# Scale Height

## Description

In various scientific contexts, a scale height is a distance over which a quantity decreases by a factor of e (approximately 2.71828, the base of natural logarithms). It is usually denoted by the capital letter H.

Scale height used in a simple atmospheric pressure model

For planetary atmospheres, scale height is the increase in altitude for which the atmospheric pressure decreases by a factor of e. The scale height remains constant for a particular temperature. It can be calculated by the formula shown here.

Planetary examples

Approximate scale heights for selected Solar System bodies follow.

Venus: 15.9 km

Earth: 8.5 km

Mars: 11.1 km

Jupiter: 27 km

Saturn: 59.5 km

Titan: 40 km

Uranus: 27.7 km

Neptune: 19.1–20.3 km

## Variables

H | scale height (m) |

R | specific gas constant (J*kg^{-1}*K^{-1}) |

T | mean atmospheric temperature in kelvins (250 K for Earth) (K) |

g | acceleration due to gravity on planetary surface (m/s^{2}) |