Calculating surface of wire mesh

Two ways: you can approximate it as a wire grid, use known formula for area of 1mm cylinder with height = length of wire. The 'length' will ignore the fact that the wire grid is not straight wire but slightly bent.
Or, you can use a scale to weigh the grid, and the known formula for volume of a length of 1mm wire, and density of the metal (copper = 8.9 gm/cm^3) to get the length. Then use the formula for area of a cylinder.

How accurate does it have to be? Why do you need to know?
Anyway, the usual method is to approximate the mesh as having been woven from round wire of the same circumference as the average cross section between crossover points, and do the obvious math. Or, one can assume wire of rectangular cross-section. The wires being on diagonals makes the math messy (lengths vary with position), but still not that hard.
Joe Gwinn

Perhaps manufacturer may have detailed spec's.
Otherwise, probably easiest to estimate from weight/unit area and the open area percentage that is generally available. To first approximation that and the individual strand diameter should get reasonably close.

First: I think that the linked screen is expanded metal, if it makes a difference. See this zoomed-in pic:
The angled blue lines show what I think is the cut line. Notice at the intersection how the zig-zag vertical element is/seems-to-be continuous.
As far as calculating the surface, I would take the X-shape in the rectangle, whose size is 5 x 7 (?). The surface area is then the area of the 2 cylinders that are the diagonals (diameter 1mm).
Then there are 100/5 x 100/7 of these rectangles.
But if it is expanded metal, then those aren't wires/cylinders and it's a whole other ball game. Unless assuming wire is close enough.
HTH, Bob

... If it is expanded metal, the sheet stock was probably 1mm thick and it was probably "cut" at 1mm intervals, making the "wires" 1mm x 1mm square. Even easier than actual round wire.
Bob

A picture? That's a definite plus.
What's the thickness of the stock and the width of each expanded wire? Is it copper, or is it steel with copper (paint?) flashed over the top?
That's expanded metal. What are you trying to calculate for? Electrical properties (like resistance or current carrying ability), wind resistance, strength, or what?
Key Ironic Question: Why do people who post questions like these _invariably_ leave out 99% of the key data which would help others help them? Now there will be 99 questions, many duplicates, to find the other data...OR, the thread might never end. It's one of those.

I made a fish out of hammered brass sheet and wrapped it in expanded metal. It looked like scales.
It was a red snapper.

I think he wants the wetted area of a fish.

----------------- It is expanded copper metal that i have to replace with copper mesh wire of 1mm thickness. The surface is important because of the size and density. I have to replace this expanded mesh with something that will look like woven copper mesh.
If the wire is 1mm thick, one meter of this wire would have 31.4 cm2.
This woven copper mesh should have at least 4 times the surface of this expanded metal and when this is defined, copper mesh will be set in production. Final product will be 1x1 meter sheet that will be cut into 10x10 squares and used and shielding.
Because this is custom made i can not buy woven copper mesh, i have to created it. This is also no problem.
The only thing that i have to sent to the factory is the surface, length of the wire and thickness of holes.

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"woven copper mesh should have at least 4 times the surface of this expanded metal"
What does the above, mean, precisely? It seems that you're mixing up the projected area the mesh covers w/ the surface area of the wire.
The normal way it would be specified would be either the size of the openings or mesh (as in number of threads/unit distance) or as the fractional open area.
I can't really tell what you're trying to spec, precisely.
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Any chance you can post the factory request for spec's for reading their specifications directly?