The first cold morning of fall
Every autumn, many drivers find the tire pressure warning light on during the first cold morning. The tires have not sprung a leak: the air inside them has simply cooled and contracted. The amount is easy to predict with the gas law.
The formula
At constant volume, the absolute pressure of a gas is proportional to its absolute temperature:
P₂ = (P₁ + P_atm) × T₂ ÷ T₁ − P_atm
- P₁ is the gauge reading at the first temperature.
- P_atm is atmospheric pressure, about 14.7 psi (1.013 bar) at sea level.
- T₁ and T₂ are absolute temperatures: °F + 459.67 gives degrees Rankine, °C + 273.15 gives kelvins.
A tire’s volume does change a little with pressure, but the effect is small enough to ignore.
Example
You set your tires to 35 psi in a 70 °F garage, and the next morning it is 20 °F outside:
- Absolute pressure: 35 + 14.7 = 49.7 psi
- Temperatures: 529.7 °R and 479.7 °R
- New absolute pressure: 49.7 × 479.7 ÷ 529.7 = 45.0 psi
- New gauge reading: about 30.3 psi, a drop of 4.7 psi
That matches the rule of thumb of about 1 psi for every 10 °F.
Inflating in a warm garage
If you check your tires indoors at 70 °F but will drive at 20 °F, set them higher so they reach the recommended value outside. In the example, inflating to about 40 psi in the garage gives 35 psi in the cold. The calculator shows this value on the third line.
Good habits
- Check the pressure once a month and before long trips, with the tires cold: before driving or after at least three hours parked.
- Use the pressure on the sticker inside the driver’s door, not the maximum printed on the tire sidewall.
- Do not let air out of hot tires after driving. The pressure rises a few psi as they warm up, and that is expected.
- Under-inflated tires wear faster at the edges, increase fuel consumption and braking distance, and can overheat.
Since 2007, new cars sold in the United States must have a tire pressure monitoring system that warns when a tire is 25% or more below the recommended pressure. A light that goes off after a few miles of driving usually means the tires are just under the limit and need topping up.