It is only 6 steps shown below, to evaluate surface tension of the liquid. As for details, please see Ref.[1].

1. Measure r, z, and θ at any surface point P, as shown in Fig.1(a).
2. Calculate z/r.
3. Find point Q in Fig.1(b), using a curve for θ.
4. Find point R in Fig.1(c), using a curve for θ.
5. Evaluate z˜ from Fig.1(c).
6. Calculate Surface tension of the liquid, using Eq.(1).
   ...(1)
   where ρ[kg/m³] : density of the liquid, g[m/s³] : gravitational acceleration. Be careful of their units as z[m], surface tension[N/m]..

Fig.1
You can download Fig.1(a) and Fig.1(b) .

Above steps are automatically carried out using a program.

1. Measure r, z, and θ at any surface point P, as shown in Fig.1(a).
2. Input r, z, and θ to the program.
3. Input the density of the liquid.

Then, the surface tension will be displayed. You need the density of the liquid, because Eq.(1) is used.

Detailed theory on the surface profile of the liquid is clearly expressed in Ref.[2].