[katieHaylor (OP)]

Mark asks:

Is there a mathematical formula for working out the amount of gold in a rock specimen?

What do you think?

[Bored chemist]

Not really. You need to measure it in some way.

[evan_au]

Measuring the gold concentration often requires crushing the ore, and extracting the gold using toxic chemicals like cyanide and mercury.

Presumably, you could also use less-destructive effects like measuring X-Ray or gamma-ray absorption in the rock, compared to a rock sample with no gold. This could be complicated if the rock also has other heavy elements like Silver, Selenium or other Telluride minerals.

But the concentration of gold is very low, even in rich ores: perhaps 5 grams of gold in each ton of rock.

So to a first approximation, you could say that the rock in your hand is 0% gold.

See: https://en.wikipedia.org/wiki/Gold_extraction

[Bored chemist]

You could try this
https://en.wikipedia.org/wiki/Metallurgical_assay#Fire_assay/cupellation