Centripetal Force Calculator: F = mv²/r, With g-Force • The Science 360

By Shounak Das · Updated November 2026 · 6 min read

How do you calculate centripetal force?

Multiply the mass by the speed squared and divide by the radius: F = mv² ÷ r. A 1,500 kg car taking a 50 m bend at 60 km/h (16.67 m/s) needs 8,333 N pointing to the centre of the bend, an acceleration of 5.556 m/s² or 0.567 g. The calculator takes the speed as m/s, km/h, mph, rpm, rad/s or seconds per turn, and shows the arrows on the case you pick.

Centripetal means "centre seeking". It is not a new kind of force: it is whatever real force pulls the object inward, such as tyre grip, a drum wall, a string or gravity. Why you feel thrown outward on a bend is explained in Why do you feel pushed outward on a bend?.

Key results

Formula: F = mv² ÷ r = mω²r, and the acceleration is a = v² ÷ r = ω²r. Double the speed and the force goes up four times.
Converting speed: ω = v ÷ r; rpm × 2π ÷ 60 gives ω in rad/s; one turn takes T = 2πr ÷ v.
In g: divide the acceleration by 9.80665 m/s², the standard acceleration of gravity.
Vertical circles: at the top the slowest speed is √(gr). For a 1 m swing that is 3.132 m/s.

Six worked examples

Each button loads the example into the calculator.

A car on a 50 m bend at 60 km/h: 0.567 g

speed in km/h

60 km/h is 16.67 m/s. a = 16.67² ÷ 50 = 5.556 m/s², which is 0.567 g. For a 1,500 kg car the force is 8,333 N, all of it supplied by the grip of the tyres on a flat road.

At 90 km/h on the same bend the force would be (90 ÷ 60)² = 2.25 times as large, which is why speed limits drop before sharp bends.

Speed 16.67 m/s Acceleration 5.556 m/s² In g 0.567 g Force 8,333 N

A washing machine drum at 1200 rpm: 422.7 g

speed in rpm

A 525 mm drum (radius 26.25 cm, from a Haier 1200 rpm machine's specification) turning at 1200 rpm has ω = 1200 × 2π ÷ 60 = 125.7 rad/s. The wall moves at 32.99 m/s and the acceleration is ω²r = 4,145 m/s², 422.7 g.

A 100 g wet sock is pressed against the wall with 414.5 N, the weight of about 42.3 kg. The water in it has nothing holding it on a circle once it reaches a hole, so it leaves in a straight line.

ω 125.7 rad/s Wall speed 32.99 m/s In g 422.7 g One turn 50 ms

The ISS: 0.88 g towards Earth

orbit

On 13 November 2026 JPL Horizons puts the ISS about 6,797 km from Earth's centre, 418 km above the equator, moving at 7.658 km/s. a = v² ÷ r = 8.629 m/s², 0.88 g, and one orbit takes 1.55 h.

Gravity at that distance, GM ÷ r², is 8.629 m/s², the same number: gravity alone supplies the centripetal force. For the station's 419,725 kg (NASA) that is 3.622 MN.

A bucket swung overhead: at least 3.132 m/s

vertical circle, minimum speed

At the top of the swing the water stays in only if the bucket needs at least g of centripetal acceleration, so that gravity alone cannot pull the water out of the circle. v²/r ≥ g gives v ≥ √(gr). On a 1 m swing that is 3.132 m/s, or one turn every 2.01 s.

At that speed the bucket pushes on the water with almost nothing at the top, and with 98.08 N at the bottom for 5 kg: twice its weight.

Min speed 3.132 m/s Turn every 2.01 s Top 0 g felt Bottom 2 g felt

A loop of 10 m radius at 14 m/s: 2 g

vertical circle

a = 14² ÷ 10 = 19.6 m/s², 2 g. At the top, gravity provides 1 g of that and the seat pushes down on the rider with the other 0.999 g, so a rider feels about their normal weight, upside down. The slowest speed that would keep them in the seat at the top is √(9.80665 × 10) = 9.903 m/s.

Acceleration 19.6 m/s² In g 2 g Felt at top 0.999 g Min speed 9.903 m/s

A 200 g ball on a 50 cm string, once a second: 3.948 N

speed as rpm

60 rpm is one turn a second, ω = 2π rad/s, so the ball moves at 3.142 m/s. The string must pull with m ω² r = 0.2 × (2π)² × 0.5 = 3.948 N. Let go and the ball flies off along the tangent, not straight outward.

ω 6.283 rad/s Speed 3.142 m/s In g 2.01 g Tension 3.948 N

Centripetal acceleration at a glance

Case	Radius	Speed	Acceleration	In g
Car, 60 km/h bend	50 m	16.67 m/s	5.556 m/s²	0.567 g
Washing machine, 1200 rpm	26.25 cm	32.99 m/s	4,145 m/s²	422.7 g
ISS orbit	6,797 km	7.658 km/s	8.629 m/s²	0.88 g
Bucket at minimum speed	1 m	3.132 m/s	9.809 m/s²	1 g
Coaster loop	10 m	14 m/s	19.6 m/s²	2 g
Ball on a string, 60 rpm	50 cm	3.142 m/s	19.74 m/s²	2.01 g

The drum size is from a Haier HW120-BP12357S8 specification (525 mm drum, 1200 rpm). The ISS distance and speed are hourly JPL Horizons values for 13 November 2026, averaged; its orbit is slightly oval, so both vary a little round each orbit. The car, bucket, loop and ball are example inputs.

How the calculator works

Mass, radius and speed are converted to kilograms, metres and metres per second. Speed given as ω uses v = ωr, rpm uses ω = rpm × 2π ÷ 60, and a period uses v = 2πr ÷ T.

Then a = v² ÷ r, F = ma, and the acceleration in g is a ÷ 9.80665 m/s² (the standard value, NIST).

For a vertical circle the support pushes with m(a − g) at the top and m(a + g) at the bottom, and the slowest speed at the top is √(gr). For a flat bend, friction must supply all of F, which needs a grip of at least a ÷ g times the weight.

What the model leaves out

Banked bends: on a tilted road part of the inward force comes from the road surface itself, so less friction is needed.
Changing speed: a loop car slows down as it climbs, so the speed at the top is lower than at the bottom. Enter the speed at the point you care about.
Oval orbits: the ISS orbit is close to a circle; for strongly elliptical orbits v²/r does not apply with a single r.

Common misconceptions

"Centrifugal force throws you outward." From the ground, nothing pushes you outward: you carry on in a straight line while the car turns under you.

"Centripetal force is a separate force." It is the name for the inward part of real forces, such as friction, tension, a normal force or gravity.

"Things fly straight out when released." They leave along the tangent, at right angles to the radius.

Frequently asked questions

What is the formula for centripetal force?

F = mv² ÷ r, or F = mω²r with ω in radians per second. m is the mass in kg, v the speed in m/s and r the radius in m.

How do I convert rpm to centripetal acceleration?

Turn rpm into ω with ω = rpm × 2π ÷ 60, then a = ω²r. A 1200 rpm drum of 26.25 cm radius gives 125.7 rad/s and about 4,145 m/s², or 423 g.

How do I get the g-force?

Divide the centripetal acceleration by 9.80665 m/s². A car on a 50 m bend at 60 km/h pulls 0.567 g.

What is the minimum speed at the top of a vertical circle?

v = √(gr). For a bucket on a 1 m swing it is about 3.13 m/s, about one turn every two seconds.

Is centrifugal force real?

Only as an apparent force in a turning frame of reference. Seen from outside, the only real forces point inward; the outward feeling is your body trying to keep going straight.