The calculation, without hidden assumptions
Centripetal force is the net inward force required for circular motion, not a separate new force. OpenStax gives F₍c₎ = ma₍c₎ with a₍c₎ = v²/r = rω², so the same state can be written F₍c₎ = mv²/r or F₍c₎ = mrω². MAXScanner solves the missing force, mass, tangential speed or radius and accepts linear speed, angular speed, RPM or period when speed is known indirectly.
How to use this calculator
Choose whether to solve force, mass, tangential speed or radius.
When force, mass or radius is the target, choose how circular speed is known: linear speed, angular speed, RPM or period.
Enter the remaining known values and select units; the calculator normalizes to SI before solving.
Check centripetal acceleration, g-force, angular speed, period and the substituted formula. Use the scenario table to see the square-law sensitivity to speed.
Where people use it
- •Physics and circular-motion homework with direct or reverse solving
- •Centrifuge/rotor checks when rotational speed is given in RPM
- •Vehicle/track examples where force, speed and curve radius are related
- •Converting between tangential speed, angular velocity, RPM and period for the same circular motion state
Worked example — 2 kg at 10 m/s on a 5 m radius
a₍c₎ = 10²/5 = 20 m/s². F₍c₎ = 2 × 20 = 40 N inward. The same motion has ω = v/r = 2 rad/s, about 19.10 RPM and a period of π seconds.
What the result does not assume
- •Centripetal force is the required net radial force. The real force supplying it may be friction, tension, gravity, a normal force or a combination of forces.
- •The basic equations assume circular motion with the entered instantaneous tangential speed and radius. Nonuniform motion can also have tangential acceleration, which this radial-force calculation does not model.
- •Do not interpret g-force here as a complete human-load or structural-safety assessment; direction, duration, restraint, geometry and other loads matter.
- •For safety-critical rotating machinery, roads, rides or structures, use applicable standards, OEM data and a qualified engineering analysis.
Frequently asked questions
Is centripetal force a separate type of force?+
No. It is the name for the net inward force component that produces centripetal acceleration. Depending on the system, friction, tension, gravity, a normal force or several forces can supply it.
Can I enter RPM instead of metres per second?+
Yes. Choose RPM as the speed basis. MAXScanner converts RPM to angular speed with ω = RPM × 2π/60, then uses F = mrω² and reports the equivalent tangential speed.
Can the calculator solve radius or speed?+
Yes. With linear speed, r = mv²/F and v = √(Fr/m). If angular speed/RPM/period is known while radius is unknown, the equivalent angular form F = mrω² is used.
Why does doubling speed quadruple centripetal force?+
At fixed mass and radius, force is proportional to v². Doubling v multiplies v² by four, so the required inward force is four times larger.
Which direction do velocity and centripetal force point?+
Tangential velocity points along the path. Centripetal acceleration and the net centripetal force point radially inward toward the center of curvature, perpendicular to the instantaneous tangential velocity.
Semantic next steps
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