Centrifugal Force Calculator

Centrifugal Force Calculator for F = mv²/r with speed in m/s, rpm or rad/s. It solves for force, mass, radius, velocity or acceleration and converts centrifuge rpm to RCF and back.

Using the Centrifugal Force Calculator

The Centrifugal Force Calculator has one Solve For menu with two groups. The first works with F = mv² ÷ r and returns the force, the mass, the radius, the velocity or the centrifugal acceleration. The second is for centrifuges and converts rotor speed in rpm to RCF and back.

Speed goes in one field, and its unit list decides the formula. Pick m/s, km/h, ft/s or mph for a tangential velocity, or rpm, rad/s or rev/s for an angular velocity. With an angular unit the tool switches to F = mω²r and shows that form in the working.

Four cards sit under the answer. They give the force in lbf with the mass that would weigh as much, the centrifugal acceleration and g-force, the rotation rate, and how much of an optional force limit is used. The limit panel is closed on load and never changes the main result.

For physics homework, the Step-by-Step Working panel of the Centrifugal Force Calculator lists every value in SI units before the final line. The Force at Other Speeds table then shows the same mass and radius at half, 1.5, 2 and 3 times your speed.

What Is Centrifugal Force?

Centrifugal force is the outward push you feel when you move in a circle. Britannica defines it as a fictitious force with the same magnitude and dimensions as the centripetal force, pointing the opposite way. It appears only when the motion is described from inside the rotating frame.

Seen from the ground, nothing pushes outward. A stone whirled on a string is pulled inward by the string, and if the string breaks the stone leaves along a straight tangent line. Inside a turning car the same event feels like being thrown toward the door.

What is another name for centrifugal force?

Centrifugal force is also called a fictitious force or an inertial force, and many textbooks use pseudo force for the same idea. OpenStax University Physics calls it an inertial force that is felt in a rotating frame and has no physical source.

Why is it called centrifugal?

The word means center-fleeing. Merriam-Webster traces it to the New Latin centrifugus, built from centr- and the Latin fugere, to flee, with a first known use in 1709. Centripetal, its partner, means center-seeking, which fits a real force that points inward.

What are the 7 types of forces?

School physics usually lists applied force, gravity, the normal force, friction, air resistance, tension and spring force, the set used by The Physics Classroom, which adds electrical and magnetic forces as well. Centrifugal force is not on that list. Each of those comes from an interaction between two objects, while centrifugal force comes from the choice of a rotating viewpoint.

Centrifugal Force Formula

The centrifugal force formula is the centripetal force formula with the direction reversed. It needs the mass of the object, its tangential velocity and the radius of its circular path, with the radius measured from the axis of rotation.

$$F = \frac{m v^2}{r}$$

How do I calculate centrifugal force?

Square the speed, multiply by the mass and divide by the radius. The default entries are 10 kg moving at 5 m/s on a 2 m circle, so F = 10 × 5² ÷ 2 = 125 N. The first card shows the same force as 28.101 lbf and an effective mass of 12.746 kg, the mass that weighs 125 N at rest. The 10 kg load itself weighs 98.066 N.

OpenStax works a 900 kg car on a flat 500 m curve at 25 m/s. In the Centrifugal Force Calculator those entries give 1,125 N, the textbook value. The g-force row reads 0.12746, which is also the lowest tire friction coefficient that holds the car on the curve, 0.13 in the book.

Set Solve For to Mass, Radius or Velocity to run the formula backward from a known force. With 125 N, 10 kg and 2 m, the velocity comes back as √(125 × 2 ÷ 10) = 5 m/s, and the rotation card adds 23.873 rpm.

Centrifugal force formula with RPM

When the spin is given in rpm, convert it to angular velocity first and then use the angular form of the formula. One rpm is 2π ÷ 60 rad/s, or 0.10472 rad/s, and the Angular Velocity Calculator covers that conversion on its own.

$$F = m \omega^2 r, \quad \omega = \frac{2 \pi N}{60}$$

Pick rpm as the speed unit and the Centrifugal Force Calculator does both steps. A 2 kg part turning at 300 rpm on a 0.5 m arm has ω = 31.416 rad/s and F = 2 × 31.416² × 0.5 = 986.96 N. Force rises with the square of speed, so 600 rpm gives 3,947.8 N. Britannica makes the same point with a jump from 10 to 100 rpm, which raises the force 100 times.

Centripetal vs centrifugal force formula

The two share one formula and one value. They differ in direction and in who observes them. The Centrifugal Force Diagram in the tool draws both arrows on the same mass, with the centripetal arrow solid and the centrifugal arrow dashed.

Centrifugal Force Unit

The SI unit of centrifugal force is the newton, N, the same as for any force. One newton is 1 kg·m/s², which makes the centrifugal force dimensional formula M L T⁻². You can check it from mv² ÷ r, since kg × (m/s)² ÷ m reduces to kg·m/s².

$$[F] = M L T^{-2}$$

Other units are a fixed factor away. One newton is 0.22481 lbf and 0.10197 kgf, and the Centrifugal Force Calculator accepts kN, lbf and kgf when you solve for something else. In centrifuge work the force is replaced by RCF, a pure number that counts multiples of gravity, and the RCF fields carry a fixed × g label.

How is centrifugal force measured?

It is usually calculated from mass, radius and speed, since those are simple to measure. A direct reading comes from the real inward force that matches it, such as the tension in a string read on a spring scale or load cell. An accelerometer on the rotating part gives the acceleration, and multiplying by the mass gives the force.

Centrifugal Acceleration and g-Force

Dividing the force by the mass leaves the centrifugal acceleration, which depends only on speed and radius. People who search for a centrifugal acceleration calculator want this value. Set Solve For to Centrifugal Acceleration (a) and the tool asks for a radius and a speed only.

$$a = \frac{v^2}{r} = \omega^2 r$$

How do I calculate g force?

Divide the acceleration by standard gravity, 9.80665 m/s². The default case has a = 5² ÷ 2 = 12.5 m/s², which is 12.5 ÷ 9.80665 = 1.2746 × g, or 41.01 ft/s². The 10 kg mass therefore presses outward as if it weighed 1.2746 times its normal weight.

In that mode the Centrifugal Force Calculator loads 2 m and 5 m/s and returns a = 12.5 m/s². The working reads v² ÷ r, or ω² × r when the speed is in rpm or rad/s. Mass is optional there. Open Mass and Force Limit to add one and the first card gives the force, which is 0.625 N for a 50 g mass.

Mass does not enter the g-force. A heavier object at the same speed and radius feels more force and the same acceleration. This is why centrifuge settings are quoted in × g, which applies to every tube in the rotor whatever it holds.

RCF and RPM in a Centrifuge

RCF stands for relative centrifugal force, the centrifugal acceleration on a sample as a multiple of g. RPM is the rotor speed in revolutions per minute. The two are tied together by the rotor radius, and a Thermo Fisher technical note gives the working formula with the radius in centimeters.

$$\text{RCF} = 1.118 \times 10^{-5} \times r \times N^2$$

What is the formula for RCF?

RCF equals 1.118 × 10⁻⁵ times the radius in cm times the rpm squared. This is the formula for centrifugation in the Thermo Fisher note, written there as g = (1.118 × 10⁻⁵) R S². The constant is (2π ÷ 60)² ÷ 9.80665 for a radius in cm, and the tool carries it as 1.11824 × 10⁻⁵.

To calculate RCF for a centrifuge, measure from the center of the rotor to the sample and read the rpm from the dial. Thermo Fisher’s own example is 5,000 rpm at 7 cm, which gives 1,957 × g. Choose RCF (g-force) from RPM in the Solve For menu of the Centrifugal Force Calculator and the same entries return 1,956.9 × g.

What is 12000 RPM in RCF?

It depends on the rotor. At a 10 cm radius, 12,000 rpm is 16,103 × g, which is the example the Centrifugal Force Calculator loads in this mode. On a 5 cm rotor the same speed gives 8,051.4 × g, and at 15 cm it gives 24,154 × g.

The table answers the common lookups. 1,000 rpm in RCF is 111.82 × g at 10 cm, and to convert 15,000 rpm to g at that radius the answer is 25,160 × g. Tripling the radius triples the RCF, while tripling the rpm raises it nine times.

How do I convert 500 RCF to RPM?

Rearrange the formula for speed. Divide the RCF by 1.118 × 10⁻⁵ times the radius in cm, then take the square root. For 500 × g on a 10 cm rotor, N = √(500 ÷ (1.118 × 10⁻⁵ × 10)) = 2,114.5 rpm. That is the default result of the RPM from RCF mode in the Centrifugal Force Calculator.

$$N = \sqrt{\frac{\text{RCF}}{1.118 \times 10^{-5} \times r}}$$

So 200 g in RPM is 1,337.4 rpm on a 10 cm rotor, 1,300 RCF is 3,409.6 rpm and 500 RCF is 2,114.5 rpm. A protocol that only says 1,300 × g cannot be turned into rpm until you know your own rotor radius.

Is RCF equal to g?

Yes, RCF and × g are two names for one number. 300 g is the same as 300 RCF, 1,000 g is 1,000 RCF, 1,500 g is 1,500 RCF, and 5,000 g or 10,000 g are 5,000 and 10,000 RCF. The g here means multiples of gravity, not grams.

RPM is not also g. An rpm figure becomes a g-force only after it is combined with a radius, which is why 12,000 rpm can mean 8,051.4 × g on one rotor and 24,154 × g on another.

Why is RCF better than RPM?

RCF describes what the sample feels, so it carries from one centrifuge to another. A Thermo Fisher buying guide says the RCF value more accurately represents the separation force applied to your samples. The same rpm on a wider rotor would spin them harder.

Beckman Coulter gives its JS-4.2 rotor as an example, with a top speed of 4,200 rpm and a maximum radius of 254 mm. That works out to about 5,010 × g at the bottom of the bucket, and only 1,136.1 × g when the rotor is slowed to 2,000 rpm.

What is centrifugal force in a centrifuge?

It is the outward force on each tube, and it is far larger than the weight of the sample. In the Centrifugal Force Calculator, open Sample, Rating, Rotors and enter the mass. A 50 g tube at 16,103 × g is pushed outward with 7.8957 kN, as if it weighed 805.14 kg.

The same panel takes the maximum RCF rating of your tube or rotor. With a 25,000 × g rating, 16,103 × g uses 64.411% of it, a safety factor of 1.5525, and the rating would be reached at 14,952 rpm. The card turns red once the RCF passes the rating.

RCF at minimum radius and on a second rotor

A tube does not sit at one radius. The top of the liquid is closer to the axis than the bottom, so it feels less force. Enter the Minimum Radius (r min) in the same panel and the RCF at Common Speeds table adds the RCF at that point. At 12,000 rpm, a 10 cm rotor gives 16,103 × g at the bottom and 8,051.4 × g at a 5 cm minimum radius.

To move a protocol to another centrifuge, keep the RCF and change the rpm. The speeds scale with the square root of the radius ratio, and the Second Rotor Radius field in the Centrifugal Force Calculator fills that column of the table.

$$N_2 = N_1 \sqrt{\frac{r_1}{r_2}}$$

For the default rotor pair, 12,000 rpm at 10 cm matches 12,000 × √(10 ÷ 15) = 9,798 rpm at 15 cm, and both give 16,103 × g. Pelleting time also depends on the rotor’s k-factor, which the tool does not work out, so check the rotor manual before you shorten a run.

How to calculate centrifuge capacity?

Capacity is the number of tube positions times the volume of each tube. Thermo Fisher lists rotors this way, for example 8 × 15 mL or 4 × 50 mL, so a 4 × 50 mL rotor holds 200 mL in one run. The stated figure changes with the rotor and adapters fitted.

Why centrifuge at 4 degrees? Cooling protects samples that break down when warm. The Thermo Fisher guide recommends refrigerated models for heat-labile materials and for any protocol that must hold a set temperature such as 4 °C, to prevent heat-induced degradation.

Centrifugal Force Examples

The same formula covers a tube in a rotor, a car in a bend and a person standing on the spinning Earth. Three cases below show the range, from thousands of newtons to a force too small to notice.

For a weight on a string, the string tension is the centripetal force. Set the Force Limit to the breaking load, and the limit card shows how close you are. With the 400 N default, the 125 N example uses 31.25% and the string would fail at 8.9443 m/s. The Tension Calculator handles the string itself.

For a car, the 900 kg OpenStax example needs 1,125 N of sideways grip at 25 m/s on a 500 m curve. Banking the road can supply that force without friction, at the angle found by the Angle of Banking Calculator.

For the Earth, a 70 kg person at the equator circles the axis at 6,378,137 m with ω = 7.2921 × 10⁻⁵ rad/s. The outward force is 2.3741 N against a weight of 686.47 N, about 0.35%. The radius list in the Centrifugal Force Calculator includes km and miles, so the same entry can be typed as 6,378.137 km.

What is 1 RPM equal to?

One rpm is one full turn each minute. That equals 0.10472 rad/s, 6 degrees per second, or one sixtieth of a turn per second. On a 10 cm rotor it produces just 0.00011182 × g, which shows how steeply RCF has to climb with the square of speed to reach useful values.

A rotor does not reach its speed at once. The time it takes depends on the motor torque and the rotor’s inertia, which the Angular Acceleration Calculator works out. A loaded rotor at speed also carries the angular momentum found in the Angular Momentum Calculator.

How do I calculate CFM from RPM?

This question belongs to centrifugal fans, not to force. Airflow in CFM cannot be found from rpm alone, but for a given fan it changes in direct proportion to speed. New York Blower’s example is a fan that moves 10,000 CFM at 1,000 rpm and 20,000 CFM at 2,000 rpm.

More tools for spinning bodies, from torque to moment of inertia, are grouped under Rotational Motion Calculators. Print / PDF in the Centrifugal Force Calculator saves the answer, the cards and the working as one sheet.