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RCF to RPM Calculator (Centrifuge g-Force Conversion)

Enter the rotor radius, then either the speed or the g-force, and get the other one. Useful when a protocol gives ×g but your centrifuge only lets you set rpm.

Inputs

Convert

cm

r max: distance from the rotor axis to the tube bottom

×g

Results

Speed
11,583 rpm

Formula

RCF (×g) = 1.118 × 10⁻⁵ × r (cm) × rpm²

rpm = √(RCF ÷ (1.118 × 10⁻⁵ × r))

Tip: Use r max, the distance from the rotor axis to the tube bottom. Results are rounded to whole numbers so you can enter them directly.

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How the formula works

  1. Centrifugal force comes from centripetal acceleration: a = ω² × r, where ω is the angular velocity in rad/s and r is the distance from the axis of rotation.
  2. rpm is revolutions per minute. Convert it to angular velocity with ω = 2π × rpm ÷ 60.
  3. RCF says how many times stronger that acceleration is than gravity: RCF = ω² × r ÷ g, with g = 9.80665 m/s².
  4. With r entered in cm, divide by 100 to get meters. Combining the constants, (2π ÷ 60)² ÷ (100 × 9.80665) ≈ 1.118 × 10⁻⁵, which gives RCF = 1.118 × 10⁻⁵ × r (cm) × rpm².
  5. Solving for speed: rpm = √(RCF ÷ (1.118 × 10⁻⁵ × r)). Force goes with the square of the speed, so doubling the rpm gives four times the ×g.
  6. Which radius: different parts of the tube sit at different distances from the axis. The tube bottom is farthest out (r max), the liquid surface is closest (r min), and the midpoint between them is the average radius (r av). At a given rpm the force is highest at r max. Manufacturers and most protocols quote ×g at r max; some protocols, more often in ultracentrifugation, quote it at r av. Use whichever radius your protocol specifies.
  7. Rounding: this calculator rounds speed to the nearest whole rpm, and rounds force to a whole number at 10 ×g and above, or to one decimal place below 10 ×g.

Worked examples

Microcentrifuge: what is 12,000 rpm at r = 8.4 cm in ×g?

  1. Plug in: RCF = 1.118 × 10⁻⁵ × 8.4 × 12000².
  2. 12000² = 1.44 × 10⁸.
  3. 1.118 × 10⁻⁵ × 8.4 × 1.44 × 10⁸ = 13,523.328.
  4. Rounded: 13,523 ×g. The 8.4 cm radius is only an example; use the r max printed on your rotor or in its manual.

Swing-bucket rotor: what rpm gives 500 ×g at r = 15 cm?

  1. Use the reverse formula: rpm = √(500 ÷ (1.118 × 10⁻⁵ × 15)).
  2. 1.118 × 10⁻⁵ × 15 = 1.677 × 10⁻⁴.
  3. 500 ÷ (1.677 × 10⁻⁴) ≈ 2,981,515.
  4. √2,981,515 ≈ 1726.7, which rounds to 1727 rpm.
  5. If your centrifuge only steps in 100 rpm, 1700 rpm gives about 485 ×g, slightly under target; if it steps in 10 rpm, 1730 rpm gives about 502 ×g. Whether that deviation is acceptable is up to your protocol.

Common mistakes

Using the wrong rotor radius

Plugging in r min, or the radius of a different rotor. At the same 12,000 rpm, r = 8.4 cm gives 13,523 ×g while 4.5 cm gives only about 7245 ×g, a little over half. Check whether your protocol means r max or r av, then look up that radius for the rotor you are using.

Entering ×g as rpm

The protocol says 5000 ×g and the centrifuge gets set to 5000 rpm. Many centrifuges can switch the display between rpm and RCF, so check which unit is showing before you set it.

Keeping the same rpm after changing rotors

Swap the rotor on the same centrifuge and the radius changes, so the same rpm no longer gives the same ×g. Record ×g in your notes, or the rotor model together with the rpm, and recalculate when you change rotors.

Treating fixed-angle and swing-bucket rotors as the same

In a fixed-angle rotor the tube is held at an angle and the pellet forms on the outer wall near the bottom, with a short sedimentation path. In a swing-bucket rotor the tube swings out horizontal, the pellet forms at the center of the tube bottom, and r max is usually larger. At the same ×g, switching rotor types can change where the pellet sits and how long the spin needs, so if your protocol names a rotor type, follow it.

FAQ

My protocol says 12,000 ×g but my centrifuge only takes rpm. What do I set?+
Find the rotor radius r (r max in cm, printed on the rotor or in the manual), then solve for speed: rpm = √(RCF ÷ (1.118 × 10⁻⁵ × r)). With r = 8 cm, √(12000 ÷ (1.118 × 10⁻⁵ × 8)) ≈ 11,583 rpm. If your centrifuge only steps in hundreds, use 11,600 rpm.
How do I find the rotor radius?+
Use the distance from the center of rotation to the bottom of the tube, listed as r max in cm. It is usually printed on the rotor or given in the centrifuge manual or on the manufacturer's site. Fixed-angle and swing-bucket rotors have different radii, so recalculate when you change rotors.
Why does the same rpm give a different g-force on another centrifuge?+
g-force scales with the radius and with the square of the speed. A larger rotor produces more force at the same rpm, which is why papers and kit manuals give ×g: it carries over to any centrifuge.
Roughly how many ×g is 3000 rpm?+
It depends on the rotor. A 15 cm swing-bucket rotor gives 1.118 × 10⁻⁵ × 15 × 3000² ≈ 1509 ×g, while an 8 cm rotor gives only about 805 ×g.
Do I need to change the spin time after converting?+
No. Once the g-force matches, keep the time from the protocol. If your centrifuge cannot reach the required ×g, a longer spin will not reliably make up for it, so use one that can.
What is the formula to convert RCF to rpm?+
RCF = 1.118 × 10⁻⁵ × r × rpm², where r is the rotor radius in cm. To go from rpm to ×g, plug the speed in directly. To go from ×g to rpm, use rpm = √(RCF ÷ (1.118 × 10⁻⁵ × r)). For example, 12,000 rpm at r = 8.4 cm is about 13,523 ×g, and 500 ×g at r = 15 cm needs about 1727 rpm.
Why do protocols give ×g instead of rpm?+
What pellets your sample is the force it feels, not how fast the rotor turns. The same rpm gives a different force on rotors of different radius, while ×g is the physical quantity itself, so anyone can convert it back to rpm for their own rotor. That is why kit manuals and methods sections usually give ×g and a time.
Where does the 1.118 × 10⁻⁵ constant come from?+
From RCF = ω² × r ÷ g. Angular velocity is ω = 2π × rpm ÷ 60, r entered in cm is divided by 100 to get meters, and g is 9.80665 m/s². Combining the constants gives (2π ÷ 60)² ÷ (100 × 9.80665) ≈ 1.118 × 10⁻⁵. Some references use 1.12 × 10⁻⁵, which is the same value with fewer significant figures; the results differ by about 0.2%.
How many ×g is 13,000 rpm?+
It depends on the rotor radius. At r = 8.4 cm, 1.118 × 10⁻⁵ × 8.4 × 13000² ≈ 15,871 ×g; at r = 7 cm it is about 13,226 ×g. The rotor or the manual often lists the ×g at maximum speed, so go by what your machine states.

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