People ask us this because our servers run on solar power, so here is the honest maths. These are estimates from typical component figures, not a meter reading of your specific server. Treat them as the right order of magnitude.
One machine
A game-server node here is a refurbished desktop-class AMD Ryzen system with NVMe storage and no graphics card. Systems like that draw roughly 30-50 W at the wall when idle and 100-150 W under full load. Game servers rarely load all cores at once, so a node hosting a mix of servers sits somewhere around 60-100 W most of the day.
For comparison: a gaming PC with a graphics card draws 300-500 W while playing; a single old-style 60 W bulb is, well, 60 W.
One game server
Divide the machine by the servers on it. With eight to twelve servers per node, one small Paper server's share is about 10-15 W, roughly what a phone charger or a Wi-Fi router draws. Over a 30-day month that is:
12 W × 24 h × 30 days = 8.6 kWhA heavy modpack server or a Rust server that keeps two or three cores busy is closer to 30-40 W, or 20-30 kWh a month. Idle servers (nobody online, world not ticking) drop to a few watts.
What that means in CO2
The German grid averaged roughly 350-400 g CO2 per kWh in recent years (Umweltbundesamt figures; it varies by year and hour). A small server on grid power would therefore cause about 3-3.5 kg CO2 a month. On solar power the operating emissions are near zero; the panels themselves have an embedded footprint that is paid back within a few years of production, after which the electricity is effectively clean. Our network entry point in Frankfurt is a rented server on the data center's power, so a small share of every server's footprint is not solar. More in How our solar power works.
Why "green hosting" claims deserve a question
Many hosts buy certificates (guarantees of origin) rather than running on renewable power. That is not wrong, but it is a different thing from a roof full of panels feeding the machines. Ask a host where the electricity physically comes from; the answer tells you which kind you are dealing with.