There are lots of different types of emissions that contribute to climate change, and for simplicity these are all summed together and expressed as kilograms of CO2 equivalent (kgCO2e).
Dell, helpfully, publish carbon footprint figures for their hardware, but unfortunately don't explain their methodology and some of the figures look suspiciously like a work of fiction to me. I'll look at the Dell PowerEdge R440 as an example.
Dell's data sheet estimates a total carbon footprint and breaks down the carbon footprint into several aspects by percentage. So I can use that total and the breakdown to calculate the carbon footprint of each aspect:
The data sheet estimates it uses 1480.002 KWh / year, and they assume a 4 year life, so that's 5920.008 KWh over its life. They don't say what "Use" actually includes - I'm assuming that it is just the electrical power consumed by the server.
The amount of CO2e created in order to generate a KWh of electricity depends on how you're generating it - wind, hydro, solar, nuclear, etc. produce low emissions, coal produces very high emissions, gas is somewhere in the middle. In the UK, DEFRA publish annual conversion factors based on the current generation mix on the national grid. This changes year to year (the trend is downwards as we add more green capacity to the grid) and in 2019, this conversion factor is 0.2773 kgCO2e / KWh including transmission and distribution. Other countries have a different mix of generating capacities, so will need a different conversion factor.
So, given the electricity consumption that Dell estimate over the server's life (5920.008 KWh), the emissions quoted for "Use" seem outrageously high - the conversion factor they seem to have used works out at 1.043 kgCO2e / KWh - almost 4 times the DEFRA figures.
A 2011 report from the Parliamentary Office of Science & Technology estimates that coal power (which is the worst case) produces 0.786-0.990 kgCO2e / KWh, so Dell's figure is even worse than the worst case of running the hardware off 100% coal power.
Its possible that their "Use" figure also includes the air conditioning required to keep the server cool. If this is the case it makes their figures quite useless since they don't actually say that's what they're doing. A rule of thumb is that about 50% of the power consumed by a data centre goes on air conditioning, so that would make their conversion factor 0.5215 kgCO2 / KWh - still way above DEFRA's figures for 2019. In fact, even DEFRA's conversion factor from 2002 is significantly lower than this.
Unfortunately, very few other server vendors seem to publish figures to use as a comparison. I couldn't find anything for HP kit (they provide a carbon footprint calculator, but this is only for printers, workstations and stuff rather than servers, and it also doesn't work at all). Lenovo don't publish any information for their servers, but they do for workstations - although I haven't analysed their numbers in depth, they do look more reasonable than Dell's, attributing around 50% of the emissions to "use".
Recalculating Dell's figures using DEFRA's conversion factors, I would expect something like:
This looks more in line with Lenovo's figures.