How do we calculate the total trade volume of the market?

When we calculate the overall trading volume, we want to know the combined (US dollar) value of all transactions on every trading pair. So we directly sum up the trading volume of each individual pair. A transaction on the trading pair ETH/BTC of 1 BTC exchanged for 28 ETH results in the dollar equivalent of 1 BTC. In this way, we make sure we don't count the trading volume of pairs twice.

Counting trading pairs twice
We count the volume of a trading pair once instead of twice, like many of other crypto price indexes do. Some of these indexes sum up the volume of all pairs containing BTC, then for ETH, etcetera. After that, they combine these volumes. This results in counting market volumes twice, because the ETH/BTC pair on a particular exchange gets counted when calculating the total BTC volume, and after that gets counted again when calculating the total ETH volume.

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