Centripetal Force Calculator
Solve Fc = mv²/r for any of centripetal force, mass, speed, or radius. A live 3D mass swings on a string with tangential-velocity and inward-force arrows, and charts show how force depends on speed and radius.
Reviewed by the ToolNestr Editorial Team — July 2026
Two ideas that trip students up
1. The force always points inward
A mass at four positions around its circular path — every red force arrow points toward the centre, never outward or forward, no matter where the mass is on the circle.
2. Force grows with the square of speed
Three Fc-vs-v curves at different radii — every curve is a parabola, so doubling speed always quadruples the required force, regardless of radius.
Centripetal force graphs
How it works
The core idea in one line: centripetal force is whatever net inward push or pull keeps an object moving along a circular path instead of flying off in a straight line.
Fc = m v² / r
centripetal force from mass, speed, and radius
Fc = m ω² r
from angular velocity ω (rad/s)
Fc = m (4π² r) / T²
from the period T (time per revolution)
Rearranged, Fc = mv²/r solves any variable: m = Fc·r/v², v = √(Fc·r/m), and r = mv²/Fc. Because Fc grows with the square of speed, doubling your speed around the same curve quadruples the force needed to hold the path — which is exactly why fast corners feel so much more demanding than slow ones.
Worked example 1 — car rounding a curve
Given: A 1200 kg car rounds a curve of radius 50 m at 20 m/s. Find the centripetal force needed.
This force is supplied by friction between the tyres and the road — if friction cannot supply 9,600 N, the car slides outward.
Worked example 2 — solving for speed
Given: A 0.50 kg ball on a string can withstand a maximum tension of 45 N before the string snaps. The string is 0.90 m long. Find the maximum speed before it breaks.
Centripetal force in common scenarios
Approximate values — real systems vary with exact mass, speed, and radius.
| Scenario | Masskg | Speedm/s | Radiusm | FcN |
|---|---|---|---|---|
| Car cornering | 1200 | 20 | 50 | 9,600 |
| Spinning fairground ride | 70 | 8 | 4 | 1,120 |
| Satellite in low orbit | 500 | 7,600 | 6.8×10⁶ | ~4,240 |
| Ball on a string | 0.5 | 9.0 | 0.9 | 45 |
| Centrifuge sample | 0.02 | 15 | 0.1 | 45 |
Fc = mv²/r in every case; the source of the force differs — friction, tension, gravity, or a container wall.
Where centripetal force actually matters
🚗 Cars on curves
Friction between tyres and road supplies the centripetal force that keeps a car turning. If a curve is taken too fast for the available friction (wet or icy roads reduce it), the required Fc exceeds what friction can provide and the car skids outward in a straight line.
🎢 Roller coasters and rides
Loops and spinning rides rely on centripetal force supplied by the track's normal force or a harness/seat. At the top of a vertical loop, gravity contributes to (or entirely supplies) the centripetal force needed to keep riders on the track.
🛰️ Orbits
Gravity supplies the centripetal force that keeps satellites and planets in orbit: GMm/r² = mv²/r. Setting these equal is how orbital speed and period are derived — no engine thrust is needed to "hold" a stable orbit, only gravity.
🧪 Centrifuges
Spinning a sample at high angular velocity creates a large centripetal force requirement; denser particles need more force to stay on the circular path and effectively migrate outward relative to lighter ones, which is how centrifuges separate mixtures.
Common misconceptions
"Centripetal force is a separate, distinct force pushing outward."
Centripetal force is not a new force and it points inward, not outward. It is just the label for whatever net force — tension, friction, gravity, normal force — is directed toward the centre and causes circular motion.
"An object moving in a circle at constant speed has no acceleration."
Constant speed does not mean constant velocity — direction is always changing in circular motion, so there is a continuous centripetal acceleration (v²/r) directed inward, even though speed itself stays constant.
"If you cut the string, the object flies straight outward."
It flies off tangent to the circle at the point of release — perpendicular to the radius, not directly outward along it — because Newton's first law says it continues in the direction it was already moving at that instant.
"Bigger radius always means bigger centripetal force."
For fixed speed, Fc = mv²/r actually decreases as r increases — a larger circle at the same speed needs less inward force. Force only grows with radius if speed is held fixed by increasing ω or if v grows with r (as it does for fixed ω, since v = ωr).
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §6.3 "Centripetal Force" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 6, Force and Motion II, Uniform Circular Motion.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 6, Circular Motion and Other Applications of Newton's Laws.
Fc = mv²/r assumes uniform circular motion (constant speed). Results are rounded for display.
How to use this calculator
Choose the unknown
The calculator solves for force, mass, speed, or radius from the other three.
Enter the other values
Use consistent SI units: kg, m/s, m, N.
Watch the orbit
Use the sliders to see how speed and radius change the inward force arrow in 3D.
Related tools
Frequently asked questions
What is centripetal force?
Centripetal force (Fc) is the net force required to keep an object moving in a circular path — it always points toward the centre of the circle. Fc = mv²/r, where m is mass, v is speed, and r is the radius of the circular path. Units are newtons (N).
Is centripetal force a new, separate kind of force?
No. "Centripetal" describes the direction and role of a force — toward the centre, causing circular motion — not a new fundamental force. It is supplied by something real: tension in a string, gravity for orbits, friction for a car on a curve, or the normal force on a banked track.
What is the difference between centripetal and centrifugal force?
Centripetal force is real and points inward, keeping an object on its circular path. "Centrifugal force" is the outward-feeling force experienced only in the rotating object's own (non-inertial) reference frame — it is a fictitious force that does not appear in an outside, inertial observer's analysis.
How else can centripetal force be written?
Using angular velocity ω (rad/s): Fc = mω²r. Using the period T (time per revolution): Fc = m(4π²r)/T². All three forms are equivalent because v = ωr = 2πr/T.
What happens if the centripetal force disappears?
The object stops moving in a circle and travels in a straight line (Newton's first law) tangent to the circle at the instant the force vanishes — this is why a spun object flies off in a straight line, not outward along a radius, when released.