Centripetal Force Calculator
Calculate the centripetal force needed to hold a mass on a circular path with F = mv2/r, from its mass, speed, and the radius of the circle.
Centripetal Force Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser — no data is sent to any server.
Formula: F = mv²/r
Worked example — 8000 N
Formula
F = mv²/r
Force required to keep an object moving in a circular path. Points toward the center of the circle.
Worked Examples
Example 1: Car turning
Problem:1000 kg car at 20 m/s, r=50m
Solution:F=1000×400/50=8000 N
Result:8000 N
Frequently Asked Questions
What is centripetal force?
Centripetal force is the net force directed toward the center of a circular path that keeps an object in circular motion. It is not a new type of force — it is provided by existing forces such as tension, gravity, or friction, depending on the situation. Formula: F = mv²/r.
How do you calculate centripetal force?
Use F = mv²/r, where m is mass (kg), v is tangential speed (m/s), and r is the radius of the circular path (m). For a 1000 kg car moving at 20 m/s around a curve of radius 50 m: F = 1000 × 400 / 50 = 8000 N directed toward the center of the curve.
What units does the centripetal force calculator use?
Mass is in kilograms (kg), velocity in meters per second (m/s), and radius in meters (m). The resulting centripetal force is in Newtons (N), centripetal acceleration in m/s², orbital period in seconds (s), and g-force as a dimensionless multiple of 9.81 m/s².
What is a real-world example of centripetal force?
A satellite orbiting Earth at 7800 m/s at a radius of about 6,571 km experiences centripetal acceleration of v²/r ≈ 9.25 m/s². Gravity provides exactly this force, keeping the satellite in a stable orbit without any thrust.
How does a laboratory centrifuge use circular motion to separate a sample?
Spinning a tube creates a required centripetal acceleration of omega squared times r at each point in the sample. Denser particles need more inward force than the surrounding fluid can supply, so they migrate outward to the tube bottom while lighter material stays behind. Performance is quoted as relative centrifugal field, omega squared times r divided by g, which is why rotor radius matters as much as rotation speed.
How does centripetal force relate to angular velocity and orbital period?
Since the tangential speed is omega times r, the force can be written as m omega squared r as well as m v squared over r. With omega equal to 2 pi divided by the period, the force also equals 4 pi squared m r divided by the period squared. Those forms are more convenient for rotating machinery and orbits, where rotational speed or period is known but linear speed is not.
What sets the maximum safe speed on a flat, unbanked curve?
On a level curve friction alone supplies the inward force, so the limit is reached when the required m v squared over r equals the maximum friction, mu times m g. The mass cancels, leaving a maximum speed equal to the square root of mu g r. With a friction coefficient of 0.7 on a 50 m radius bend that is about 18.5 m/s, and it falls sharply once the road is wet.
Why are highway ramps and racetrack bends banked?
On a banked surface the normal force tilts inward, and its horizontal component can supply the centripetal force without relying on friction. The ideal angle satisfies tan theta equal to v squared divided by r g, so it depends on the design speed and radius but not on the vehicle mass. Banking keeps the friction budget in reserve for braking and for wet conditions.
What is the minimum speed needed at the top of a vertical loop?
At the very top of a loop the weight and the track's normal force both point downward toward the centre, so mg + N = mv squared over r. The limiting case is N = 0, when gravity alone supplies the whole centripetal requirement, giving v = the square root of g times r. For a 5 m radius loop that is about 7 m per second. Go slower and the cart loses contact with the track before reaching the top.
Why does doubling the speed quadruple the required force?
The force depends on the square of the tangential speed while varying inversely with radius. Doubling speed on the same radius therefore demands four times the inward force, and halving the radius at fixed speed doubles it. This quadratic sensitivity is why cornering forces climb so quickly with speed and why tight, fast bends are the ones that exceed available tyre grip first.
Background & Theory
Where Centripetal Force Shows Up
Centripetal force isn't a separate force of nature — it's the label for whatever existing force (tension, friction, gravity, the normal force from a banked track) happens to be pointed toward the center of a circular path. If that inward force vanishes, the object doesn't fly outward "away" from the center; it simply travels in a straight line tangent to the circle it was following, per Newton's first law. That's why a spinning object released from a string flies off tangentially, not radially.
| Scenario | Approx. centripetal acceleration |
|---|---|
| Car on a highway cloverleaf ramp (r≈30m, 40 km/h) | ~0.35g |
| Formula 1 car in a fast corner | 4-6g |
| Fighter-jet high-g turn | up to 9g (pilot G-suit limit) |
| Centrifuge (lab, ~15cm radius, 3000 RPM) | ~1,500g |
| ISS in low Earth orbit | ~0.9g (balanced by gravity, giving apparent weightlessness) |
Sustained accelerations above about 5g cause most untrained people to gray out as blood is pulled away from the brain — this is why roller coasters cap sustained turns well below that threshold even though brief peaks can go higher.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
Related Calculators
🧮Friction Force Calculator
Calculate friction force with inputs, formulas, and instant results.
🧮Buoyancy Force Calculator
buoyancy force calculator. Get instant, accurate results.
💪Force Calculator
Calculate force using Newton's Second Law
🧮Acceleration Calculator
Calculate acceleration with inputs, formulas, and instant results.
🧮Motion on Incline with Friction Calculator
Calculate motion on incline with friction with inputs, formulas, and instant results.
🧮Relative Velocity Calculator
Calculate relative velocity with inputs, formulas, and instant results.
🧮Velocity Calculator
Calculate velocity with inputs, formulas, and instant results.
🧮Coupled Spring Damper Calculator
Calculate coupled spring damper with inputs, formulas, and instant results.