RCF Calculator
The RCF calculator uses RCF = 1.118 × 10^-5 × r × rpm², with r in cm. Convert a protocol's × g into the rpm your rotor needs, or a speed into g.
RCF
- Relative centrifugal force At 10 cm from the axis, spinning at 5,000 rpm.
- 2,796 × g
- Working RCF = 1.118 × 10^-5 × r × rpm², with r in centimeters. The force goes with the square of the speed: double the rpm and the g-force is four times as large.
- 1.11824 × 10^-5 × 10 cm × 5,000² = 2,796 × g
- Where 1.118 × 10^-5 comes from Centripetal acceleration is ω²r. 2π/60 converts rpm to radians per second, 9.80665 m/s² is standard gravity (exact, by definition), and the 100 converts the radius from centimeters to meters.
- (2π/60)² ÷ 9.80665 ÷ 100 = 1.118244 × 10^-5
- Angular velocity ω = 2π × 5,000 ÷ 60.
- 524 rad/s
- Acceleration ω² × r = 524² × 0.1 m. Divided by 9.80665 m/s², that is the RCF.
- 27,416 m/s²
| Radius | × g at 5,000 rpm | rpm for 2,796 × g |
|---|---|---|
| 5 cm | 1,398 | 7,071 |
| 6 cm | 1,677 | 6,455 |
| 7 cm | 1,957 | 5,976 |
| 8 cm | 2,236 | 5,590 |
| 9 cm | 2,516 | 5,270 |
| 10 cm | 2,796 | 5,000 |
| 12 cm | 3,355 | 4,564 |
| 15 cm | 4,193 | 4,082 |
| 18 cm | 5,032 | 3,727 |
| 20 cm | 5,591 | 3,536 |
- RCF depends on where in the tube you measure. Rotors quote r max (tube bottom), r min (tube top) and sometimes r av; protocols that do not say usually mean r max. At r min the same speed gives proportionally less g.
- Never exceed the rotor's or the tubes' rated maximum speed or RCF, whatever this gives. Those limits are on the rotor and in its manual.
- Time to pellet depends on more than g: the rotor's path length, the sample's viscosity and the particle size. Keeping RCF the same keeps the force the same, not necessarily the pelleting time across very different rotors.
How the RCF Calculator works
The formula:
RCF = 1.118 × 10^-5 × r × rpm²
where RCF is in multiples of g, r is the radius in centimeters from the center of the rotor, and rpm is the speed in revolutions per minute. Solved for speed, rpm = √(RCF ÷ (1.118 × 10^-5 × r)).
A worked example, the one above: a rotor with a 10 cm radius at 5,000 rpm. 1.118 × 10^-5 × 10 × 5,000² = 1.118 × 10^-5 × 10 × 25,000,000 = 2,795 × g (2,796 with the constant unrounded). Going the other way, 1,000 × g at 10 cm needs √(1,000 ÷ (1.118 × 10^-5 × 10)) = 2,990 rpm.
Where the constant comes from. Relative centrifugal force is the centripetal acceleration of the sample, ω²r, divided by standard gravity. A speed in rpm is 2π × rpm ÷ 60 radians per second, so ω² is (2π/60)² × rpm². Standard gravity, g0, is 9.80665 m/s², exact by definition. With r in centimeters, one more factor of 100 turns it into meters:
(2π/60)² ÷ 9.80665 ÷ 100 = 0.0109662 ÷ 9.80665 ÷ 100 = 1.11824 × 10^-5
So the constant is unit conversion, not an empirical fit, and the only physics in it is that the acceleration grows with the square of the speed and in proportion to the radius.
Why protocols give × g, not rpm. The same rpm produces very different forces in different rotors. At 5,000 rpm a 6 cm microcentrifuge rotor gives 1,677 × g and a 15 cm swing-bucket rotor 4,193 × g. The sample feels the g-force, not the speed, so a protocol written in × g transfers between machines and one written in rpm does not. Converting a protocol to your centrifuge means taking its × g and solving for the rpm on your rotor's radius, which is the second mode here; the table gives the rpm for the same g across a range of radii.
Which radius. A tube sits across a span of radii, from r min at its top to r max at the bottom, and the force varies along it in proportion. Rotor manuals list r max, r min and often r av. When a protocol does not say, r max is the usual assumption.
Quadratic, not linear. Because g goes with rpm squared, doubling the speed quadruples the force, and a protocol at half the g needs only 71% of the rpm. Halving the radius at the same rpm halves the force.
What this calculator does not cover: the time a run takes to pellet a given particle (that depends on the rotor's k-factor, the sample and the particle), and the rotor's own speed limits, which are on the rotor and in its manual and always take precedence.
RCF Calculator FAQ
How do you convert rpm to g?
RCF = 1.118 × 10^-5 × r × rpm², with r the rotor radius in cm. At 10 cm and 5,000 rpm: 1.118 × 10^-5 × 10 × 25,000,000 = 2,795 × g. You need the radius; rpm alone does not determine the force.
How do you convert g to rpm?
rpm = √(RCF ÷ (1.118 × 10^-5 × r)). For 1,000 × g on a 10 cm rotor: √(1,000 ÷ 0.0001118) = about 2,990 rpm. On a 6 cm rotor the same force needs 3,861 rpm.
What is relative centrifugal force?
The acceleration a centrifuge gives a sample, in multiples of standard gravity (9.80665 m/s²). 2,000 × g means the sample is pushed outward 2,000 times as hard as gravity pulls it down. It is the figure protocols should give, because it is the same on any centrifuge.
Where does 1.118 × 10^-5 come from?
It is (2π/60)² ÷ 9.80665 ÷ 100: the conversion from rpm to radians per second, squared, divided by standard gravity, with a factor of 100 so the radius can be entered in centimeters. It comes out at 1.11824 × 10^-5.
Which radius should I use?
Usually r max, the distance from the rotor's axis to the bottom of the tube, which is printed on the rotor or in its manual. If a protocol specifies r av or r min, use that instead. The g-force at the top of the tube is lower in proportion to its radius.