The air holds almost nothing
A 24 by 18 foot room with a ten foot ceiling is 4,320 cubic feet, and at standard density that is 324 pounds of air. At 0.24 Btu per pound per degree, lifting all of it by one degree takes 77.8 Btu. Twenty-two kilowatts is 75,067 Btu per hour. Divide and the air alone climbs at 16 degrees a minute.
That is the floor under every answer here, and it is why a room with the cooling off does not feel like a slow problem. If nothing else in the room took any heat, 72 degrees would become 90 in a minute and seven seconds.
The metal is the whole answer, and nobody has measured it
Six thousand pounds of cabinets and equipment at 0.12 Btu per pound per degree is 720 Btu per degree if every bit of it follows the air. That is nine times the air. Count it all and the same room takes 11 minutes 29 seconds to reach 90. Count a fifth of it and the answer is 3 minutes 11 seconds. The default sits at 45 percent and gives 5 minutes 47 seconds.
The right figure is somewhere in that range and it depends on how the metal is arranged. A chassis with air being driven over its heatsinks by its own fans is coupled to the room air well and follows it quickly. A steel side panel with still air on both sides does not. A sealed disk array with 40 pounds of drives inside an insulating enclosure is barely coupled at all on a five minute timescale. The page prints the whole range for that reason, rather than pretending to know.
Why the answer matters at all
The UPS and the cooling are not on the same side of the outage. Batteries pick the load up in the same cycle the mains drops. A chiller with a compressor restart delay, a condenser that has to come up on generator power, and a control sequence that will not start pumps until it is happy, is minutes away at best. During that gap the load is running, the heat is being made, and nothing is removing it — and the arithmetic above says the room has single-digit minutes before it reaches a temperature anybody would want to act at.
That is why the cooling load on the generator, or the lack of it, is the design decision this number feeds. It is also why an orderly shutdown script triggered on room temperature needs its threshold set against a rate rather than a habit: if the room climbs at three degrees a minute, an alarm at 85 and a shutdown that takes four minutes are not compatible.
Measure it rather than trusting this
Every input above except the room dimensions is an estimate, and the largest of them is a guess with a factor of five in it. The good news is that the real answer is cheap to obtain: pick a quiet window, turn the cooling off deliberately with people in the room watching the temperatures, and log the curve until it reaches a temperature you are comfortable stopping at. Ten minutes of that produces a measured rate for your room, with your equipment and your mass, and it replaces every assumption on this page at once.
The measured curve will also bend, which the straight line here does not. As the room warms, heat leaks out faster and the metal is closer to the air temperature, so the rate falls off. Reading the first two minutes of a real curve gives the worst-case rate, and that is the number a shutdown threshold should be set from.
Questions people ask
How long before a server room overheats without cooling?
Minutes, not hours, and the arithmetic is not complicated: net kilowatts divided by the heat capacity of everything in the room. At the defaults here — 22 kW in a 4,320 cubic foot room with 6,000 lb of equipment, 45 percent of it counted as participating — the room climbs 3.11 degrees a minute and takes 5 minutes 47 seconds to go from 72 to 90. Halve the room and it halves. Double the load and it halves again.
Why does the answer change so much with the participating mass?
Because the metal holds roughly nine times as much heat as the air does, so almost the whole answer is a question about metal rather than about air. Whether a given pound of steel follows the room over five minutes depends on whether air is moving over it. The page prints the answer at five different participation levels so the size of that uncertainty is visible rather than hidden inside one confident number.
Should I put the cooling on the generator?
That is an engineering and cost decision for the people who own the design, and this page has no view on it. What it gives is one input: the number of minutes between the cooling stopping and the room reaching a temperature you have chosen to care about. If that number is smaller than the restart sequence for your plant, the two facts are worth putting side by side in front of whoever signs the design.
Does opening the door help?
It changes the arithmetic by giving the heat somewhere to go, and how much depends entirely on what is on the other side. A door into a large cool space is a real heat path; a door into a corridor that is itself sealed buys a few minutes and then stops working. The loss field on the form takes a figure for it, but an honest figure is hard to get without measuring, and zero is the conservative entry.
Is the temperature the same everywhere in the room?
No, and that is the main way this page is optimistic. It treats the room as one well-mixed volume with one temperature. In reality the air at the top of a cabinet with no cooling airflow is well above the room average within a minute, because exhaust air is no longer being carried away and simply piles up. The equipment that trips first will be at the top of the tallest rack, at a temperature the room average never reaches.