I have some 'horticultural charcoal' still left, so I weighed it.[bag says Product of USA, Red McLellan Co, Whitney Farms, PO Box 70, Independence, OR 97351,
Whitney Farms Organic Garden Products Mind you, particle size IS extremely important to weight per unit volume, and I will have those experiment results presently.
Since my source shows the highest carbon content charcoal is only 92.5% carbon, I think Phillip's estimates are too large.
So, 1 cup of 'horticultural charcoal' pieces in the 1cm to 2cm size range weighs 93.272gms.
1 cup of my native soil weighs 242.354gms
I have 1/2 cup of the charcoal bits in my mortor, and I will measure the volume after crushing them to fine particles. Regardless of what the other fellas tell you, size matters.

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Nemo me impune lacesset. ~Unattested