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☁️ ISO 2533 Standard Atmosphere

Calculate atmospheric properties (temperature, pressure, density) at a given altitude per ISO 2533.

Inputs

Calculations based on Troposphere model (-2km to 11km)

Results

Temperature (T)
32.00 °F
Pressure (P)
0.000 psi
Air Density (ρ)
0.0000 lb/ft³
Speed of Sound (a)
0.0 ft/s

Atmospheric Profile

0 m

Calculator Description

The ISO 2533 Standard Atmosphere is an internationally agreed reference model that defines how air temperature, pressure, and density vary with altitude. Because the real atmosphere constantly changes with weather, aviation performance, instrument calibration, and engineering calculations rely on a consistent "average atmosphere," which this standard provides.

What this calculator finds

This calculator computes the temperature (T), pressure (P), density (ρ), and speed of sound (a) at a specified altitude using the standard atmosphere model.

Why it matters

  • Providing reference atmospheric conditions for aircraft lift, drag, and engine performance
  • Serving as the calibration basis for altimeters and airspeed indicators
  • Computing the altitude-dependent speed of sound for Mach number estimates

Formula

ISO 2533 Standard Atmosphere Equations

In the troposphere (from sea level up to 11 km or 36,089 ft), temperature decreases linearly with altitude. Pressure is derived from hydrostatic equilibrium combined with this temperature profile, while density and speed of sound follow from the ideal-gas relations.

T=T0+LhT = T_0 + L h
P=P0[1+LhT0]−g/(RL)P = P_0\left[1 + \dfrac{L h}{T_0}\right]^{-g/(RL)}
ρ=PRT\rho = \dfrac{P}{RT}
a=γRTa = \sqrt{\gamma R T}
  • T, P, ρ, a — Temperature [K], pressure [Pa], density [kg/m³], and speed of sound [m/s] at altitude
  • h — Altitude [m]
  • T₀, P₀ — Sea-level standard temperature (288.15 K) and pressure (101,325 Pa)
  • L — Temperature lapse rate (−0.0065 K/m)
  • R — Specific gas constant for air (287.05 J/(kg·K))
  • γ — Heat capacity ratio for air (1.4)
  • g — Acceleration of gravity (9.80665 m/s²)

How the formula works

  • Because the lapse rate L is negative, temperature T falls linearly as altitude increases.
  • Pressure P decreases exponentially, with the exponent −g/(R·L) governing how fast it drops.
  • As temperature falls, the speed of sound a = √(γ·R·T) also decreases, so the same true airspeed gives a higher Mach number at altitude.

Worked example

At 5,000 m, T = 288.15 + (−0.0065 × 5000) = 255.65 K (about −17.5 °C). Pressure is P = 101325 × [1 + (−0.0065 × 5000 / 288.15)]^(−9.80665/(287.05×−0.0065)) ≈ 54,000 Pa, and the speed of sound is a = √(1.4 × 287.05 × 255.65) ≈ 320 m/s.

Useful Tips

Practical tips

  • Lower density reduces lift and engine power — use the density value when assessing high-altitude takeoff/landing performance.
  • Mach number is M = V / a; with the altitude speed of sound a, it follows directly from true airspeed.

Limitations & cautions

  • The linear-lapse formula is valid only in the troposphere (below 11 km); the stratosphere requires different relations as temperature becomes constant or rises.
  • The standard atmosphere is an idealized average; real weather (temperature, humidity, pressure) can differ substantially.
  • Humidity effects are neglected — dry air is assumed.