI Units|SI units]] are used, the numerical calculation of a formula can be done by first working out the factor, and then plug in the numerical values of the given/known quantities.

For example, in the study of [[Bose–Einstein condensate]],<ref>{{Cite book |last=Foot |first=C. J. |url=https://books.google.com/books?id=kXYpAQAAMAAJ|title=Atomic physics |date=2005|publisher=Oxford University Press |isbn=978-0-19-850695-9|language=en}}</ref> [[atomic mass]] {{math|''m''}} is usually given in [[Dalton (unit)|daltons]], instead of [[kilogram]]s, and [[chemical potential]] {{math|''μ''}} is often given in the [[Boltzmann constant]] times [[nanokelvin]]. The condensate's [[Gross–Pitaevskii equation#Healing length|healing length]] is given by:
<math display="block">\xi=\frac{\hbar}{\sqrt{2m\mu}}\,.</math>

For a <sup>23</sup>Na condensate with chemical potential of (the Boltzmann constant times) 128&nbsp;nK, the calculation of healing length (in micrometres) can be done in two steps:

=== Calculate the factor ===
Assume that {{tmath|1= m=1 \,\text{Da},\mu = k_\text{B}\cdot 1\,\text{nK} }}, this gives
<math display="block">\xi=\frac{\hbar}{\sqrt{2m\mu}} = 15.574 \,\mathrm{\mu m}\,,</math>
which is our factor.

=== Calculate the numbers ===
Now, make use of the fact that {{tmath|1= \xi\propto\frac{1}{\sqrt{m\mu} } }}. With {{tmath|1= m=23 \,\text{Da},\mu=128\,k_\text{B}\cdot\text{nK} }}, {{tmath|1= \xi=\frac{15.574}{\sqrt{23 \cdot 128} } \,\text{μm}=0.287\,\text{μm} }}.

This method is especially useful for programming and/or making a [[worksheet]], where input quantities are taking multiple different values; For example, with the factor calculated above, it is very easy to see that the healing length of <sup>174</sup>Yb with chemical potential 20.3&nbsp;nK is 
:{{tmath|1= \xi=\frac{15.574}{\sqrt{174\cdot20.3} } \,\text{μm}=0.262\,\text{μm} }}.