{
    "name": "Centripetal Force Calculator",
    "url": "https://calculators.geekmidst.com/calculators/centripetal-force-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/centripetal-force-calculator.md",
    "category": "Science & engineering",
    "description": "Find the centripetal force for an object moving in a circle, or the speed or radius it allows, with speed in m/s, km/h, mph, rpm or rad/s.",
    "summary": "Anything moving in a circle needs an inward force of m v² ÷ r. Enter the speed as a linear speed or as rpm to get the force, acceleration, period and angular velocity.",
    "also_called": [
        "Circular motion calculator",
        "Centripetal acceleration calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "solve",
            "label": "Solve for",
            "type": "segmented",
            "default": "force",
            "options": {
                "force": "Force",
                "speed": "Speed",
                "radius": "Radius"
            }
        },
        {
            "name": "mass",
            "label": "Mass",
            "type": "number",
            "default": "1000"
        },
        {
            "name": "mass_unit",
            "label": "Mass unit",
            "type": "select",
            "default": "kg",
            "options": {
                "kg": "kilograms (kg)",
                "g": "grams (g)",
                "t": "tonnes (t)",
                "lb": "pounds (lb)",
                "oz": "ounces (oz)"
            }
        },
        {
            "name": "radius",
            "label": "Radius of the circle",
            "type": "number",
            "default": "50",
            "shown_when": {
                "solve": [
                    "force",
                    "speed"
                ]
            }
        },
        {
            "name": "radius_unit",
            "label": "Radius unit",
            "type": "select",
            "default": "m",
            "options": {
                "m": "metres (m)",
                "cm": "centimetres (cm)",
                "mm": "millimetres (mm)",
                "km": "kilometres (km)",
                "ft": "feet (ft)",
                "in": "inches (in)",
                "mi": "miles (mi)"
            }
        },
        {
            "name": "speed",
            "label": "Speed",
            "type": "number",
            "default": "72",
            "shown_when": {
                "solve": [
                    "force",
                    "radius"
                ]
            }
        },
        {
            "name": "speed_unit",
            "label": "Speed unit",
            "type": "select",
            "default": "kmh",
            "options": {
                "ms": "m/s",
                "kmh": "km/h",
                "mph": "mph",
                "fts": "ft/s",
                "kn": "knots",
                "rpm": "revolutions per minute (rpm)",
                "rads": "radians per second (rad/s)"
            }
        },
        {
            "name": "force",
            "label": "Centripetal force",
            "type": "number",
            "default": "8000",
            "shown_when": {
                "solve": [
                    "speed",
                    "radius"
                ]
            }
        },
        {
            "name": "force_unit",
            "label": "Force unit",
            "type": "select",
            "default": "n",
            "options": {
                "n": "newtons (N)",
                "kn": "kilonewtons (kN)",
                "lbf": "pounds-force (lbf)",
                "kgf": "kilograms-force (kgf)"
            }
        }
    ],
    "outputs": [
        {
            "key": "answer",
            "label": "Result",
            "format": "text"
        },
        {
            "key": "force_n",
            "label": "Centripetal force",
            "format": "number"
        },
        {
            "key": "acceleration_ms2",
            "label": "Centripetal acceleration",
            "format": "number"
        },
        {
            "key": "acceleration_g",
            "label": "Centripetal acceleration",
            "format": "number"
        },
        {
            "key": "speed_ms",
            "label": "Linear speed",
            "format": "number"
        },
        {
            "key": "radius_m",
            "label": "Radius",
            "format": "number"
        },
        {
            "key": "angular_velocity_rads",
            "label": "Angular velocity",
            "format": "number"
        },
        {
            "key": "rpm",
            "label": "Rotation rate",
            "format": "number"
        },
        {
            "key": "period_s",
            "label": "Time per revolution",
            "format": "number"
        }
    ],
    "formula": {
        "text": "F = m v² ÷ r = m ω² r;  a = v² ÷ r;  v = ω r;  T = 2π ÷ ω",
        "variables": {
            "F": "centripetal force in N",
            "m": "mass in kg",
            "v": "linear speed in m/s",
            "r": "radius in m",
            "ω": "angular velocity in rad/s (1 rpm = 2π/60 rad/s)",
            "T": "period of one revolution in s"
        }
    },
    "worked_example": {
        "inputs": {
            "solve": "force",
            "mass": "1000",
            "mass_unit": "kg",
            "radius": "50",
            "radius_unit": "m",
            "speed": "72",
            "speed_unit": "kmh",
            "force": "8000",
            "force_unit": "n"
        },
        "steps": [
            "72 km/h ÷ 3.6 = 20 m/s.",
            "a = v² ÷ r = 400 ÷ 50 = 8 m/s² (about 0.82 g).",
            "F = m a = 1,000 × 8 = 8,000 N."
        ],
        "result": "A 1,000 kg car taking a 50 m radius curve at 72 km/h needs 8 kN of sideways grip from its tyres."
    },
    "interpretation": "The force must come from something real: tyre friction, a string’s tension, a banked road or gravity. If that source cannot supply F, the object moves to a wider path. Solving for speed gives the fastest the curve can be taken with a known maximum force.",
    "assumptions": [
        "Uniform circular motion at constant speed."
    ],
    "limitations": [
        "Does not model banking angles, tyre friction coefficients or changing speed."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "What about centrifugal force?",
            "answer": "Centrifugal force is the outward force you seem to feel in the rotating frame. It has the same size as the centripetal force calculated here."
        },
        {
            "question": "Why does halving the radius double the force?",
            "answer": "At the same linear speed, F = m v² ÷ r, so the force is inversely proportional to the radius. At the same rpm the opposite happens: F = m ω² r grows with radius."
        }
    ],
    "sources": [
        {
            "title": "BIPM: The International System of Units (SI)",
            "url": "https://www.bipm.org/"
        }
    ],
    "related": [
        {
            "name": "Force Calculator (F = ma)",
            "url": "https://calculators.geekmidst.com/calculators/force-mass-acceleration-calculator"
        },
        {
            "name": "Speed Calculator",
            "url": "https://calculators.geekmidst.com/calculators/speed-calculator"
        },
        {
            "name": "Pendulum Period Calculator",
            "url": "https://calculators.geekmidst.com/calculators/pendulum-period-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}