What Is Centripetal Force and How Is It Calculated?
Centripetal force is the net inward force that keeps an object moving along a circular path. It always points toward the center of the circle, is perpendicular to the object's velocity, and changes the direction of motion without changing its speed.
The centripetal force formula, derived from Newton's second law and Christiaan Huygens' 1659 analysis of circular motion, is: F = m × v² ÷ r, where F is force in newtons (N), m is mass in kilograms, v is tangential speed in metres per second, and r is the radius of the circle in metres. Equivalent forms are F = m × ω² × r using angular velocity ω (rad/s), and F = m × a with a = v²/r.
Because force scales with the square of speed, doubling speed on the same curve quadruples the force required. The Moon, for example, orbits Earth at about 1,022 m/s at a mean distance of 384,400 km, requiring roughly 2.0 × 10²⁰ N of gravitational pull, according to NASA's lunar fact sheet.
How to Use This Centripetal Force Calculator
Pick the quantity you want to solve for, then fill in the remaining three fields:
- Solve for: Force, speed, radius or mass — the calculator rearranges F = mv²/r automatically.
- Mass: Mass of the object moving in the circle (kg or lb).
- Speed: Tangential speed along the path, not angular speed (m/s or mph).
- Radius: Distance from the center of the circle to the object (m or ft).
Toggle between metric (kg, m/s, m, newtons) and US customary units (lb, mph, ft, pounds-force). Acceleration, g-force, orbital period and rpm are shown alongside the main result, and all inputs are stored in the URL so you can share a calculation.
Centripetal Force Examples and Typical Values
The table shows centripetal acceleration (a = v²/r) in familiar situations. The International Space Station, moving at about 7,660 m/s at 6,780 km from Earth's center, experiences about 8.65 m/s² (0.88 g), supplied entirely by gravity. Ultracentrifuges used in laboratories spin fast enough to exceed 100,000 g.
| Situation | Speed / Radius | Acceleration |
|---|---|---|
| Car on a curve | 15 m/s, 50 m | 4.5 m/s² (0.46 g) |
| Fighter jet turn | 250 m/s, 2,000 m | 31.3 m/s² (3.2 g) |
| Roller coaster loop | 20 m/s, 10 m | 40 m/s² (4.1 g) |
| Lab centrifuge, 3,000 rpm | 31.4 m/s, 0.1 m | 9,870 m/s² (≈1,006 g) |
| Earth orbiting the Sun | 29,780 m/s, 1.496 × 10¹¹ m | 0.0059 m/s² |
The formula is the same worldwide, but units differ: SI countries use newtons and metres, while the US often uses pounds-force, feet and miles per hour. Toggle the unit tabs to convert.
Frequently Asked Questions About Centripetal Force
What is the formula for centripetal force?
Centripetal force equals mass times velocity squared divided by radius: F = mv²/r. It can also be written F = mω²r using angular velocity, or F = ma where a = v²/r is the centripetal acceleration. The SI unit is the newton (N).
What is the difference between centripetal and centrifugal force?
Centripetal force is a real inward force, such as tension, friction or gravity, that keeps an object on a circular path. Centrifugal force is the apparent outward push felt in the rotating frame of reference; it is an inertial effect, not a force exerted by another object.
Does centripetal force do work?
No. Centripetal force is always perpendicular to the direction of motion, so it does zero work and changes only the direction of velocity, never the speed or kinetic energy of the object.
What provides the centripetal force for a car turning a corner?
Static friction between the tyres and the road supplies the centripetal force on a flat curve. The maximum safe speed is v = √(μ × g × r), so wet roads with a lower friction coefficient μ require slower speeds or banked curves.
How accurate is this centripetal force calculator?
The calculator uses the exact classical formula F = mv²/r and is precise for any uniform circular motion given accurate inputs. It assumes constant speed and a perfectly circular path; real vehicles, non-uniform motion and relativistic speeds need more detailed models.