BYTETOOLS

Centripetal Force Calculator

Solve F = mv² ÷ r for force, mass, speed or radius, with speed entered directly or from a period or rpm, plus g-force and banking angle.

8,000 N
Centripetal force
8 m/s²
Acceleration a
0.816 g
G-force
0.4 rad/s
Angular velocity ω

F = m · v² ÷ r

  • F = 1,000 kg × (20 m/s)² ÷ 50 m = 8,000 N
  • Tangential speed entered directly: 20 m/s.
  • Centripetal acceleration a = v² ÷ r = 8 m/s² (0.816 g).
  • Angular velocity ω = v ÷ r = 0.4 rad/s.
  • One lap takes T = 2πr ÷ v = 15.708 s, i.e. 3.82 rpm.
  • A frictionless banked track would need θ = arctan(v² ÷ (r·g)) = 39.207° of bank to hold this turn.

Centripetal force is not a new kind of force — it is the name for whatever real force (friction, tension, gravity, a track's normal force) happens to point at the centre of the circle. The banking angle assumes a frictionless surface and constant speed; real roads are banked more gently and rely on tyre grip for the rest. Worked example: a 1000 kg car taking a 50 m bend at 20 m/s needs 8000 N, an acceleration of 8 m/s² (0.82 g), and a 39.2° bank if friction is ignored.

What is the Centripetal Force Calculator?

Centripetal force is the inward force that keeps an object moving in a circle: F = m·v² ÷ r. A 1000 kg car taking a 50 m bend at 20 m/s needs 8000 N, an acceleration of 8 m/s² or about 0.82 g.

  • Solves F = mv² ÷ r for force, mass, speed or radius
  • Speed from a direct value, a period (v = 2πr ÷ T) or rpm
  • Reports acceleration, equivalent g-force and angular velocity ω
  • Gives the lap time and the frictionless banking angle for the turn
  • Mass, radius, speed and force unit dropdowns converted to SI first
  • Runs 100% in your browser with nothing uploaded

How to use the Centripetal Force Calculator

  1. 1

    Pick the unknown: centripetal force, mass, tangential speed or radius.

  2. 2

    Choose how the speed is given — directly, as a period in seconds per lap, or in rpm.

  3. 3

    Enter the mass, radius and remaining values, setting the unit dropdown beside each one.

  4. 4

    Read the force, acceleration, g-force and angular velocity in the four result tiles.

  5. 5

    Open the working panel for the lap time and the frictionless banking angle, and copy it if you need it.

About the Centripetal Force Calculator

The ByteTools Centripetal Force Calculator solves F = m·v² ÷ r for any of the four quantities in it. You can type the tangential speed straight in, or let the tool derive it from the time for one lap with v = 2πr ÷ T, or from a rotation rate in revolutions per minute — useful for turntables, centrifuges and anything else quoted in rpm rather than metres per second.

Alongside the force it reports the centripetal acceleration a = v² ÷ r, the same figure expressed in g, the angular velocity ω = v ÷ r, the lap time, and the bank angle a frictionless track would need, θ = arctan(v² ÷ rg). Mass, radius, speed and force each have their own unit dropdown, and every value is converted to SI before the arithmetic runs.

Everything is computed locally in your browser with plain JavaScript — no uploads, no accounts and no stored history. Results refresh as you type, so you can sweep a speed or a radius through a range and watch the force respond, and the page continues to work with no network connection once it has been loaded.

Frequently asked questions

What is the formula for centripetal force?

Centripetal force is F = m·v² ÷ r, where m is the mass, v is the tangential speed and r is the radius of the circular path. Because the speed is squared, doubling the speed quadruples the force needed to stay on the same circle.

Is centripetal force a real force?

Centripetal force is not a separate kind of force — it is the name for whichever real force happens to point at the centre of the circle. Depending on the situation that is tyre friction, string tension, gravity or the normal force from a banked track.

How do you find centripetal force from rpm?

Convert the rotation rate to a tangential speed first with v = 2πr × N ÷ 60, then apply F = mv² ÷ r. This calculator does both steps when you choose the rpm option in the speed dropdown.

What is centripetal acceleration in g?

Divide the centripetal acceleration a = v² ÷ r by 9.80665 m/s² to express it in g. A 50 m bend taken at 20 m/s gives 8 m/s², which is about 0.82 g, so a passenger feels roughly four fifths of their own weight pushing sideways.

How accurate is the banking angle this tool gives?

The angle θ = arctan(v² ÷ rg) assumes a frictionless surface and a constant speed, which is the ideal design case. Real roads and tracks are banked more gently because tyre grip supplies the rest of the inward force, so treat the figure as an upper bound.

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