Centrifugal Force Calculator

F = m·v²/r, where m is mass in kilograms, v is tangential speed in meters per second, and r is the radius in meters — the result is in newtons. Equivalently, with angular speed ω in radians per second: F = m·ω²·r. Worked example: a 1,000 kg car cornering at 20 m/s on a 50 m radius curve gives F = 1,000 × 20² ÷ 50 = 8,000 N (8 kN). The solver tab above computes any one of F, m, v (or ω), or r from the other three.

Convert RPM to angular speed first: ω = RPM × 2π ÷ 60. Then use F = m·ω²·r with r in meters and m in kilograms. Example: a 2 kg object spinning at 3,000 RPM (ω = 314.1593 rad/s) on a 0.1 m radius gives F = 2 × 314.1593² × 0.1 = 19,739.21 N (about 19.74 kN, or 4,437 lbf). Tip: select the "Angular speed (ω)" mode in the solver and type RPM directly — the tool converts it for you.

The magnitude is identical — both equal m·v²/r — but the framing differs. Centripetal force is the real, physical force pointing toward the center that keeps an object on a curved path (e.g. tire friction pushing a car inward, or a string pulling a ball inward). "Centrifugal force" is the inertia effect felt in the rotating frame: from the passenger's seat, it feels like something pushes you outward with exactly the same magnitude, m·v²/r. This tool computes that magnitude either way; physicists call it centrifugal in the rotating frame and centripetal in the inertial frame.

Honestly: it depends on your reference frame. In a rotating frame (sitting in the spinning centrifuge), the outward push is absolutely real to you — it presses clothes against the drum and separates cream from milk. In an inertial (non-rotating) frame, physicists say the only real force is the centripetal one pulling inward; the "outward force" is inertia — the object's tendency to keep flying straight. The number, m·v²/r, is the same in both descriptions, so the calculator's result is valid regardless of which picture you use.

Force: newtons (N), kilonewtons (kN), pound-force (lbf, where 1 lbf = 4.44822 N). Mass: kilograms (kg), grams (g), pounds (lb). Speed: meters per second (m/s), kilometers per hour (km/h), plus angular speed in RPM or radians per second. Radius: meters (m), centimeters (cm), feet (ft). Everything is converted to SI internally with exact defined constants (1 lb = 0.45359237 kg, 1 ft = 0.3048 m) before the formula runs.

Divide the force by the object's weight: g's = F ÷ (m × 9.80665). Example: a 5 kg load in a washing machine spinning at 1,000 RPM with a 0.25 m drum radius experiences F = 13,707.78 N — that is 13,707.78 ÷ (5 × 9.80665) = 279.56 g. This is why spin cycles extract so much water: the laundry is pressed outward with nearly 280 times its own weight. The solver shows the g-value for every calculation.

A 1,500 kg car taking a 100 m radius curve at 90 km/h (25 m/s): F = 1,500 × 25² ÷ 100 = 9,375 N (9.375 kN), which is 9,375 ÷ (1,500 × 9.80665) = 0.637 g of lateral acceleration. That is the sideways force the tires must supply through grip — on a wet road with limited friction, it is what pushes the car toward the outside of the curve. Halve the radius or raise the speed and the force climbs fast, because it grows with v².

It inverts the formula: from a force limit F, mass m, and radius r, the fastest allowed angular speed is ω = √(F ÷ (m·r)), converted to RPM as ω × 60 ÷ 2π. Use it for machines like centrifuges, spin dryers, or grinding wheels, where you know the force the hardware can take and need the speed ceiling. Example: if a 2 kg rotor at 0.1 m radius must stay under 19,739.21 N, the ceiling is exactly 3,000 RPM. Important: this is a math ceiling only — it is not a safety certification. Always apply a safety margin and follow the manufacturer's rated limits.

Use the "Solve for" dropdown. The algebra is exact: m = F·r ÷ v², v = √(F·r ÷ m), r = m·v² ÷ F, and in angular terms ω = √(F ÷ (m·r)). For instance, to hold a 1,000 kg car at 20 m/s with tires that can supply at most 8,000 N of lateral grip, the minimum curve radius is r = 1,000 × 20² ÷ 8,000 = 50 m. Every rearrangement is verified against the frozen test vectors shipped with this tool.

Because speed is squared in F = m·v²/r. Double v and v² becomes 4×, so the force becomes 4×; triple the speed and the force becomes 9×. Radius, by contrast, is linear: halving the radius only doubles the force. This is why a small increase in cornering or spin speed is far more dangerous than it feels — the g-load climbs with the square.

Three, in order: (1) plugging RPM straight into m·ω²·r without converting — you must use rad/s (ω = RPM × 2π ÷ 60); 3,000 RPM is 314.16 rad/s, not 3,000. (2) Using the diameter instead of the radius — the formula needs the radius; a 0.5 m drum diameter means r = 0.25 m. (3) Mixing units, e.g. grams with meters, or pounds of mass with pound-force — pick each unit from the dropdowns and the tool normalizes everything to SI first.

Three honest limits. (1) It computes the idealized m·v²/r magnitude — it does not certify that your machine, rope, or bracket can actually survive that force; structural limits, fatigue, and balance need engineering analysis. (2) It assumes a point mass at a fixed radius with constant speed; real rotors have distributed mass and vibration. (3) The max-RPM mode gives a mathematical ceiling for your chosen force limit, not a safety approval — always derate with a safety factor and respect the manufacturer's ratings.

F = m·v²/r: massa (kg) dikali kecepatan tangensial (m/s) kuadrat, dibagi jari-jari (m) — hasilnya dalam newton. Dengan kecepatan sudut: F = m·ω²·r. Contoh: mobil 1.000 kg menikung 20 m/s di radius 50 m menghasilkan F = 1.000 × 400 ÷ 50 = 8.000 N (8 kN). Kalkulator di atas bisa menyelesaikan keempat variabel (F, m, v/ω, r) dan mendukung satuan RPM, km/h, lbf, dan lain-lain.