Editing Centrifuge (section)

== Mathematical description ==

Protocols for centrifugation typically specify the amount of [[acceleration]] to be applied to the sample, rather than specifying a [[rotational speed]] such as [[revolutions per minute]]. This distinction is important because two rotors with different diameters running at the same rotational speed will subject samples to different accelerations. During [[circular motion]] the acceleration is the product of the [[radius]] and the square of the [[angular velocity]] <math>\omega</math>, and the acceleration relative to "''g''" is traditionally named "relative centrifugal force" (RCF). The acceleration is measured in multiples of "''g''" (or ×&nbsp;"''g''"), the standard acceleration due to [[gravity]] at the Earth's surface, a [[dimensionless quantity]] given by the expression:

: <math> \text{RCF} = \frac{r \omega^2}{g}</math>

where
:<math>\textstyle g </math> is earth's [[Standard gravity|gravitational acceleration]],
:<math>\textstyle r </math> is the rotational radius,
:<math>\omega</math> is the [[angular velocity]] in radians per unit time

This relationship may be written as
: <math> \text{RCF} = \frac{10^{-3} r_\text{mm} \, \left(\frac{2 \pi N_\text{RPM}}{60}\right)^2}{g}</math>

or

: <math> \text{RCF} = 1.118(2)\, \times 10^{-6}\, r_\text{mm} \, N_\text{RPM}^2</math>

where
:<math>\textstyle r_\text{mm} </math> is the rotational radius measured in millimeters (mm), and
:<math>\textstyle N_\text{RPM} </math> is [[rotational speed]] measured in [[revolutions per minute]] (RPM).

To avoid having to perform a mathematical calculation every time, one can find [[nomograms]] for converting RCF to rpm for a rotor of a given radius. A ruler or other straight edge lined up with the radius on one scale, and the desired RCF on another scale, will point at the correct rpm on the third scale.<ref>{{Cite web |title=Nomogram for converting maximum relative centrifugal force (RCF, i.e., g-force) to RPM |url=http://aquaticpath.umd.edu/nomogram.html |archive-url=https://web.archive.org/web/20131209161103/http://aquaticpath.umd.edu/nomogram.html |archive-date=December 9, 2013 |publisher=University of Maryland Aquatic Pathobiology Center}}</ref> Based on automatic rotor recognition, modern centrifuges have a button for automatic conversion from RCF to rpm and vice versa.{{cn|date=March 2025}}