Measure the diameter of your electrode (with a calipers) let's say 20 times over the length of the electrode if and only if the electrode is a circular in its section. Calculate the circumference for each circle. Integrate the circumference over the electrode length and you obtain the surface area of your electrode.
If the section is not circular, you will have to determine the circumference by destructively cutting 20 sections and determing the circumference of each of these sections. The rest of the procedure is the same as for an electrode with a circular section. Of course if you only have one non -circular on section, electrode, you will have to apply the Archimedes approach, which gives you the volume of your electrode. Divide the volume by the height and I guess you have surface area, at least according to a dimensional analysis.
It is well known that the electrical current of an electrochemical process is proportional to the real surface area of the electrode. The presence of surface rugosities due to steps, holes, kinks, and terraces can result in an electrode real surface area that is larger than the geometric one. The electrode real surface area can be evaluated by determining the amount of gas that adsorbs onto the electrode surface. This calculation is possible because every adsorbed gas molecule is attached to one metal atom on the electrode surface, forming a gas monolayer. From crystallographic data the surface atom density can be obtained in consideration of a theoretically flat metal surface. These data allow us to determine the real electrode surface area.
Extract from the summary of the article whose title"Determination of the Real Surface Area of Pt Electrodes by Hydrogen Adsorption Using Cyclic Voltammetry" by José M. Doña Rodríguez et al.
The presence of surface rugosities due to steps, holes, kinks, and terraces can result in an electrode real surface area that is larger than the geometric one. The electrode real surface area can be evaluated by determining the amount of gas that adsorbs onto the electrode surface. This calculation is possible because every adsorbed gas molecule is attached to one metal atom on the electrode surface, forming a gas monolayer. From crystallographic data the surface atom density can be obtained in consideration of a theoretically flat metal surface. These data allow us to determine the real electrode surface area.