The way to measure your pot size is to find a container of a verifiable size and measure dirt into your container. One gallon is pretty easy to find: nursery pots are the most obvious. Various kitchen containers are gallons or half gallons. To give you a sense of scale, those big buckets with handles from all sorts of industrial products are five gallons. Coincidentally, a friend just texted me the same question yesterday and I took this picture
The bucket is five gallons. The pot on the left is what nurseries are selling as the "5 gallon" plant size, but they are actually closer to four. Sometime back Amazon was showing "five gallon" nursery pots and the product description said 4.4 gallons. Go figure