Centripetal Force & Acceleration Calculator

Centripetal force is the net inward radial force required to maintain an object along a curved circular trajectory.

Without centripetal force, Newton’s First Law dictates that the body will continue in a straight line along the instantaneous tangent to the path.

Even when tangential speed is constant, the velocity vector continuously rotates direction.

This change in velocity vector over time produces an inward acceleration ac = v²/r directed toward the instantaneous center of curvature.

Applying Newton’s Second Law gives the necessary force Fc = m·(v²/r).

Centripetal Force (N): The total inward grip or tension necessary to stay on path.

Acceleration (m/s²): Lateral acceleration experienced by the vehicle or object.

G-Force: Acceleration expressed as multiples of standard Earth gravity (9.81 m/s²).

Angular Velocity (rad/s & RPM): Rate of angular rotation around the curve center.

• Speed: The dominant factor due to quadratic scaling.
• Radius: Sharper turns (smaller radius) sharply increase radial acceleration.
• Mass: Heavier vehicles demand proportionately greater force to negotiate curves.

• Automotive and civil highway ramp curve design.
• Centrifuge separation calculations in chemistry and biology.
• Roller coaster loop dynamics and satellite orbital mechanics.

• Assumes planar circular motion with constant radius.
• Vehicle is modeled as a lumped point mass neglecting roll dynamics.