How does tire pressure vary as a function of temperature?

Today, I changed my winter tires. I estimate the storage temperature is about +10 degrees Celsius. The average operating temperature is expected to be about -5 degrees Celsius.

I measured the tire pressures using a precision mechanical tire pressure gauge. All four tires had a pressure of 2.48 bar. However, that's the pressure at the storage temperature, not the pressure at the expected operating temperature.

My question is: how does tire pressure vary as a function of temperature?

There is a law in physics, the ideal gas law: pV = nRT. Here, p is the pressure, V is the volume, n is the amount of ideal gas in moles, R is the ideal gas constant and T is the temperature.

However, to apply this law, you need to use the absolute temperature (or any quantity proportional to it), i.e. Kelvins, not a temperature that can be either positive or negative (such as Celsius or Fahrenheit).

You also need to note that p is the total pressure, not the reading of the tire pressure sensor. So, if the tire pressure sensor reads 2.48 bar, the total pressure is actually 3.48 bar, because the tire pressure sensor is measuring (or at least showing) pressure difference and not absolute pressure!

So, the answer is that the pressure at -5 degrees Celsius is (2.48 + 1) * (273.15 - 5) / (273.15 + 10) - 1 = 3.2956 - 1 = 2.2956 (and the unit is bar).

If using Fahrenheit, the 273.15 must be replaced with 459.67. So, -5 degrees Celsius is 23 degrees Fahrenheit and 10 degrees Celsius is 50 degrees Fahrenheit. Therefore, the result is (2.48 + 1) * (459.67 + 23) / (459.67 + 50) - 1 = 2.2956 (and the unit is bar). So, we get the same result.

If using PSI instead of bar, you need to replace 1 by 14.5. So, 2.48 bar is 35.97 PSI, and the formula is (35.97 + 14.5) * (273.15 - 5) / (273.15 + 10) - 14.5 = 33.30 or (35.97 + 14.5) * (459.67 + 23) / (459.67 + 50) - 14.5 = 33.30 (and the unit is PSI now).

33.30 PSI is 2.296 bar, so we get the same value (sans a small rounding error).

This way, the storage temperature versus operating temperature difference can be accounted for in tire pressures.

By the way, the pressure was correct. The manufacturer of the car has specified 2.3 bar front and rear, and that's exactly the pressure the tires will have once they cool down to -5 degrees Celsius.