# What is the centrifuge RCF (× g)?

Converts a centrifuge’s speed in rpm and rotor radius to the relative centrifugal force (RCF, × g), or finds the rpm or radius for a given g-force.

- Page: https://www.acalculator.org/biology/centrifuge-calculator
- JSON spec: https://www.acalculator.org/biology/centrifuge-calculator.json
- Version: 49f7ee527844

## Default answer

Example with the default inputs (Speed (rpm) 3,000, Radius 10 cm): At 3,000 rpm and a radius of 10 cm, the relative centrifugal force is 1,006.42 × g.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| rpm | Speed (rpm) | The rotor speed in revolutions per minute. |
| r | Radius | The distance from the center of the rotor to the sample, usually to the bottom of the tube. |
| g | RCF (× g) | The relative centrifugal force: the acceleration at the radius as a multiple of standard gravity. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| rpm | Speed (rpm) | 60 ÷ 2π × √(RCF × g ÷ r). |
| r | Radius | RCF × g ÷ ω². |
| rcf | RCF (× g) | r × ω² ÷ 9.80665 m/s². |
| omega | Angular speed (rad/s) | ω = 2π × rpm ÷ 60. |
| accel | Centripetal acceleration (m/s²) | a = r × ω², the acceleration at the radius. |

## Method

RCF = r × ω² ÷ g with ω = 2π × rpm ÷ 60 and g = 9.80665 m/s², which is RCF = 1.11824 × 10⁻⁵ × r(cm) × rpm²; rpm = (60 ÷ 2π) × √(RCF × g ÷ r); r = RCF × g ÷ ω².

## Assumptions

- The radius is measured from the center of the rotor to the point of interest, usually the bottom of the tube (the maximum radius).
- RCF is the centripetal acceleration divided by the standard acceleration of gravity, 9.80665 m/s²; the pull of Earth’s gravity itself is not added.
- The constant 1.118 × 10⁻⁵ often quoted for r in cm is (2π ÷ 60)² ÷ 9.80665 ÷ 100 = 1.118244 × 10⁻⁵, rounded; this page uses the unrounded value.

## Worked examples

1. rpm = 75,000, r = 0.075 gives g = 471,759.16985, omega = 7,853.981634. Source: OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18).
2. rpm = 3,000, r = 0.1 gives g = 1,006.419562, accel = 9,869.604401. Source: OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18).
3. g = 1,000, r = 0.1 gives rpm = 2,990.416772. Source: OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18).
4. g = 16,000, rpm = 13,300 gives r = 0.080887. Source: OpenStax, College Physics 2e, §6.2 Centripetal Acceleration (a_c = rω²; Example 6.3: a point 7.50 cm from the axis of an ultracentrifuge at 7.50 × 10⁴ rev/min has ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g = 9.80 m/s²), https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18); NIST, CODATA 2022, standard acceleration of gravity g_n = 9.806 65 m s⁻² (exact), https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18).

## FAQ

### How do I convert rpm to RCF (× g)?

Use RCF = 1.118 × 10⁻⁵ × r × rpm², with the radius r in centimeters. At 3,000 rpm and r = 10 cm: 1.118244 × 10⁻⁵ × 10 × 3,000² = 1,006 × g. The constant comes from (2π ÷ 60)² ÷ 9.80665 m/s² ÷ 100.

### How do I convert RCF to rpm?

Rearrange the same formula: rpm = √(RCF ÷ (1.118 × 10⁻⁵ × r)). For 1,000 × g at r = 10 cm, rpm = √(1,000 ÷ 0.0001118244) = 2,990 rpm.

### What radius should I use?

The distance from the center of the rotor to the sample. Protocols usually mean the maximum radius, to the bottom of the tube; rotor manuals list it as r max. The RCF at the top of the tube is lower, in proportion to its smaller radius.

### Why do protocols give × g instead of rpm?

The force on a sample depends on both the speed and the radius, so the same rpm gives different forces in different rotors. A value in × g gives the same result in any centrifuge once it is converted to rpm for that rotor.

### What is the difference between RCF and g-force?

They are the same thing here: the centripetal acceleration of the sample divided by standard gravity, 9.80665 m/s². RCF is written as a multiple of g, such as 16,000 × g.

### Why does doubling the speed give four times the force?

The acceleration is r × ω², so it grows with the square of the speed. Twice the rpm gives 4 times the RCF; twice the radius gives only twice the RCF.

## Sources

- OpenStax, College Physics 2e, §6.2 Centripetal Acceleration: a_c = v² ÷ r = rω²; Example 6.3, How Big Is the Centripetal Acceleration in an Ultracentrifuge? (7.50 cm, 7.50 × 10⁴ rev/min, ω = 7854 rad/s, a_c = 4.63 × 10⁶ m/s², 4.72 × 10⁵ times g). https://openstax.org/books/college-physics-2e/pages/6-2-centripetal-acceleration (retrieved 2026-10-18)
- NIST, Fundamental Physical Constants (CODATA 2022): standard acceleration of gravity, g_n = 9.806 65 m s⁻² (exact). https://physics.nist.gov/cgi-bin/cuu/Value?gn (retrieved 2026-10-18)