What is the correct equation for rotor solidity? I'm working in a project that uses"blade solidity ratio", or "rotor solidity", the problem is, there are several articles which defines the equation in a different way changing in the section of the Radius analysis. I found 3 equations that I will describe below:

$$1. \frac{Nc}{2πR}$$ $$2. \frac{Nc}{2R}$$ $$3. \frac{Nc}{R}$$ 
N=Number of Blades, c= Chord Length, R= Radius of the rotor

Which one is correct or there is some case where each of this equation is applied?
Thanks.
Rotor solidity is the area of the rotor disk that is actually occupied by blade area.

Area of rotor blades = $N \cdot c \cdot R$

Area of rotor disk = $\pi \cdot R^2$

$$Rotor \ solidity = \frac{N \cdot c}{\pi \cdot R} \tag{4}$$

So all three of the equations OP found would not be usual. Good reference books are:


Helicopter Performance, Stability and Control by Raymond R. Prouty
Principles Of Helicopter Aerodynamics by J. Gordon Leishman.


Both these books use equation (4) for rotor solidity. It is possible for a factor 2 to pop up in the coefficients which are usually considered regarding disk area and solidity: $C_T, C_P$ and $C_Q$. From Leishman: