ISO 2533 Standard Atmosphere

The International Standard Atmosphere (ISA) is a reference model that defines the vertical distribution of atmospheric temperature, pressure, density, and other properties from −5 km to 80 km altitude.

What is the Standard Atmosphere?

The Standard Atmosphere provides a common reference frame for aerospace engineering, scientific research, and industrial applications. Rather than representing any specific location or weather condition, it defines a set of baseline atmospheric conditions that enable consistent calculations worldwide.

The model divides the atmosphere into layers, each with a defined temperature gradient. Within each layer, temperature varies linearly (or is constant, in isothermal layers), and pressure and density are derived from fundamental thermodynamic equations.

ISO 2533 specifies these layers, the associated physical constants, and the equations that relate altitude to atmospheric properties. The result is a deterministic model: given any valid altitude, all atmospheric properties can be calculated precisely.

The model assumes dry air as a perfect gas free from moisture and dust, with conventional initial values of temperature, pressure, and density at mean sea level. These simplifications make the model reproducible but mean it does not represent any specific real-world condition — for observed conditions by latitude and season, see ISO 5878.

Model-Only Data

ISO 2533 is a purely deterministic mathematical model — it contains no empirical observations. Every value in this standard is either a defined constant or calculated from defined constants using exact equations. Given any altitude, the same atmospheric properties will always be produced.

Defined Fixed physical or conventional constants (e.g. g_n, R*, κ)Calculated Derived from defined constants via thermodynamic equations (e.g. T, p, ρ at altitude)

History

The concept of a standard atmosphere dates back to the early 20th century, driven by the needs of aviation and meteorology. ISO 2533 was first published in 1975, establishing the international standard for atmospheric reference conditions.

ISO 2533:1975 — Standard Atmosphere, identical with the ICAO and WMO Standard Atmospheres from −2 km to 32 km, extended to 80 km using data from recent research. It specifies temperature, pressure, density, and other thermodynamic properties as functions of geometric and geopotential altitude. ISO Store ↗
Addendum 1:1985 — Hypsometrical tables relating geopotential altitude to atmospheric pressure, intended for calibration of aneroid and manometer-type instruments. Covers pressure ranges in hPa and mmHg at fine intervals. ISO Store ↗
Addendum 2:1997 — Extension of the altitude range to −5,000 m (from −2,000 m), and standard atmosphere tables as a function of altitude in feet (−16,500 ft to 262,500 ft). ISO Store ↗
ISO 2533:2026 — Second edition that cancels and replaces the 1975 first edition. Incorporates all addenda and errata, extends the lower altitude range to −5 km, adds hypsometrical tables in hPa, and recalculates all values using modern computational methods with improved accuracy. ISO Store ↗

Why a Standard Atmosphere?

The concept of a standard atmosphere is crucial for numerous applications:

Reference Framework

A common basis for consistent and reliable characterization of atmospheric conditions, enabling accurate calculations, simulations, and assessments across industries.

Interoperability

Ensures measurements, models, and simulations from different sources can be compared, promoting harmonization across international boundaries.

Performance Evaluation

Enables objective assessment of aircraft performance, weather model accuracy, and system efficiency against a known baseline.

Safety Compliance

Crucial for maintaining safety standards in aviation and aerospace, ensuring systems are designed to withstand expected atmospheric conditions.

International Collaboration

Promotes knowledge sharing among researchers and practitioners worldwide by adopting a common reference for atmospheric phenomena.

Key Constants

For the complete list of symbols, variables, and their definitions, see the Symbols & Variables reference page.

The following fundamental constants define the Standard Atmosphere model. These are fixed physical and conventional values used in all ISA calculations. Defined

$g_{n}$: 9.80665 m/s²; Standard acceleration of free fall
$N_{A}$: 6.02257e+26 mol⁻¹; Avogadro constant
$p_{n}$: 101325 Pa; Standard air pressure at sea level
$ρ_{n}$: 1.225 kg/m³; Standard air density
$T_{n}$: 288.15 K; Standard thermodynamic air temperature at sea level (15 °C)
$R^{*}$: 8.31432 J/(mol·K); Universal gas constant
$r_{0}$: 6356766 m; Nominal Earth radius (at 45°32'33" latitude)
$κ$: 1.4; Adiabatic index (ratio of specific heats)
$S$: 110.4 K; Sutherland's temperature (for dynamic viscosity)
$β_{s}$: 1.468 × 10⁻⁶ kg/(m·s·K^½); Sutherland's empirical coefficient
$σ$: 0.365 × 10⁻⁹ m; Effective collision diameter of an air molecule
$M$: 0.028964 kg/mol; Molar mass of dry air (derived)
$R$: 287.05287 J/(kg·K); Specific gas constant for air (derived)

Foundational Physics

The ISA model is built from a small set of fundamental equations. Understanding these makes the entire model transparent.

The hydrostatic equation

A static atmosphere in equilibrium satisfies the relation between pressure, density, gravity, and altitude:

- dp = ρ \times g \times dh

The perfect gas law

At the altitudes covered by ISO 2533, air behaves as a perfect gas with constant molar mass. The full form uses the universal gas constant, while the simplified form uses the specific gas constant R = R²/M:

p = ρ \times R \times T

Gravity vs. altitude

The acceleration of free fall decreases with distance from the Earth’s centre, following Newton’s gravitation law. The nominal Earth radius r = 6,356,766 m is from the Smithsonian Meteorological Tables, most accurate at latitude 45°32'33":

g = g_{n} \times {(\frac{r}{r + h})}^{2}

This approximation differs from the more accurate equation in the US Standard Atmosphere 1976 by less than 0.001% at 60,000 m.

Geopotential altitude

Geopotential altitude H is defined by integrating gravity over geometric altitude, then dividing by the standard gravity g_n:

H = \frac{1}{g_{n}} \times \int_{0}^{h} g (h) dh

This gives the conversion formulas between geopotential and geometric altitude:

\begin{matrix} H = \frac{r \times h}{r + h} \\ h = \frac{r \times H}{r - H} \end{matrix}

Atmospheric Composition

Dry clean air composition remains practically constant up to altitudes of 90–95 km. The ISA uses the following composition near sea level (from ISO 2533:2026 Table 2). CO₂ content is updated from NOAA Global Monthly Mean data (December 2025).

Gas	Name	Volume %	Molar Mass (kg/kmol)
N₂	Nitrogen	78.084	28.0134
O₂	Oxygen	20.9476	31.9988
Ar	Argon	0.934	39.948
CO₂	Carbon dioxide	0.0427	44.00995
Ne	Neon	0.00182	20.183
He	Helium	0.000524	4.0026
CH₄	Methane	0.000192	16.04303
Kr	Krypton	0.000114	83.80
H₂	Hydrogen	0.000055	2.01594
N₂O	Nitrous oxide	0.0000339	44.0128
Total dry air		100	0.028964

Sea-level Characteristics

In addition to the primary constants, ISO 2533:2026 Table 3 defines the following derived physical characteristics at mean sea level (H = 0). Calculated Each value below is computed from the defined constants above — none are measured.

Property	Symbol	Value	Unit
Speed of sound	$a_{n}$	340.294	`m/s`
Pressure scale height	$H_{p n}$	8434.5	`m`
Mean free path of air particles	$l_{n}$	66.328 × 10⁻⁹	`m`
Air number density	$n_{n}$	25.471 × 10²⁴	`m⁻³`
Mean air-particle speed	$\overset{̅}{v} n$	458.94	`m/s`
Specific weight	$γ_{n}$	12.013	`N/m³`
Kinematic viscosity	$ν_{n}$	14.607 × 10⁻⁶	`m²/s`
Thermal conductivity	$λ_{n}$	25.343 × 10⁻³	`W/(m·K)`
Dynamic viscosity	$μ_{n}$	17.894 × 10⁻⁶	`Pa·s`
Collision frequency	$ω_{n}$	6.9193 × 10⁹	`s⁻¹`

Temperature Layers

The atmosphere is divided into 9 layers, each characterized by a base geopotential altitude, base temperature, and vertical temperature gradient ( $β_{s}$ ). A gradient of zero indicates an isothermal layer. Defined Layer boundaries and gradients are specified by the standard.

Layer	Base $H$ (m)	Base $T$ (K)	$β_{s}$ (K/m)	Description
1	-2000	301.15	-0.0065	Lower Troposphere
2	0	288.15	-0.0065	Tropopause
3	11000	216.65	0	Lower Stratosphere
4	20000	216.65	0.001	Stratosphere
5	32000	228.65	0.0028	Upper Stratosphere
6	47000	270.65	0	Stratopause
7	51000	270.65	-0.0028	Mesosphere
8	71000	214.65	-0.002	Upper Mesosphere
9	80000	196.65	-0.002	Top

Calculation Approach

The ISA formulas are implemented in our open-source library. Below is a summary of the approach used for each layer type. Calculated All atmospheric properties at altitude are computed from the defined constants and layer parameters using these exact equations.

Non-isothermal layers ( $β_{s} \neq 0$ )

When the temperature gradient $β_{s}$ is non-zero, temperature varies linearly with geopotential altitude $H$ :

\begin{matrix} T (H) = T_{b} + β_{s} \times (H - H_{b}) \\ p (H) = p_{b} \times {(\frac{T (H)}{T_{b}})}^{- \frac{g_{n}}{β_{s} \times R}} \\ ρ (H) = \frac{p (H)}{R \times T (H)} \end{matrix}

Isothermal layers ( $β_{s} = 0$ )

In isothermal layers, temperature remains constant and pressure decreases exponentially:

\begin{matrix} T (H) = T_{b} & (constant) \\ p (H) = p_{b} \times \exp (\frac{- g_{n} \times (H - H_{b})}{R \times T_{b}}) \\ ρ (H) = \frac{p (H)}{R \times T_{b}} \end{matrix}

Density and specific weight

Density is calculated from pressure and temperature via the perfect gas law:

ρ = \frac{p}{R \times T}

Specific weight is the weight per unit volume of air:

γ = ρ \times g

Speed of sound

The speed of propagation of an infinitesimal perturbation in the gas. Not valid for shock waves or above the altitude limits of the standard.

a = \sqrt{κ \times R \times T} \approx 20.04676 \times \sqrt{T}

Dynamic viscosity (Sutherland’s formula)

Based on kinetic theory with experimentally derived constants. Invalid above 90 km altitude.

μ = \frac{β_{s} \times T^{3 / 2}}{T + S}

Kinematic viscosity

ν = \frac{μ}{ρ}

Thermal conductivity

Calculated from an empirical formula with coefficients derived from experiments.

λ = \frac{2.648151 \times 10^{- 3} \times T^{3 / 2}}{T + 245.4 \times 10^{- 12 / T}}

Pressure scale height

H_{p} = \frac{R \times T}{g}

Air number density

The number of neutral air particles per unit volume:

n = \frac{N_{A} \times p}{R^{*} \times T}

Mean air-particle speed

Arithmetic average of air-particle speeds from Maxwell’s distribution of molecular speeds:

\bar{v} = \sqrt{\frac{8}{π} \times R \times T} \approx 1.595769 \times \sqrt{R \times T}

Mean free path

The average distance an air particle travels between successive collisions:

l = \frac{R^{*} \times T}{\sqrt{2} \times π \times N_{A} \times σ^{2} \times p} = \frac{1}{\sqrt{2} \times π \times σ^{2} \times n}

Collision frequency

The mean air-particle speed divided by the mean free path:

ω = 4 \times σ^{2} \times N_{A} \times \sqrt{\frac{π}{R^{*} \times M}} \times \frac{p}{\sqrt{T}}

Related Standards

The ISA model is related to several international standards. For the full bibliography and detailed comparisons, see the References page.

Standard	Altitude Range	Relationship
ISO 2533:1975	-2 km to 32 km	Foundation document
ICAO Doc 7488/3	-2 km to 80 km	Extends ISA to 80 km
US Std Atm 1976	-2 km to 1,000 km	Identical to ISA to 32 km
WMO	-2 km to 32 km	Identical to ISA
ISO 2533:2026	−5 km to 80 km	Modern revision
ISO 5878	Reference atmospheres for aerospace use	Companion: observed conditions by latitude and season

Try the Calculator

Compute atmospheric properties at any altitude using our interactive calculator, featuring 3D visualization, 2D charts, and table generation.

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Get the Official Standard

Purchase the ISO 2533 documents from the ISO Store for the complete specification, all equations, and authoritative reference tables.

Current revision

ISO/DIS 2533 — Second edition that cancels and replaces ISO 2533:1975 and all its addenda. Covers −5 km to 80 km, includes hypsometrical tables, and recalculates all values using modern computational methods.

Purchase ISO/DIS 2533

Previous edition (superseded by ISO/DIS 2533)

ISO 2533:1975 — First edition. Standard Atmosphere from −2 km to 80 km geopotential altitude.

ISO Store

Addendum 1:1985 — Hypsometrical tables for instrument calibration (pressure to altitude in hPa and mmHg).

ISO Store

Addendum 2:1997 — Extension to −5,000 m and atmosphere tables in feet.

ISO Store

ISO 2533 Standard Atmosphere

What is the Standard Atmosphere?

Model-Only Data

History

Why a Standard Atmosphere?

Reference Framework

Interoperability

Performance Evaluation

Safety Compliance

International Collaboration

Key Constants

Foundational Physics

The hydrostatic equation

The perfect gas law

Gravity vs. altitude

Geopotential altitude

Atmospheric Composition

Sea-level Characteristics

Temperature Layers

Calculation Approach

Non-isothermal layers (βs≠0)

Isothermal layers (βs=0)

Density and specific weight

Speed of sound

Dynamic viscosity (Sutherland’s formula)

Kinematic viscosity

Thermal conductivity

Pressure scale height

Air number density

Mean air-particle speed

Mean free path

Collision frequency

Related Standards

Try the Calculator

Get the Official Standard

Current revision

Previous edition (superseded by ISO/DIS 2533)

Non-isothermal layers ( $β_{s} \neq 0$ )

Isothermal layers ( $β_{s} = 0$ )