Centripetal Force Calculator

Use this template to find the Centripetal Force & Centripetal Acceleration acting on an object while in circular motion. You can also find related missing parameters such as mass, tangential velocity and angular velocity of the object and the radius of the circular path.
Calculation📃Description of parameters
Inputs❗Important: you only need to input three parameters for the Output table to fully populate
﻿
Mass (m)​
kg​
Tangential Velocity (v)​
m/s​
Angular Velocity (w)​
rad/s​
Radius (r)​
m​
Centripetal Force (F)​
N​
Centripetal Acceleration (a)​
m/s2​
Output﻿
Mass (m)​
kg​
100​
Tangential Velocity (v)​
m/s​
0.005​
Angular Velocity (w)​
rad/s​
100​
Radius (r)​
m​
5e-5​
Centripetal Force (F)​
N​
50​
Centripetal Acceleration (a)​
m/s2​
0.5​
ExplanationThe centripetal force acts on an object moving in a circular path, directing it towards the centre of the circle. It is responsible for keeping an object in circular motion and preventing it from moving in a straight line. 
Centripetal force can arise from various sources, such as tension in a string, gravitational attraction or friction.
﻿
Centripetal Force/Acceleration Diagram
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You can use three different formulas to calculate centripetal force depending on the parameters given or yet to be found.
Formula 1
Force (﻿F
) w.r.t mass    (﻿m
) and tangential velocity (﻿v
) of the object and radius of the circle (﻿r
)
Formula 2
Force (﻿F
) w.r.t mass (﻿m
) and angular velocity (﻿w
) of the object and radius of the circle (﻿r
)
Formula 3
Force (﻿F
) w.r.t mass    (﻿m
) and centripetal acceleration (﻿ac​
) 
﻿
F = mv2rF\ =\ \frac{mv^2}{r}F = rmv2​
﻿
F = mrw2F\ =\ mrw^2F = mrw2
﻿
F = macF\ =\ ma_cF = mac​
You can also use other bridging formulas to calculate parameters that aren't directly a part of each individual formula. Here are a few bridging relationships.
﻿
v = wr v\ =\ wr\ v = wr 
﻿
a = v2r = w2 ra\ =\ \frac{v^2}{r}\ =\ w^2\ ra = rv2​ = w2 r
We can rearrange the equations above to create many combinations of formulas for all our parameters!
Parameter
Formulas
﻿
﻿
Centripetal Force (﻿F
)
﻿﻿F=rmv2​
﻿
﻿﻿F=mw2r
﻿
﻿﻿F=ma
﻿
Mass (﻿m
)
﻿﻿m=v2Fr​
﻿
﻿﻿m=rω2F​
﻿
﻿﻿m=aF​
﻿
Tangential Velocity (﻿v
)
﻿﻿v=mFr​​
﻿
﻿﻿v=ar​
﻿
﻿﻿v=ωr
﻿
Angular Velocity (﻿ω
)
﻿﻿ω=mrF​​
﻿
﻿﻿ω=ra​​
﻿
﻿﻿ω=rv​
﻿
Radius (﻿r
)
﻿﻿r=rmv2​
﻿
﻿﻿r=ω2a​
﻿
﻿﻿r=mω2F​
﻿
﻿﻿r=ωv​
﻿
﻿﻿r=av2​
﻿
Centripetal Acceleration (﻿a
)
﻿﻿a=rv2​
﻿
﻿﻿a=ω2r
﻿
﻿﻿a=mF​
﻿
﻿

Mass (m)	kg
Tangential Velocity (v)	m/s
Angular Velocity (w)	rad/s
Radius (r)	m
Centripetal Force (F)	N
Centripetal Acceleration (a)	m/s2

Mass (m)	kg	100
Tangential Velocity (v)	m/s	0.005
Angular Velocity (w)	rad/s	100
Radius (r)	m	5e-5
Centripetal Force (F)	N	50
Centripetal Acceleration (a)	m/s2	0.5