Centripetal Force Calculator
Calculate centripetal force and acceleration from mass, velocity, and radius. Solve from linear or angular velocity, orbital periods. Find g-force, banking angle, and minimum loop speed.
Centripetal Force (N)
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Centripetal Acceleration (m/s²) —
G-Force —
Extended More scenarios, charts & detailed breakdown ▾
Centripetal Force F = mv²/r (N)
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Centripetal Acceleration (m/s²) —
G-Force —
Professional Full parameters & maximum detail ▾
Core Results
Centripetal Force (N) —
Centripetal Acceleration (m/s²) —
G-Force —
Engineering Applications
Ideal Banking Angle (degrees) —
vs Gravitational Force —
Min Speed for Vertical Loop (m/s) —
Orbital Velocity at this Radius (m/s) —
How to Use This Calculator
- Enter mass (kg), velocity (m/s), and radius (m) for instant centripetal force and acceleration.
- Use From Angular Velocity if you know ω (rad/s) instead of linear speed.
- Use Orbital tab for satellite/orbital calculations using period and radius.
- Switch to Professional for g-force, ideal banking angle, minimum loop speed, and gravitational force comparison.
Formula
F = mv²/r (from linear velocity)
F = mω²r (from angular velocity)
a = v²/r = ω²r
Banking angle θ = arctan(v²/rg)
Min loop speed v = √(gr)
Example
Example: 2 kg mass, 10 m/s, 5 m radius. a = 10²/5 = 20 m/s². F = 2 × 20 = 40 N. G-force = 20/9.81 = 2.04 g.
Frequently Asked Questions
- Centripetal force is the net force that keeps an object moving in a circular path, directed toward the center. F = mv²/r, where m = mass, v = velocity, r = radius. It is not a separate force — it is the name for the net inward force (gravity, tension, friction, etc.).
- Centripetal force is real — it is the inward force that causes circular motion. Centrifugal force is a fictitious force felt in a rotating reference frame (the apparent "outward push"). In an inertial frame, only centripetal force exists.
- If you know angular velocity ω (rad/s): F = mω²r and a = ω²r. Linear velocity v = ωr. Use the "From Angular Velocity" tab for this calculation.
- θ = arctan(v²/rg). For a car at 20 m/s on a curve of radius 50 m: θ = arctan(400/490) ≈ 39.3°. This angle eliminates the need for friction to maintain the curve.
- At the top of a loop, centripetal force must at least equal gravity: mv²/r ≥ mg, so v_min = √(gr). Below this speed, the object falls away from the circular path.