Centripetal Force Calculator
Centripetal force is the net inward radial force required to continuously constrain an object along a curved or circular trajectory (Fc = m × v² / r). Whether engineering banked highway curves, amusement park rollercoasters, centrifuge separation systems, or satellite orbits, calculating required centripetal force and lateral g-forces ensures mechanical integrity and passenger safety.
Mass of the cornering or rotating body in kilograms (kg)
Tangential speed around the curve in metres per second (20 m/s = 72 km/h)
Radius of circular curvature from path to center of rotation in metres (m)
Required inward radial force in Newtons
How to Use This Calculator
- Enter the mass of the moving object or vehicle in kilograms.
- Enter the linear cornering speed in metres per second (1 m/s = 3.6 km/h).
- Enter the turn radius of the curve or orbit in metres.
- Examine inward centripetal force, radial acceleration, and lateral G-forces instantly.
Formula & Calculation Methodology
Because velocity is a vector, constantly altering direction around a circular bend requires a continuous inward radial acceleration ac = v² / r. Multiplying by body mass gives the necessary net physical centripetal force Fc = m × ac.
Worked Example
A 1,200 kg car taking a highway exit ramp of 60 m radius at 24 m/s (86.4 km/h)
Frequently Asked Questions
What is the difference between centripetal force and centrifugal force?↓
Centripetal force is a real inward force (such as tire friction, rope tension, or gravity) acting on a body in an inertial frame. Centrifugal force is an apparent or fictitious outward inertial force perceived only by an observer situated inside the accelerating rotating reference frame.
Why does doubling vehicle cornering speed quadruple the required tire grip?↓
Centripetal force is quadratic with respect to velocity (v²). Doubling speed from 30 km/h to 60 km/h requires (2)² = 4 times more inward lateral tire grip friction from the pavement to avoid spinning out.
How does banking a roadway curve reduce lateral skid risk?↓
Banking the road surface angles the normal support force inward. A component of the road's normal force directly supplies the necessary centripetal acceleration, eliminating reliance on pavement friction alone.
What limitation applies if the trajectory is elliptical rather than circular?↓
This formula strictly models uniform circular motion with constant radius r. For elliptical orbits (like planetary orbits governed by Kepler's laws), radius and speed vary continuously, requiring instantaneous radius of curvature calculations.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.