bar
m
m
Result
Gauge reading now (same temperature)2.936 bar
How it is calculated, with your numbers
- Air pressure at the start
a0 = 101.325 × (1 − 0.0000225577 × h0)^5.25588101.325 × (1 − 0.0000225577 × 0)^5.25588 = 101.33 kPa - Air pressure now
a1 = 101.325 × (1 − 0.0000225577 × h1)^5.25588101.325 × (1 − 0.0000225577 × 4,500)^5.25588 = 57.73 kPa - Gauge reading now (same temperature)
p1 = p0 + (a0 − a1) / 1002.5 + (101.325 − 57.7283) / 100 = 2.936 bar
Working uses the metric units the formula is written in.
- p0 Gauge pressure set at the start (bar)
- h0 Altitude where it was set (m)
- h1 Altitude now (m)
- a0 Air pressure at the start
- a1 Air pressure now
- p1 Gauge reading now (same temperature)
What it means
The air inside the tyre does not change when you climb, but the air outside thins. A gauge measures the difference, so it reads higher on a high pass than it did at the bottom: roughly 0.1 bar (1.5 psi) more for every 1,000 m in the lower atmosphere.
If you let air out at altitude to get back to the "normal" reading, the tyre will be under-inflated when you come back down. Colder air at altitude works the other way (see the temperature calculator).
Assumptions and limits
- Standard atmosphere pressure profile; weather changes local pressure by a few kPa.
- Same tyre temperature at both points.
Sources
- U.S. Standard Atmosphere, 1976 (NOAA, NASA, USAF): pressure and density with altitude.