Centripetal Force Calculator
Find the inward force that keeps a mass moving in a circle from its speed or its rpm, or turn the formula around to find the mass, radius or speed. Along with the force you get the centripetal acceleration, the period, the frequency and the friction a car would need. A conversion mode turns rpm, rad/s, period and frequency into one another. Runs in your browser; free, no sign-up.
The centripetal force is the net force pointing toward the centre of the circle — tension, friction, gravity or the normal force, whichever supplies it.
Calculated
Measured from the centre of the circle to the object.
Results
4800 N
Centripetal force Fc
The working
- Start from Fc = m × v² ÷ r.
- Convert to SI units: v = 72 km/h = 20 m/s.
- Fc = 1200 × 20² ÷ 100 = 4800 N
More about the motion
4 m/s²
Centripetal acceleration
0.4079
Centripetal acceleration in g
0.2 rad/s
Angular speed ω
31.42 s
Period T (time for one lap)
0.03183 Hz
Frequency f
1.91 rpm
Revolutions per minute
0.4079
Friction coefficient needed on a flat road
Assumes uniform circular motion: constant speed on a circle. Fc is the net inward force. The friction coefficient shown is the smallest static value that keeps a car on a flat, unbanked curve.
How to Use the Centripetal Force Calculator
- 1. Choose how you describe the motion. Use the speed if you know v in m/s, km/h or mph; the angular speed if you know ω or rpm; or convert to switch between speed, angular speed, period and frequency.
- 2. Pick the unknown. Solve for the force, the mass, the radius or the speed (or angular speed). The box you solve for becomes the answer, with a unit menu of its own.
- 3. Read the answer and the extras. Alongside the force you get the centripetal acceleration (also in g), the angular speed, the period, the frequency and the rpm.
- 4. Check the working. Each step shows the formula with your numbers and any unit conversions.
The Formulas
| Quantity | Formula | Notes |
|---|---|---|
| Centripetal acceleration | a = v² ÷ r = ω² r | Directed toward the centre |
| Centripetal force | Fc = m v² ÷ r = m ω² r | The net force toward the centre |
| Speed and angular speed | v = ω r | ω in rad/s |
| Angular speed, period, frequency | ω = 2π f = 2π ÷ T | f = 1 ÷ T |
| rpm to rad/s | ω = rpm × 2π ÷ 60 | 1 rpm = 0.10472 rad/s |
Reference: OpenStax University Physics, Volume 1, sections 4.4 and 6.3.
Centripetal force is not a new kind of force. It is the name for whatever real force points toward the centre: tension in a string, friction on a tyre, gravity on a satellite, or the normal force on a roller-coaster loop. Without it the object would fly off in a straight line, tangent to the circle.
Worked Examples
A car on a curve. A 1,200 kg car takes a curve of radius 100 m at 72 km/h (20 m/s). Fc = 1200 × 20² ÷ 100 = 4,800 N, supplied by friction between the tyres and the road (the calculator's default). The centripetal acceleration is 4 m/s², or 0.4079 g, so the friction coefficient must be at least 0.4079 on a flat road. Its period around the circle would be 31.42 s.
A ball on a string. A 0.2 kg ball whirled at 120 rpm on a 0.5 m string has ω = 120 × 2π ÷ 60 = 12.57 rad/s. Fc = 0.2 × 12.57² × 0.5 = 15.79 N, the tension in the string, and the acceleration is 78.96 m/s², about 8.05 g.
Converting. A centrifuge rotor at 3,000 rpm has ω = 314.2 rad/s, a period of 0.02 s and a frequency of 50 Hz. At a radius of 0.1 m, the speed is 31.42 m/s and the centripetal acceleration is 9,870 m/s² — about 1,006 g.
How Fast Can a Car Take a Curve?
On a flat road, friction provides the centripetal force, so the most it can supply is μs m g. Setting that equal to m v² ÷ r gives the top speed v = √(μs g r), independent of the car's mass. On wet concrete with μs near 0.5 (OpenStax lists 0.5–0.7), a 100 m curve limits speed to √(0.5 × 9.80665 × 100) = 22.14 m/s, which is 79.7 km/h. Banking the road lets the normal force help, raising the limit.
Centripetal and Centrifugal
The outward push you feel in a turning car is not a force pulling you outward. It is your body's inertia: you tend to continue in a straight line while the car turns under you. Physicists call the apparent outward force centrifugal and treat it as a fictitious force that exists only in the rotating frame. In an inertial frame, the only real force is the inward one.
Frequently Asked Questions
- What is the formula for centripetal force?
- Fc = m v² ÷ r, with mass m, speed v and radius r. In terms of angular speed it is Fc = m ω² r. Both give the same value because v = ω r. The force is in newtons when mass is in kilograms, speed in m/s and radius in metres.
- Is centripetal force a real force?
- It is the net inward force, not an extra force to add to a free-body diagram. Tension, friction, gravity or the normal force, or a combination, supplies it. If you draw both a real force and a separate Fc, you count the same thing twice.
- What is the difference between centripetal and centrifugal force?
- Centripetal force is the real inward force that bends the path into a circle. Centrifugal force is the apparent outward force felt in the rotating frame; it is a consequence of inertia, not an interaction with another object.
- Does mass affect centripetal acceleration?
- No. The acceleration is v² ÷ r, which depends only on speed and radius. A heavier object needs a larger force to achieve the same acceleration, which is why Fc grows with mass.
- How do I convert rpm to rad/s?
- Multiply by 2π and divide by 60, so ω = rpm × 0.10472. For example, 3,000 rpm is 314.16 rad/s. To go from rad/s to rpm, multiply by 60 ÷ 2π, about 9.549.
- How do I find the period of circular motion?
- The period is the time for one lap: T = 2π r ÷ v = 2π ÷ ω = 1 ÷ f. A car going round a 100 m circle at 20 m/s takes 2π × 100 ÷ 20 = 31.42 s.