Productive ToolboxCentripetal Force Calculator
Calculate centripetal force instantly using mass, velocity, and radius (F = mv²/r) or angular velocity (F = mrω²). Real-time results, step-by-step breakdown, and unit conversion for physics and engineering.
Centripetal Force Calculator
Calculate the centripetal force for circular motion using mass, velocity, and radius (F = mv²/r) or angular velocity (F = mrω²). Supports metric and imperial units with real-time results.
Centripetal Force
Settings & Actions
e.g. Car ≈ 1500 kg
e.g. Highway ≈ 30 m/s
e.g. Road curve ≈ 50 m
Press Esc to reset
Quick Presets
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What is a Centripetal Force Calculator?
A Centripetal Force Calculator is a physics tool that computes the inward force required to keep an object moving along a circular path. Without this force, the object would travel in a straight line — centripetal force is what continuously redirects it toward the center.
The primary formula is F = mv² / r, where F is the centripetal force in Newtons, m is mass in kilograms, v is velocity in meters per second, and r is the radius of the circular path in meters. An alternative form using angular velocity is F = mrω², where ω is angular velocity in radians per second.
This calculator supports both formulas with full unit conversion for mass (kg, g, lb, metric ton), velocity (m/s, km/h, mph), and radius (m, cm, ft), making it useful for students, engineers, and researchers across different unit systems.
How to Use the Centripetal Force Calculator
Step-by-Step Guide
- 1Choose the formula: Use speed (F = mv²/r) when you know how fast the object moves, or angular velocity (F = mrω²) when you know how fast it rotates, in rad/s.
- 2Enter the mass: Type the mass in kg, g, lb or metric tons.
- 3Enter the speed or angular velocity: Type the speed in m/s, km/h or mph, or the angular velocity in rad/s.
- 4Enter the radius: Type the radius of the circular path in m, cm or ft.
- 5Read the force: See the centripetal force in newtons, kilonewtons and pound-force with the step-by-step working; copy it or export it as a text file.
Key Features
- ✓Real-time calculation as you type
- ✓Two formula modes — velocity and angular velocity
- ✓Multi-unit support — metric and imperial
- ✓Step-by-step calculation breakdown
- ✓Live formula display with your actual values
- ✓Unit conversion breakdown (N, kN, lbf)
- ✓Calculation history that persists between visits
- ✓Export results as a TXT file
- ✓Quick presets for common scenarios
- ✓Scientific notation for very large/small values
Centripetal Force Formulas Explained
Velocity Formula
Use this when you know the linear speed of the object. Velocity is squared, so doubling speed quadruples the required force. This is the most common form used in physics education.
Angular Velocity Formula
Use this when you know the rotational speed in radians per second. Common in engineering applications involving motors, rotating machinery, and orbital mechanics.
Example Calculations
| Mass | Velocity | Radius | Force | Scenario |
|---|---|---|---|---|
| 10 kg | 5 m/s | 2 m | 125 N | Physics example |
| 1,500 kg | 20 m/s | 50 m | 12,000 N | Car turning |
| 80 kg | 25 m/s | 15 m | 3,333 N | Roller coaster |
| 0.5 kg | — | 1.5 m | 75 N | ω = 10 rad/s |
| 5,000 kg | 7,800 m/s | 6,371 km | ~9,800 N | Orbital motion |
Real-World Applications
Physics Education
F = mv²/r is a core formula in classical mechanics, taught in high school and university physics courses worldwide.
Vehicle Dynamics
Engineers calculate centripetal force to design safe road curves, determine maximum cornering speeds, and size tires.
Roller Coaster Design
Loop and curve radii are calculated to ensure riders experience safe g-forces while maintaining structural integrity.
Orbital Mechanics
Satellites stay in orbit because gravity provides the centripetal force needed to maintain circular motion.
Rotating Machinery
Centrifuges, turbines, and motors require centripetal force analysis to prevent component failure at high RPM.
Aerospace Engineering
Aircraft banking in turns and spacecraft trajectory calculations both rely on centripetal force principles.
Frequently Asked Questions
What is the centripetal force formula?
F = mv²/r, where m is the mass in kg, v the speed in m/s and r the radius in m, giving F in newtons. With angular velocity ω in rad/s, F = mω²r. Example: a 1,500 kg car taking a 50 m radius curve at 20 m/s (72 km/h, about 45 mph) needs 1,500 × 20² ÷ 50 = 12,000 N, about 2,700 lbf.
What is centripetal force?
The net inward force that keeps an object moving in a circle, always pointing toward the center. It is not a separate kind of force: friction on a car's tires, the tension in a string or gravity on a satellite provides it. Without it, the object would carry on in a straight line.
What is the difference between centripetal and centrifugal force?
Centripetal force is the real inward force on the object. Centrifugal force is an apparent outward force that only appears when you describe the motion from inside the rotating frame; the outward push you feel in a turning car is your body's inertia trying to go straight.
Why is speed squared in the formula?
Going faster means both covering the curve sooner and changing direction faster, so the required force grows with the square of the speed. Doubling the speed on the same curve needs four times the force, which is why speed limits on bends matter so much.
How do I convert RPM to angular velocity?
Multiply by 2π and divide by 60: ω = 2π × RPM ÷ 60. For example 3,000 RPM is 314.2 rad/s. Enter that in angular velocity mode.
How do I find the centripetal acceleration?
Divide the force by the mass, or use a = v²/r directly. Dividing by 9.81 m/s² gives the acceleration in g; the car in the example above feels 8 m/s², about 0.82 g.
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