Calculator of Alexandria

Centrifuge RPM to RCF (× g) calculator

Convert centrifuge speed in RPM to relative centrifugal force in × g for your rotor radius, or find the RPM that gives a protocol's × g.

Solve for

Distance from the centre of the rotor to the sample. Rotor manuals list r(max) and r(av).

Formula

RCF=1.118×10−5⋅r⋅N2\text{RCF} = 1.118 \times 10^{-5} \cdot r \cdot N^2
How it's derived

The formula

RCF=1.118×10−5⋅r⋅N2\text{RCF} = 1.118 \times 10^{-5} \cdot r \cdot N^2

RCF\text{RCF} is the relative centrifugal force in multiples of Earth’s gravity (×g\times g), rr is the rotor radius in centimetres and NN is the speed in revolutions per minute.

Where it comes from

Protocols give spin conditions in ×g\times g rather than RPM because the force on a sample depends on both speed and radius. Two centrifuges at the same RPM can spin samples at very different forces.

An object moving in a circle of radius rr with angular velocity ω\omega needs a centripetal acceleration of

a=rω2a = r\omega^2

RCF expresses that acceleration as a multiple of standard gravity, g0=9.80665 m/s2g_0 = 9.80665\ \text{m/s}^2:

RCF=rω2g0\text{RCF} = \frac{r\omega^2}{g_0}

Rotors are rated in revolutions per minute, not radians per second. One revolution is 2π2\pi radians and one minute is 60 seconds, so

ω=2πN60\omega = \frac{2\pi N}{60}

Substituting, and converting rr from centimetres to metres by dividing by 100:

RCF=r100⋅1g0(2πN60)2=(2π/60)2100 g0⏟1.118×10−5⋅r⋅N2\text{RCF} = \frac{r}{100} \cdot \frac{1}{g_0} \left(\frac{2\pi N}{60}\right)^2 = \underbrace{\frac{(2\pi/60)^2}{100\, g_0}}_{1.118 \times 10^{-5}} \cdot r \cdot N^2

All the constants collapse into the single number 1.118×10−51.118 \times 10^{-5}, which is why that odd-looking factor appears in every rotor manual.

Worked example

A protocol says to spin at 1,000 × g, and your rotor radius is 10 cm. Rearranging for NN:

N=RCF1.118×10−5⋅r=10001.118×10−4≈2,990 RPMN = \sqrt{\frac{\text{RCF}}{1.118 \times 10^{-5} \cdot r}} = \sqrt{\frac{1000}{1.118 \times 10^{-4}}} \approx 2{,}990\ \text{RPM}

Watch out for

  • Which radius? The force increases along the tube. rmax⁡r_{\max} (tube bottom) gives the highest force and ravr_{\text{av}} the average. Protocols usually mean rmax⁡r_{\max} unless they say otherwise, so check your rotor’s manual.
  • Force grows with the square of speed. Doubling RPM quadruples the force, so small RPM errors matter.

Sources

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