I thought I'd summarize what kind of waste production we have at the moment, so that anyone thinking of building a similar compost as I have can estimate their space needs. So, the current compost is about 600 liters. The outer dimensions are about a meter in every direction (a bit over 3 feet), and the insulation makes the inside compartment a bit smaller, so we end up with about 600 liters, or about 160 gallons. That is divided into two sections that are being used in turns.
At the moment we have 5 adult chickens and 4 chicks, but the coop can hold about 8-9 adult chickens and this is still fine for the composting capabilities of my box. The birds have hemp bedding inside the coop. It gets cleaned and turned daily, the most visible poop is removed daily. Not really much stuff coming from inside the coop on a daily basis. The run is mostly filled with leaves and straw at the moment. Hay is removed from under the roosts in the run on a daily basis, we use a 20 liter (5 gallon) bucket for that, it's usually about half full of straw and poop. The coop is completely emptied 3-4 times per year, and the run maybe 4-6 times per year.
In addition to that, we get kitchen scraps, maybe a liter or two (1-2 quarts) per day, but it varies a bit. I usually throw some tea that's been standing in a thermos and any fluids that are left in cups and glasses in the compost bin too, because they add to the moisture. Our household consists of two persons.
In summer we also get some garden waste that is added to the compost. Because of the quicker composting that happens in the warmer times, this doesn't really affect the need for space in the compost.
So, for a flock of 20 birds and 4-5 people household I would recommend doubling the size of the compost box.