Air Pressure, Temperature and Density at Altitude: Standard Atmosphere Calculator

Find the air pressure and density at any altitude.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the altitude and, if you want, how much hotter or colder than standard the air is.

The calculator gives the standard temperature, pressure as a share of sea level, air density from the ideal gas law, the speed of sound and the approximate boiling point of water.

Up to 11 km the temperature falls 6.5 degrees per 1000 m, and above that it is constant to 20 km.

Formulas used

  • T = 288.15 - 0.0065\,h
  • p = 101325\left(\frac{T}{288.15}\right)^{5.2559}
  • \rho = \frac{p}{RT}
  • a = \sqrt{\gamma R T}

Worked example

With the default numbers in the calculator above:

  1. Standard temperature at this altitude: 281.65 K (8.50 C)
  2. Pressure: 89.87 kPa (88.70 percent of sea level)
  3. Actual temperature with the difference you gave: 8.50 C
  4. Air density: 1.11 kg/m3 (90.75 percent of sea level)
  5. Speed of sound: 336.43 m/s (1211.16 km/h)
  6. Boiling point of water at this pressure (approximate): 96.70 C

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

How much does the pressure fall with height?

To about 90 percent of sea level at 1000 m, 50 percent at about 5.5 km and 25 percent at about 10.5 km.

What is density altitude?

The altitude in the standard atmosphere that has the same density as the real air. On a hot day it is higher than the real altitude.

Why does water boil at a lower temperature on a mountain?

Boiling happens when the vapour pressure of the water equals the air pressure. The air pressure is lower, so the temperature is lower.

Is this the real air pressure?

No. It is the standard day. Weather changes the pressure by a few percent.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: ISO 2533 Standard Atmosphere; ICAO Doc 7488 Manual of the ICAO Standard Atmosphere.

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