CalcLibrary

Centripetal Force Calculator

Solve centripetal force, centripetal acceleration, speed, or turn radius for uniform circular motion without hand-rearranging the formulas. Enter the known turning values with explicit metric or imperial units and keep the load picture visible in force, acceleration, and g-load.

Active equation
Examples

A 0.25 kg object moving at 4 m/s on a 0.8 m radius needs 5 N of inward force, about 20 m/s² of centripetal acceleration, and just over 2 g.

Centripetal force (F_c)
5 N
Centripetal acceleration (a_c)
20 m/s²
g-load
2.0394 g

Ideal uniform-circular-motion estimate only. It does not account for tire grip, banking, suspension, wind, structural limits, or safety certification.

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Examples

How It Works

Formula

Fc=mv2rF_c = \frac{m v^2}{r}

ac=v2ra_c = \frac{v^2}{r}

v=acrv = \sqrt{a_c r}

v=Fcrmv = \sqrt{\frac{F_c r}{m}}

r=v2acr = \frac{v^2}{a_c}

r=mv2Fcr = \frac{m v^2}{F_c}

ng=acg0n_g = \frac{a_c}{g_0}

Variables

FcF_c

Centripetal force(N or lbf)

aca_c

Centripetal acceleration(m/s² or ft/s²)

mm

Mass of the object or vehicle(kg or lb)

vv

Tangential speed(m/s, km/h, mph, or ft/s)

rr

Turn radius(m or ft)

g0g_0

Standard gravity constant(9.80665 m/s²)

ngn_g

Load expressed in multiples of standard gravity(g)

Choose the quantity to solve for, then enter the known turning values with their units. The calculator converts everything into one internal basis, solves the active circular-motion equation, and reports the missing value plus any supporting force, acceleration, and g-load that can be computed honestly from the provided data.

Uniform circular motion links inward force, inward acceleration, speed, and turn radius through Fc=mv2/rF_c = m v^2 / r and ac=v2/ra_c = v^2 / r. For force and acceleration, the calculator uses speed and radius directly. For speed and radius, it asks whether the known load is a force or an acceleration so the algebra stays physically complete instead of implying a missing dependency can be guessed.

The result surface keeps the whole load picture visible whenever the inputs support it. Faster speed raises the turning load quadratically, while increasing radius spreads the same turn over more distance and lowers the required inward force and acceleration.

Frequently Asked Questions

01What does this centripetal force calculator solve?
It solves one circular-motion unknown at a time: centripetal force, centripetal acceleration, speed, or turn radius. The page always keeps the governing turning relationship visible so you do not have to rearrange the equation yourself.
02Why does speed have such a big effect on turning load?
Because both centripetal force and centripetal acceleration scale with the square of speed. If speed doubles and radius stays the same, the inward force and acceleration become four times larger.
03When do I need mass?
Mass is only required when force is part of the calculation. Acceleration and g-load depend on speed and radius alone, but converting that load into an actual force requires mass.
04Can I mix units like mph, feet, kilograms, and newtons?
Yes. Each physical input has its own nearby unit selector, and the calculator converts everything internally before solving.
05How is this different from speed-distance-time, kinetic energy, or projectile motion?
Speed-distance-time relates straight-line travel, kinetic energy focuses on energy stored in motion, and projectile motion tracks a launched path. This calculator is for continuous turning in a circular path and the inward load needed to hold that turn.

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