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Standard Atmosphere

ISA temperature, pressure, density, and speed of sound at altitude.

InputISA layers: T = T₀ + λ·Δh, P from the hydrostatic + gas-law integration per layer

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The engineering

The International Standard Atmosphere models the troposphere (lapse −6.5 °C/km to 11 km), the isothermal tropopause (to 20 km), and the lower stratosphere (+1 °C/km to 32 km).

Density is the number that bites: at 10,000 ft (~3,048 m) air is already ~74% of sea-level density — this card's last row is why your drone's props and your engine's dyno numbers both lie in Denver.

Where this math comes from

In 1648 Blaise Pascal sent his brother-in-law Florin Périer up the Puy de Dôme with a mercury barometer to prove air pressure drops with altitude — the founding experiment of this entire card. Pierre-Simon Laplace gave the drop its mathematical form, the barometric formula, in the early 1800s.

Then the atmosphere surprised everyone: Léon Teisserenc de Bort's unmanned balloons showed in 1902 that temperature stops falling around 11 km — the tropopause and stratosphere, the kinks in this card's math. When aviation went international, engineers needed one agreed atmosphere for calibrating altimeters and comparing aircraft performance: ICAN standardized it in 1924, and the U.S. Standard Atmosphere of 1976 remains the reference — including at Marshall Space Flight Center, where atmosphere models like Earth-GRAM are still maintained for launch vehicles today.

  1. 1648Blaise Pascal & Florin PérierPuy de Dôme experiment proves pressure falls with altitude.
  2. 1805Pierre-Simon LaplaceThe barometric formula — pressure vs. height, mathematically.
  3. 1902Léon Teisserenc de BortBalloon soundings discover the tropopause and stratosphere.
  4. 1924ICANFirst international standard atmosphere for aviation.
  5. 1976U.S. COESA committeeU.S. Standard Atmosphere 1976 — still the working reference.

See the full timeline of the math behind every calculator →

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