Centrifugal Force Formula for Laboratory Centrifuges, and the Relationship Between Rotational Speed and RCF

The centrifuge is a core piece of equipment used in laboratories to separate mixtures. Its fundamental principle is to utilize the centrifugal force generated by high-speed rotation to cause substances of different densities to separate into layers.
Understanding the calculation of centrifugal force (relative centrifugal force, RCF) and its relationship to rotational speed (RPM) is crucial for the proper use of centrifuges.
Imagine this: You take a glass of water mixed with sand, and you spin it vigorously—eventually, the sand sinks to the bottom, while the water stays on top. That’s exactly what a centrifuge does, except it spins so fast that it can separate cells, viruses, and even DNA—things that are invisible to the naked eye!
A centrifuge is like a high-speed spinning “spin dryer”—the faster the test tubes inside rotate, the more vigorously the contents are “spun” around. This force of “spinning” is what we call centrifugal force.

I. What exactly is the difference between rotational speed (RPM) and relative centrifugal force (RCF)?
RPM (revolutions per minute): The number of rotations per minute. For example, “1200 RPM” during the spin cycle of a washing machine.
RCF (×g): This represents how many times the actual centrifugal force is greater than Earth's gravitational force. For example, "5000×g" means the centrifugal force is 5,000 times stronger than Earth's gravity.
Key points:
Centrifugal force depends not only on the rotational speed but also on the radius of the centrifuge rotor (the distance of the tube from the central axis).
For example:
Small-radius rotor (like an electric fan blade): At the same rotational speed, the centrifugal force is smaller.
Large-radius rotor (like a Ferris wheel): At the same rotational speed, the centrifugal force skyrockets!

II. Why do laboratories place greater emphasis on RCF?
Suppose you conduct the experiment according to the literature’s requirement of “12,000 rpm”:
Using someone else’s large rotor centrifuge: The centrifugal force could exceed the limit and tear the sample apart!
Using your own small rotor centrifuge: Insufficient centrifugal force—experiment failed!
Therefore, RCF must be calculated! Formula:
Centrifugal force (RCF) = 0.00001118 × Rotor radius (cm) × Rotational speed²
Lazy person's trick:
Find the radius on the rotor (usually marked on the side).
Use the “RCF/RPM Conversion Button” built into the centrifuge, or a mobile phone calculator.

III. Practical Guide to Avoiding Pitfalls
1. Should I choose rotational speed or centrifugal force?
Document requirement: If the notation is “10,000×g,” enter the RCF value directly.
Check the machine’s features: Older centrifuges may only allow you to adjust the speed, so you’ll have to calculate the RCF yourself.
2. Never misuse the rotor!
Each rotor has a maximum speed limit (indicated on the nameplate).
Large-capacity rotors have low speeds, while small rotors have high speeds—mixing them up can cause the drone to explode!
3. Must be balanced!
The test tubes must be placed symmetrically, with a weight difference of no more than 0.1 gram! Otherwise, at the very least the machine will start to vibrate erratically; at worst, the rotor could disintegrate.

IV. What centrifugal force should be used for different experiments?

5. Dangerous operations are not advisable—when conducting centrifuge experiments, safety comes first!
Take the rotor to high speed.

Each rotor is labeled with its maximum allowable RPM and RCF. Exceeding these limits could cause the rotor to rupture (posing a risk of metal fatigue). For example:

Rotor A: Maximum RPM = 15,000, corresponding RCF = 20,000 × g ( $=10\text{cm}$ r );

Rotor B: Maximum RPM = 10,000, corresponding RCF = 22,360 × g ( $=20\text{cm}$ r ).
Do not cover the centrifuge lid.
Don’t open the lid after centrifugation—let it sit to thaw: Ice forms inside the frozen centrifuge, and the next time you open it, you’ll just snap the sealing ring right off.

VI. Common Misconceptions and Answers
1. Misconception: Does a higher rotational speed always lead to better separation performance?
Correction: An excessively high RCF may damage the sample (e.g., by lysing cells); therefore, it is necessary to select an appropriate RCF based on the density of the target substance.
2. Misconception: Can “the same RPM” from different centrifuges be used interchangeably?
Correction: The RCF must be recalculated based on the rotor radius; otherwise, the experimental conditions will not match.

The separation efficiency of a centrifuge is determined by the RCF (relative centrifugal force), not simply by the rotational speed. The formula for calculating RCF reveals the dynamic relationship among rotational speed, rotor radius, and centrifugal force. Mastering the conversion logic between RPM and RCF not only ensures experimental reproducibility but also helps avoid the risk of equipment overload. In essence, the centrifuge’s core lies in this: Rotational speed (RPM) is merely superficial—centrifugal force (RCF) is where its true strength resides!
When reading literature, start with the RCF; always check the radius whenever changing rotors—balancing must be obsessive-compulsive!