m
°C
kW
Result
Approximate power available31.3 kW
Air density0.710 kg/m³
Density compared with sea level58.0 %
How it is calculated, with your numbers
- Air pressure
p = 101.325 × (1 − 0.0000225577 × h)^5.25588101.325 × (1 − 0.0000225577 × 4,500)^5.25588 = 57.73 kPa - Air density
rho = 1.225 × (p / 101.325) × (288.15 / (t + 273.15))1.225 × (57.7283 / 101.325) × (288.15 / (10 + 273.15)) = 0.710 kg/m³ - Density compared with sea level
ratio = (p / 101.325) × (288.15 / (t + 273.15)) × 100(57.7283 / 101.325) × (288.15 / (10 + 273.15)) × 100 = 58.0 % - Approximate power available
pnow = power × (p / 101.325) × (288.15 / (t + 273.15))54 × (57.7283 / 101.325) × (288.15 / (10 + 273.15)) = 31.3 kW
Working uses the metric units the formula is written in.
- h Altitude (m)
- t Air temperature (°C)
- power Power at sea level (15 °C) (kW)
- p Air pressure
- rho Air density
- ratio Density compared with sea level
- pnow Approximate power available
What it means
An engine burns the oxygen it can draw in. Higher up, air pressure falls and each lungful contains less air, so a naturally aspirated engine makes roughly proportionally less power. Warm air is thinner too. At around 4,500 m the air is only a little over half as dense as at sea level, which is why bikes feel so flat on the highest passes.
Fuel injection keeps the mixture right as air thins, but it cannot add the missing air. Turbocharged and supercharged engines lose much less.
Assumptions and limits
- Standard atmosphere pressure profile.
- Power taken as proportional to air density, a common first approximation; real engines differ somewhat.
- Dry air.
Sources
- U.S. Standard Atmosphere, 1976 (NOAA, NASA, USAF): pressure and density with altitude.
- Heywood, J. B., Internal Combustion Engine Fundamentals, McGraw-Hill, 1988.
Related calculators
Tyre pressure at altitude calculatorWhy your gauge reads higher on a mountain pass, and by how much.Dyno correction factor calculator (SAE J1349)Correct measured power to standard conditions from temperature, pressure and humidity.Top speed from power and dragThe speed where aerodynamic drag and rolling resistance use up all the power.