What is the formula of radius of a nucleus?

Experiments that studies the size of nuclei indicate that the volume of nuclei is directly proportional to the total number of nucleons present.

V_n ∝ A  

where V_n = volume of nuclei and A = mass number

For sphere, V ∝ r³

where r = radius of a nucleus

Substituting value of V in above equation we get,

r³ ∝ A

So, r ∝ A^1/3

Using R₀ as a proportionality constant we get,

r = A^1/3 R₀

where A = mass number, r = radius of a nucleus and R₀ = proportionality constant.

R₀ = 1.25 fm (femtometre) with typical deviations of up to 0.2 fm from this value.