# Centripetal Force Calculator

> Find the centripetal force for an object moving in a circle, or the speed or radius it allows, with speed in m/s, km/h, mph, rpm or rad/s.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/centripetal-force-calculator

Anything moving in a circle needs an inward force of m v² ÷ r. Enter the speed as a linear speed or as rpm to get the force, acceleration, period and angular velocity.

Also called: Circular motion calculator, Centripetal acceleration calculator.

## Inputs
- Solve for (options: Force, Speed, Radius; default force)
- Mass (default 1000)
- Mass unit (options: kilograms (kg), grams (g), tonnes (t), pounds (lb), ounces (oz); default kg)
- Radius of the circle (default 50)
- Radius unit (options: metres (m), centimetres (cm), millimetres (mm), kilometres (km), feet (ft), inches (in), miles (mi); default m)
- Speed (default 72)
- Speed unit (options: m/s, km/h, mph, ft/s, knots, revolutions per minute (rpm), radians per second (rad/s); default kmh)
- Centripetal force (default 8000)
- Force unit (options: newtons (N), kilonewtons (kN), pounds-force (lbf), kilograms-force (kgf); default n)

## Results
- Result
- Centripetal force
- Centripetal acceleration
- Centripetal acceleration
- Linear speed
- Radius
- Angular velocity
- Rotation rate
- Time per revolution

## Formula

```
F = m v² ÷ r = m ω² r;  a = v² ÷ r;  v = ω r;  T = 2π ÷ ω
```

Where:
- F: centripetal force in N
- m: mass in kg
- v: linear speed in m/s
- r: radius in m
- ω: angular velocity in rad/s (1 rpm = 2π/60 rad/s)
- T: period of one revolution in s

## Worked example
1. 72 km/h ÷ 3.6 = 20 m/s.
2. a = v² ÷ r = 400 ÷ 50 = 8 m/s² (about 0.82 g).
3. F = m a = 1,000 × 8 = 8,000 N.

**Result:** A 1,000 kg car taking a 50 m radius curve at 72 km/h needs 8 kN of sideways grip from its tyres.

## What the result means

The force must come from something real: tyre friction, a string’s tension, a banked road or gravity. If that source cannot supply F, the object moves to a wider path. Solving for speed gives the fastest the curve can be taken with a known maximum force.

## Assumptions and limits
- Uniform circular motion at constant speed.
- Does not model banking angles, tyre friction coefficients or changing speed.

## Questions

### What about centrifugal force?

Centrifugal force is the outward force you seem to feel in the rotating frame. It has the same size as the centripetal force calculated here.

### Why does halving the radius double the force?

At the same linear speed, F = m v² ÷ r, so the force is inversely proportional to the radius. At the same rpm the opposite happens: F = m ω² r grows with radius.

## Sources
- [BIPM: The International System of Units (SI)](https://www.bipm.org/)

## Related calculators
- [Force Calculator (F = ma)](https://calculators.geekmidst.com/calculators/force-mass-acceleration-calculator)
- [Speed Calculator](https://calculators.geekmidst.com/calculators/speed-calculator)
- [Pendulum Period Calculator](https://calculators.geekmidst.com/calculators/pendulum-period-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/centripetal-force-calculator