Altitude Temperature Calculator - Standard Atmosphere Model

The altitude temperature calculator combines the U.S. Standard Atmosphere 1976 lapse rate of 6.5 C per kilometer with the barometric formula to predict air temperature and pressure, then feeds the same pressure into the Antoine equation for the boiling point of water. It is a textbook model that students use in earth science labs and that pilots, hikers, and engineers use to plan for thinner air, cooler temperatures, and a lower boiling point.

• • Hiking and mountaineering: Forecast the temperature and pressure at a base camp so you can pack the right layers.
• • Aviation planning: Translate a flight altitude into the standard temperature and pressure the altimeter assumes.
• • Cooking at altitude: Predict the boiling point of water on a backpacking stove or mountain kitchen so recipes still work.
• • Physics and earth-science homework: Reproduce the standard atmosphere values for a lab worksheet or exam problem.

The model behind the calculator is the same one used by ICAO and most aviation references. It assumes a linear temperature profile in the troposphere up to 11 km, then holds temperature near minus 56.5 C in the lower stratosphere. Once the barometric pressure is known, the calculator solves the Antoine equation for the boiling point of water.

Once you have the dry-air temperature and pressure, the Vapor Pressure Deficit Calculator adds the humidity side of the same atmospheric column.

The calculator combines the linear temperature profile of the standard atmosphere with the exponential barometric formula so that temperature and pressure are both derived from the same altitude input and the same lapse rate. The user can override the sea-level reference temperature to model a hot or cold start, but the lapse rate is fixed at 6.5 C per kilometer. The boiling point is then solved from the same pressure using the Antoine equation.

• h: Geometric altitude in meters above (or below) mean sea level.
• T0: Sea-level reference temperature in C (15 C by default).
• L: Environmental lapse rate, fixed at 0.0065 C per meter (6.5 C per km).
• P0: Sea-level reference pressure, fixed at 1013.25 hPa.
• T0K: Sea-level reference temperature in kelvin for the exponent.
• A, B, C: Antoine constants for liquid water in the 1 to 100 C range, with P in mmHg and T in C.

The barometric exponent evaluates to about 5.256 from four constants: g = 9.80665 m/s^2, M = 0.0289644 kg/mol, R = 8.31447 J/(mol*K), and L = 0.0065 K/m. The Antoine constants come from the NIST Chemistry WebBook, the same source steam tables use.

Above 11 km the calculator clamps temperature to the standard tropopause value of -56.5 C and clamps pressure at roughly 226 hPa. The boiling point is solved from that clamped pressure, so all three values stay at the tropopause reading instead of drifting toward the unrealistic limit a single linear profile would predict.

According to NASA NTRS - U.S. Standard Atmosphere 1976, the tropospheric lapse rate is 6.5 C per kilometer, the sea-level reference temperature is 15 C (288.15 K), and the tropopause sits near 11 km at -56.5 C

The pressure term in this calculator is the isothermal-approximation barometric formula, and the same PV = nRT family of relationships is implemented in detail in the Ideal Gas Calculator.

Four ideas make the model predictable: why pressure drops faster than temperature, why air thins on a mountain, and why water boils at a lower temperature as you climb.

These four ideas are the conceptual core of any standard atmosphere. The linear temperature profile and the exponential pressure profile are linked by the same lapse rate, so one atmospheric constant draws both curves.

For an empirical cross-check on what the standard atmosphere predicts, the Cricket Chirp Thermometer estimates air temperature from cricket chirp rate using Dolbear's law, a natural thermometer for hikers when radiosonde data is unavailable.

Enter an altitude, choose a unit, and pick the sea-level temperature that matches your starting conditions. The result panel updates as you type.

1. 1 Enter the altitude: Type the elevation in meters or feet. The default of 1500 m matches an alpine valley.
2. 2 Choose the altitude unit: Switch between meters and feet to enter imperial heights like 5280 ft for Denver or 29032 ft for Everest.
3. 3 Set the sea-level temperature: Leave 15 C for the standard atmosphere, or change it to a current or average sea-level value.
4. 4 Pick the output temperature unit: Choose Celsius or Fahrenheit. Both values are always calculated, so the display unit only changes the primary readout.
5. 5 Read the result panel: The first card shows the air temperature, followed by Fahrenheit, the pressure in hPa and inHg, and the boiling point from the Antoine equation.
6. 6 Reset for a new scenario: Click Reset to restore the defaults, then re-enter a new elevation.

For a flight-planning sanity check at 35000 ft, enter 35000, choose feet, leave 15 C as the sea-level temperature: air temperature will clamp to minus 56.5 C, barometric pressure will sit near the standard tropopause value of about 226 hPa, and the boiling point of pure water will read near 63 C.

If you need the same altitude translated into a different temperature scale or the pressure value matched to a non-standard reference, the Temperature Converter handles the unit math.

The altitude temperature calculator is most useful when you need a quick reference value for an atmospheric column, a homework problem, or a planning worksheet, and you do not want to recompute the standard atmosphere by hand.

• • Standard atmosphere in one place: Temperature, pressure, and boiling point come from the same 6.5 C/km model, so the numbers stay consistent.
• • Customizable sea-level conditions: Set the sea-level temperature to a current local value rather than 15 C, which matters in polar or tropical scenarios.
• • Both temperature scales ready: Celsius and Fahrenheit are calculated from the same internal value, so the calculator serves meteorology students and US general-aviation pilots.
• • Boiling point estimate included: The boiling point of pure water is solved from the barometric pressure using the Antoine equation, the same model steam tables use instead of a rough linear rule.

The calculator is also a sanity check for any other atmospheric tool. If a forecast or flight-planning app disagrees with the standard atmosphere by a few degrees, rerun the calculation here to see whether the difference comes from weather, a different reference temperature, or a lapse rate assumption.

Three input factors and two atmospheric conditions explain how the calculator responds to changes, and why real measurements can disagree with the prediction.

• • The model is a single linear temperature profile. Real weather produces curved, inverted, or warming-with-height profiles the calculator cannot reproduce.
• • Humidity lowers air density slightly, so humid columns show a few tenths of a percent lower pressure at altitude than the dry-air formula predicts.
• • The boiling point is for pure water. Salt, sugar, or cooking ingredients change the boiling point independently of ambient pressure.

For most hiking, aviation, and academic use cases the standard atmosphere is the right reference. Treat the calculator as a textbook estimate, and the sea-level temperature is the cleanest knob to turn when matching a real measurement.

According to NOAA JetStream - Air Pressure, atmospheric pressure drops with altitude because the weight of the air column above is smaller, which is exactly what the barometric formula expresses

According to NIST Chemistry WebBook - Water Antoine constants, the Antoine equation for liquid water matches steam tables within a few tenths of a degree in the 1 to 100 C range, which makes the boiling point a deterministic output of the barometric pressure

When the gap between the standard atmosphere and a real measurement is too large, the Gas Laws Calculator lets you back out what effective temperature profile the column is actually following.