Centrifugal Force Calculator - Circular Motion Solver

A centrifugal force calculator is a circular-motion tool that evaluates F = m v^2 / r (equivalently F = m omega^2 r) for a body of mass m on a circular path of radius r at tangential speed v or angular velocity omega, so you can read off the outward pseudo-force in the rotating frame plus the centripetal acceleration and rotation period that produce it.

• • Sizing centrifuge bowls: Estimate the apparent force on a sample inside a lab centrifuge or a milk-separator bowl at a given rpm and radius.
• • Rotating machinery design: Check the load on a rotor, fan, or washing-machine drum at operating speed to pick bearing hardware with enough margin.
• • Amusement ride physics: Work out apparent weight gain on a rotating ride at the rim versus closer to the axis.
• • Orbital sanity checks: Verify the balance between centrifugal pseudo-force and gravitational pull for a roughly circular satellite orbit.

The centrifugal force is a pseudo-force that appears only in the rotating reference frame. In the inertial frame the same magnitude acts inward as the centripetal force that bends the path into a circle.

This calculator supports three rotation inputs - angular velocity in rad/s, rotational speed in rpm, and tangential speed in m/s - so the same tool handles a lab centrifuge, an engineering rotor, and a textbook wheel problem.

When you want to translate the outward pseudo-force into a real-world acceleration on a known mass, the forces calculator applies F = m * a to the same rotating problem.

The calculator normalises your rotation input to a single angular velocity omega, computes a_c = omega^2 r, then solves F = m a_c for the variable you picked in the Solve For menu.

• F: Centrifugal force in newtons (N), equal in magnitude to the centripetal force in the inertial frame.
• m: Mass of the rotating body in kilograms (kg).
• r: Radius of the circular path in metres (m) from the rotation axis to the body.
• v: Tangential speed in metres per second (m/s), equal to omega * r.
• omega: Angular velocity in radians per second (rad/s), equal to 2*pi times the rotational frequency.
• n: Rotational speed in revolutions per minute (rpm); converted internally by multiplying by 2*pi/60.

The centripetal acceleration output is reported separately so you can verify the multiplication omega^2 r by hand. The period T = 2*pi / omega and the rotational speed in rpm appear alongside so you can switch freely between angular and rotational units.

If you choose a rotation mode other than angular velocity, the calculator solves for omega first: rpm multiplies by 2*pi/60, and tangential speed divides by radius.

According to Wikipedia - Centripetal force, A body of mass m moving at tangential speed v on a circular path of radius r experiences an inward centripetal force of magnitude F = m * v^2 / r, which is equal in magnitude to the outward centrifugal pseudo-force in the rotating frame.

According to HyperPhysics - Circular Motion, For a particle at radius r rotating at angular velocity omega, the centripetal acceleration is omega^2 * r and the outward pseudo-force in the rotating frame is F = m * omega^2 * r.

Once you know the centrifugal load on the rotor, the torque power speed calculator converts it into the shaft torque and motor power you need to keep the rotation steady.

Four ideas from classical mechanics that make the centrifugal force formula more than a one-line equation.

These four ideas reappear everywhere from washing-machine drum balancing to particle-physics cyclotrons, where charged particles spiral outward as their energy grows and the magnetic field bends their path inward at the same rate.

For a satellite in a circular orbit the centrifugal pseudo-force balances gravity, so the orbital period calculator gives the matching orbital period for the same radius and central mass.

Use the centrifugal force calculator in five steps.

1. 1 Pick the variable to solve for: Open the Solve For menu and choose centrifugal force, mass, radius, or angular velocity. The calculator rearranges the formula for you.
2. 2 Choose a rotation input mode: Set Rotation Input Mode to angular velocity (rad/s), rpm, or tangential speed (m/s).
3. 3 Enter the three known variables: For solve-for force, type mass, radius, and rotation rate. For mass, radius, or angular velocity, a centrifugal force field appears; enter the known force plus the other two kinematic variables.
4. 4 Type the rotation rate: Enter the value that matches the rotation mode you picked. The calculator silently updates the other rotation outputs so they stay consistent.
5. 5 Read the solved variable and supporting outputs: The primary output shows the solved variable in its natural unit, with centripetal acceleration, period, and rpm reported below as a sanity check.

For a 0.5 kg sample inside a 20 cm rotor spinning at 1200 rpm, set Solve For to centrifugal force, Rotation Input Mode to rotational speed, mass to 0.5 kg, radius to 0.2 m, and rotational speed to 1200 rpm. The calculator returns about 1579 N with a centripetal acceleration of 3158 m/s^2.

When the rotating body is a fluid inside a centrifuge, the Reynolds number calculator tells you whether the flow stays laminar or tips into turbulence before you trust the pseudo-force reading.

Practical reasons to use this centrifugal force calculator instead of rearranging the equation by hand.

• • One tool for three rotation modes: Switch between rad/s, rpm, and tangential speed without leaving the page.
• • Four solve-for choices in one place: Pick force, mass, radius, or angular velocity from the Solve For menu and the calculator rearranges F = m omega^2 r for you.
• • Auditable centripetal acceleration: Centripetal acceleration is reported in m/s^2, so you can verify the multiplication omega^2 r by hand.
• • Centrifugal and centripetal in one view: The outward pseudo-force and the inward centripetal acceleration share the same magnitude, so one number plays both roles.
• • Useful for lab and classroom problems: Test masses (1 g to 1 t), centrifuge radii (cm to m), and rotor speeds all fit inside the input ranges.

The calculator is intentionally narrow: it solves one equation across three rotation modes and four solve-for variables. For flows with significant radial pressure gradients or relativistic rotation speeds, you would still need a more detailed model.

The same F = m * a form drives deceleration analysis in a crash, so the car crash force calculator uses the same equation for straight-line inertia.

What changes the centrifugal force the calculator returns, and what it cannot capture.

• • The calculator assumes rigid rotation, so it does not capture fluid pressure gradients inside a spinning tank or relativistic speed corrections.
• • The tangential speed mode uses v = omega * r, so it requires non-zero radius; if your radius is zero, switch to rad/s or rpm instead.
• • The Solve For menu uses the static form F = m omega^2 r, so variable-mass systems such as a leaking centrifuge are out of scope.

The centrifugal force formula is the starting point for centrifuge design, orbital mechanics, and rotating machinery analysis, but each application adds extra physics on top of the static balance reported here.

According to Wikipedia - Radian, One full revolution equals 2*pi radians, so a rotational speed of n rpm corresponds to an angular velocity omega = n * 2*pi / 60 rad/s.