Centripetal Force Calculator
When an object moves at constant speed along a circular path, a net inward force is required to keep it on that path — the centripetal force. Enter mass m, radius r and any one of linear speed v, angular speed ω or period T, and this tool instantly returns the centripetal force F = m·v²/r = m·ω²·r together with centripetal acceleration a = v²/r, tangential speed, angular speed, period and rotation frequency. The centripetal force is not a new fundamental force — it is supplied by a real interaction (tension, gravity, friction, normal force, …).
Enter finite numbers. Mass and radius must be greater than 0; linear/angular speed may be 0 (at rest); period must be greater than 0.
Centripetal force F
—
Calculated
Centripetal acceleration a
—
Calculated
Tangential speed v
—
Calculated
Angular speed ω
—
Calculated
Period T
—
Calculated
Frequency f
—
Calculated
Formula
F = m · v² / r = m · ω² · r | a = v² / r | T = 2π / ω
SI units: m in kg, r in m, v in m/s, ω in rad/s, T in seconds; outputs F in newtons (N), a in m/s², f in hertz (Hz). The centripetal force is the net inward force required to keep an object on a circular path — it is supplied by some real interaction (tension, gravity, friction, normal force, …), not by itself.
Formula
F_c = m · v² / r = m · ω² · r a_c = v² / r = ω² · r v = ω · r, ω = 2π / T, f = 1 / T
- · All formulas assume uniform circular motion: the object travels at a constant speed along a fixed-radius circle. If the speed itself changes (a roller-coaster descent, for example), you also need a tangential acceleration term.
- · Units are SI throughout: m in kg, r in m, v in m/s, ω in rad/s, T in seconds; outputs F in N, a in m/s², f in Hz.
- · The centripetal force always points toward the centre, perpendicular to the velocity, so it does no work on the body — and the speed stays constant (W = F · d · cos 90° = 0).
- · "Centrifugal force" is not a real force in an inertial frame; it is the fictitious force that appears in a rotating frame so that Newton's laws keep working — equal in magnitude and opposite in direction to the centripetal force.
- · Typical applications: friction or banking angle needed for a car going round a curve, satellite orbits, spin-cycle g-loading of a washing machine drum, conical pendulum tension, normal-force difference between the top and bottom of a roller-coaster loop.
- · References: Halliday, Resnick & Walker, Fundamentals of Physics, 11th ed., §6-5; OpenStax College Physics, §6.2–6.3.
Frequently asked
What is the difference between centripetal and centrifugal force?
The centripetal force is the real, inward net force acting on a body in circular motion — it is always supplied by some physical interaction (tension, gravity, friction, normal force, electromagnetic force, …). The centrifugal force is not a real force in an inertial frame; it is a fictitious (pseudo) force that appears in a rotating reference frame so that Newton's second law keeps working there. Example: in a car going round a bend you feel pushed outward, but seen from the road (an inertial frame) you only have inertia carrying you tangentially while the door supplies an inward normal force that bends your trajectory.
Does the centripetal force do any work?
No. Work is W = F · d · cos θ, and the centripetal force always points to the centre — exactly perpendicular to the instantaneous velocity (θ = 90°), so cos θ = 0 and the work it does is identically zero at every instant. That is why the kinetic energy ½mv² (and the speed v) stay constant in uniform circular motion. If the object speeds up along the circle, that work is done by some tangential force (an engine, thruster, electromagnetic accelerator, …) — not by the centripetal force.
What real forces typically supply the centripetal force?
It depends on the situation: (1) planets and satellites in orbit — gravity, F = G·M·m/r²; (2) an electron round a nucleus — electromagnetic (Coulomb) force; (3) a conical pendulum or a ball on a string — string tension; (4) a car going round a bend — static friction between tyre and road (with banking, the horizontal component of the normal force also contributes); (5) a roller-coaster loop — rails supply the normal force, gravity adds in at the top; (6) a centrifuge or washing-machine spin cycle — the normal force from the drum wall; (7) a charged particle in a uniform magnetic field — the Lorentz force q·v × B. This tool only computes the magnitude of the required net inward force; in engineering you then check whether the chosen mechanism (friction limited by μ·N, tension limited by breaking strength, …) can actually supply it.
Worked example: how much friction does a 1,500 kg car need to round a 50 m flat curve at 60 km/h?
Convert first: v = 60 km/h ≈ 16.67 m/s. Required centripetal acceleration is a = v² / r = 16.67² / 50 ≈ 5.56 m/s². For a 1,500 kg car the required centripetal force is F = m·a ≈ 1,500 × 5.56 ≈ 8,333 N. On a flat curve this whole inward force must come from static friction between the tyres and the road. Maximum available friction is μ_s · m·g; dry asphalt has μ_s ≈ 0.7–0.9, giving ≈ 1,500 × 0.7 × 9.81 ≈ 10,300 N — only a slim safety margin. On a wet surface (μ_s ≈ 0.4) the limit drops to ≈ 5,886 N and the car slides out. That is precisely why real-world curves are banked: the horizontal component of the normal force takes part of the centripetal load off the tyres.
Related tools
Ohm's Law Calculator (V / I / R / P)
Enter any two of voltage, current, resistance, or power — the calculator solves for the other two using V = IR and P = VI.
Speed, Distance & Time Calculator
Enter any two of distance, time and speed to get the third — with km/h, mph, m/s, km, miles, hours and minutes supported.
Density Calculator (mass / volume)
Compute density from mass and volume (ρ = m / V), or solve for the missing variable. Built-in reference table for 19 common substances.
Projectile Motion Calculator
Enter launch speed, angle and height to compute projectile range, peak height and flight time (no air resistance). Pick from Earth, Moon, Mars and more.
Wind Chill Calculator
Compute the wind chill (feels-like temperature) from air temperature and wind speed using the 2001 Environment Canada / US NWS formula, with frostbite risk levels.
Dew Point Calculator
Compute dew point from air temperature and relative humidity using the Magnus formula — handy for HVAC, photography and weather analysis.
Kinetic Energy Calculator (KE = ½ m v²)
Compute kinetic energy KE = ½ m v² with mixed units (kg / g / lb and m/s / km/h / mph) and see the result in joules, kilojoules, food calories, foot-pounds and watt-hours.
Half-Life & Exponential Decay Calculator
Enter any three of initial amount, remaining amount, elapsed time and half-life to solve for the fourth — useful for radioactive decay, drug pharmacokinetics and radiometric dating.
Resistor Color Code Calculator (4 / 5 band)
Pick the colour bands and instantly read the resistance and tolerance — 4-band and 5-band notations supported, with Ω / kΩ / MΩ formatting and a closest E12 / E24 preferred-value check.
GPS Distance Calculator (Haversine)
Enter two latitude/longitude pairs to compute the great-circle distance using the haversine formula (km, miles, nautical miles), with bearing and midpoint.
Solution Dilution Calculator (C₁V₁ = C₂V₂)
Solve any one of C₁, V₁, C₂, V₂ from the dilution equation C₁V₁ = C₂V₂ — a daily lab essential for chemistry, biology and pharmacy work.
Decibel (dB) Sum Calculator
Two 80 dB sound sources do not equal 160 dB. Enter multiple dB values to compute the combined SPL, and subtract background noise to recover the signal alone.
Resistor Parallel / Series Calculator
Enter up to 8 resistor values to see the series total (R₁ + R₂ + …) and the parallel total (1 / Σ(1/Rᵢ)) at the same time.
Wavelength ↔ Frequency Calculator
Convert between electromagnetic wavelength and frequency via c = λf, with the matching spectrum band (radio / microwave / visible / X-ray / γ) and photon energy.
Tank Volume Calculator
Compute the capacity of vertical or horizontal cylindrical, rectangular and spherical tanks, including partial-fill volumes at a given liquid level.
Pendulum Period Calculator (T = 2π√L/g)
Enter the pendulum length and local gravity to get the period, frequency and angular frequency, with Earth/Moon/Mars/Jupiter presets — and reverse-solve for the length needed to hit a target period.
Heat Index Calculator
Enter air temperature and relative humidity to get the apparent temperature (NOAA Rothfusz heat index) and the corresponding heat-stress risk band.
Vehicle Stopping Distance Calculator
Enter speed, reaction time and road friction to estimate reaction, braking and total stopping distance.
Snell's Law Refraction Calculator
Enter the refractive indices of two media and an angle of incidence — get the refraction angle and critical angle from Snell's law (n₁ sin θ₁ = n₂ sin θ₂).
Capacitor Energy Calculator
Enter capacitance (F, mF, µF, nF, pF) and voltage to compute the stored energy (E = ½CV²) and charge (Q = CV) on a capacitor.
Boiling Point at Altitude Calculator
Enter altitude to compute the boiling point of water (°C / °F) and local air pressure using the ICAO standard atmosphere and the Antoine equation — useful for hiking, cooking and high-altitude baking.
Specific Heat (Q = mcΔT) Calculator
Solve Q = m × c × ΔT for any one of heat energy, mass, specific heat capacity or temperature change — with presets for water, aluminium, iron, copper, glass, air and more.
pH and Hydrogen Ion Concentration Calculator
Convert between pH, pOH, hydrogen-ion concentration [H⁺] and hydroxide concentration [OH⁻] — with acid / neutral / alkaline classification.
Ideal Gas Law (PV = nRT) Calculator
Pick the unknown (P, V, n or T), enter the other three and PV = nRT is solved instantly — works in Pa / kPa / atm / bar / mmHg / psi, m³ / L / mL, mol / mmol / kmol and K / °C / °F.
Coulomb's Law Calculator
Enter two point charges and the separation distance to compute the electrostatic force between them via F = kₑ·q₁·q₂/r² (attractive or repulsive).
Newton's Law of Universal Gravitation Calculator
Enter two masses and the distance between them to compute the gravitational attraction via F = G·m₁·m₂/r².
Thin Lens Equation Calculator
Given any two of the three quantities (object distance u, image distance v, focal length f), solve for the remaining one and the lateral magnification.
Distance to Horizon Calculator
Enter the observer eye height above the surface to compute the distance to the geometric and refraction-corrected horizon.
Hooke's Law (Spring Force) Calculator
Given any two of spring constant k, displacement x or restoring force F, solve for the third and the elastic potential energy U = ½kx².
Buoyancy Force (Archimedes' Principle) Calculator
Enter fluid density, submerged volume and gravitational acceleration to compute the buoyant force F = ρ V g, plus whether the object floats, sinks or stays neutral.
Voltage Divider Calculator
Enter the input voltage and two series resistor values to find the divider output voltage, current and power dissipated in each resistor.
Escape Velocity Calculator
Enter the mass and radius of a celestial body (or pick Earth, Moon, Mars and other presets) to compute the minimum surface launch speed v = √(2GM/r) needed to escape its gravity.
Newton's Law of Cooling Calculator
Enter initial temperature, ambient temperature, cooling constant and elapsed time to estimate an object's temperature with T(t) = T∞ + (T₀ − T∞)·e^(−kt), plus half-cooling time and time constant.
LC Resonant Frequency Calculator
Enter inductance L (H) and capacitance C (F) to compute the resonant frequency f = 1 / (2π√(LC)) of an LC tank circuit, plus its period and angular frequency.
Speed of Sound in Air Calculator
Enter the air temperature and compute the speed of sound in dry air using v = 331.3 × √(1 + T/273.15) — output in m/s, km/h, mph, ft/s plus the "count-the-seconds" thunder distance rule.
Reynolds Number Calculator
Enter fluid density, velocity, characteristic length and viscosity to compute the Reynolds number and classify the flow as laminar, transitional or turbulent.
Spring Potential Energy Calculator
Enter the spring constant k and displacement x to instantly compute the elastic potential energy stored in a Hookean spring via U = ½·k·x², with conversions to kJ, kcal, ft·lbf and Wh for easy comparison.