§ How it works

A tire is very nearly a fixed-volume container, so the air inside follows Gay-Lussac's law: absolute pressure is proportional to absolute temperature.

\frac{p_1}{T_1} = \frac{p_2}{T_2} \quad\Longrightarrow\quad p_2 = p_1\, \frac{T_2}{T_1}

The catch is the word absolute. A tire gauge reads pressure above atmospheric, and thermometers read in °C or °F. Both have to be shifted before the ratio works:

p_{\text{hot}} = \left( p_{\text{cold}} + p_{\text{atm}} \right) \frac{T_{\text{hot}} + 273.15}{T_{\text{cold}} + 273.15} - p_{\text{atm}}

with $p_{\text{atm}} = 1.013\ \text{bar} = 14.7\ \text{psi}$ and temperatures in °C.

Rule of thumb

Around normal road pressures the result is close to 0.1 bar per 10 °C, or roughly 1 psi per 10 °F. That is why a tire set on a warm afternoon triggers the pressure warning on the first frosty morning.

Working backwards for track days

Tire makers quote a hot target. Rearranging the same formula gives the cold pressure to start from:

p_{\text{cold}} = \left( p_{\text{target}} + p_{\text{atm}} \right) \frac{T_{\text{cold}} + 273.15}{T_{\text{hot}} + 273.15} - p_{\text{atm}}

References

Equation of State (Ideal Gas) — NASA Glenn Research CenterBoyle, Charles and Gay-Lussac laws combined into pV = nRT

§ How it works

A tire is very nearly a fixed-volume container, so the air inside follows Gay-Lussac's law: absolute pressure is proportional to absolute temperature.

\frac{p_1}{T_1} = \frac{p_2}{T_2} \quad\Longrightarrow\quad p_2 = p_1\, \frac{T_2}{T_1}

The catch is the word absolute. A tire gauge reads pressure above atmospheric, and thermometers read in °C or °F. Both have to be shifted before the ratio works:

p_{\text{hot}} = \left( p_{\text{cold}} + p_{\text{atm}} \right) \frac{T_{\text{hot}} + 273.15}{T_{\text{cold}} + 273.15} - p_{\text{atm}}

with $p_{\text{atm}} = 1.013\ \text{bar} = 14.7\ \text{psi}$ and temperatures in °C.

Rule of thumb

Working backwards for track days

Tire makers quote a hot target. Rearranging the same formula gives the cold pressure to start from:

p_{\text{cold}} = \left( p_{\text{target}} + p_{\text{atm}} \right) \frac{T_{\text{cold}} + 273.15}{T_{\text{hot}} + 273.15} - p_{\text{atm}}

References

Equation of State (Ideal Gas) — NASA Glenn Research CenterBoyle, Charles and Gay-Lussac laws combined into pV = nRT

Tire Pressure & Temp

Inputsdrag · tap · type

Fig. 14Gauge pressure against tire temperature

§ How it works

Rule of thumb

Working backwards for track days

References

Tire Pressure & Temp

Inputsdrag · tap · type

Fig. 14Gauge pressure against tire temperature

§ How it works

Rule of thumb

Working backwards for track days

References