acalculator

What is the centrifuge RCF (× g)?

Type any two of the rotor speed in rpm, the radius and the relative centrifugal force (RCF). The centrifuge RCF calculator works out the third, so you can turn a protocol’s × g into rpm for your rotor, or rpm into × g.

Your numbers

Units
RCF (× g)
1,006.42

At 3,000 rpm and a radius of 10 cm, the relative centrifugal force is 1,006.42 × g.

Angular speed (rad/s)
314.159
Centripetal acceleration (m/s²)
9,869.6

RCF (× g): 1,006.42. At 3,000 rpm and a radius of 10 cm, the relative centrifugal force is 1,006.42 × g.

RCF (× g) by speed (rpm)

How to calculate

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.

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.

Formula: 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.

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Speed (rpm) 75,000, Radius 7.5 cm gives RCF (× g) 471,759.16985, Angular speed (rad/s) 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. Speed (rpm) 3,000, Radius 10 cm gives RCF (× g) 1,006.419562, Centripetal acceleration (m/s²) 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. RCF (× g) 1,000, Radius 10 cm gives Speed (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. RCF (× g) 16,000, Speed (rpm) 13,300 gives Radius 8.08873 cm.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)

How it works

A sample at radius r on a rotor turning at ω radians per second has the centripetal acceleration a = r × ω² (OpenStax). One revolution is 2π radians, so a speed in revolutions per minute is

ω = 2π × rpm ÷ 60 rad/s

The relative centrifugal force is that acceleration as a multiple of standard gravity, g = 9.80665 m/s²:

RCF = r × ω² ÷ g = r × (2π × rpm ÷ 60)² ÷ 9.80665

with r in meters. With r in centimeters, (2π ÷ 60)² ÷ 9.80665 ÷ 100 = 1.118244 × 10⁻⁵, so RCF = 1.118244 × 10⁻⁵ × r(cm) × rpm². The 1.118 × 10⁻⁵ often printed is this constant rounded; the page uses the full value.

Type any two of rpm, radius and RCF:

  • RCF = r × (2π × rpm ÷ 60)² ÷ 9.80665
  • rpm = (60 ÷ 2π) × √(RCF × 9.80665 ÷ r)
  • r = RCF × 9.80665 ÷ (2π × rpm ÷ 60)²

The page also shows the angular speed ω = 2π × rpm ÷ 60 in rad/s and the acceleration a = r × ω² in m/s².

Rules. Speed above 0 and at most 200,000 rpm; radius above 0 and at most 1 m (100 cm); RCF above 0 and at most 50,000,000 × g. A solved value outside these limits has no answer. The radius can be typed in mm, cm or inches (1 in = 2.54 cm exactly).

Output format. Each value shows 6 significant figures; a solved radius shows in cm.

Worked examples by hand

An ultracentrifuge (OpenStax Example 6.3). 75,000 rpm at r = 7.50 cm = 0.075 m. ω = 2π × 75,000 ÷ 60 = 7,853.98 rad/s. a = 0.075 × 7,853.98² = 4,626,377 m/s². RCF = 4,626,377 ÷ 9.80665 = 471,759 × g. OpenStax divides by 9.80 m/s² and rounds to 4.72 × 10⁵.

A benchtop run. 3,000 rpm at r = 10 cm. RCF = 1.118244 × 10⁻⁵ × 10 × 3,000² = 1,006.42 × g. The acceleration is 0.1 × 314.159² = 9,869.6 m/s².

rpm for 1,000 × g at 10 cm. rpm = √(1,000 ÷ (1.118244 × 10⁻⁵ × 10)) = √8,942,592 = 2,990.42 rpm.

Radius for 16,000 × g at 13,300 rpm. r = 16,000 ÷ (1.118244 × 10⁻⁵ × 13,300²) = 16,000 ÷ 1,978.06 = 8.08873 cm.

Other questions people ask

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.