Biology and life-science lab
Centrifuge RCF and rpm converter
Convert between relative centrifugal force (× g) and rotor speed (rpm) for a given radius, or find the radius, using RCF = 1.118 × 10⁻⁵ r N².
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Result
- Relative centrifugal force
- 1006 × g
- Constant (2π/60)² ÷ gₙ
- 1.11824 × 10⁻⁵ per cm per rpm²
Working
- RCF = r (2πN/60)² ÷ gₙ = 1.11824 × 10⁻⁵ × r(cm) × N², with gₙ = 9.80665 m/s² (exact)
- RCF = r ω² ÷ gₙ = 10 cm × (2π × 3000 ÷ 60 s)² ÷ 9.80665 m/s² = 1006 × g
- Use the radius from the rotor axis to the point of interest: rotor makers quote r_max (tube bottom), r_av and r_min, which give different RCF values at the same speed. Protocols usually mean r_max or r_av; check your rotor’s manual and never exceed its rated speed.
- Rounded to 4 significant figures.
Method and limits
Protocols should give a force in × g, because the same rpm produces different forces in different rotors. Enter the rotor radius from its manual and convert in either direction.
RCF = r ω² ÷ gₙ = r (2πN ÷ 60)² ÷ gₙ = 1.11824 × 10⁻⁵ × r(cm) × N²
N = √(RCF ÷ (1.11824 × 10⁻⁵ × r(cm)))
ω is the angular speed in rad/s, N the speed in revolutions per minute, r the radius and gₙ = 9.806 65 m/s² the standard acceleration of gravity (exact by definition). The constant 1.11824 × 10⁻⁵ is (2π/60)² ÷ 9.806 65 per centimetre.
Limits
RCF grows along the tube: rotor manuals list r_min, r_av and r_max, and a speed gives a different force at each. Never exceed the rotor’s maximum speed or the tubes’ rated force. Results are shown to four significant figures, the resolution of a centrifuge’s speed setting.
Worked example
A rotor with r = 10.0 cm at 3000 rpm: RCF = 1.11824 × 10⁻⁵ × 10.0 × 3000² = 1006 × g. For 16 000 × g in a microcentrifuge with r = 8.4 cm, N = √(16 000 ÷ (1.11824 × 10⁻⁵ × 8.4)) = 13 050 rpm.
References
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