Find the temperature at any altitude in feet or meters with the standard atmosphere (ISA) or a known ground temperature, or solve altitude from temperature.
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Temperature At Altitude Formula
The constant-lapse formula uses temperature at a reference point and height above that same point. In the calculatorโs custom model, enter the known reference conditions rather than assuming they are local weather observations:
- T_a is the temperature at altitude (ยฐC)
- T_g is the ground-level temperature (ยฐC)
- LR is the lapse rate (ยฐC/m); the ISA standard value is 0.0065 ยฐC/m (6.5 ยฐC/km)
- A is the altitude above the measurement point (meters)
The standard-profile decrease is 6.5 ยฐC/km from 0 to 11,000 geopotential meters, followed by โ56.5 ยฐC from 11 to 20 km. This tool retains a linear extension down to โ500 m and stops at 20,000 m; it does not calculate higher layers. Exactly โ56.5 ยฐC has a nonunique inverse over 11โ20 km, while nearby warmer temperatures have a unique lower-segment solution. For custom input rates in ยฐC/km, the equivalent reference formula is T = Tโ โ L ร (h โ hโ) / 1,000.
What is Temperature At Altitude?
Temperature at altitude is air temperature at a specified height, with the height definition stated. The fixed standard profile cools through its lower segment, but real atmospheric profiles vary and can include inversions. Geometric elevation and geopotential height are different coordinates; this calculator does not silently convert one into the other.
ISA Standard Atmosphere: Temperature by Layer
The reference lower-atmosphere profile uses 15 ยฐC at sea level, a 6.5 ยฐC/km decrease to 11 km and a constant โ56.5 ยฐC to 20 km. The NASA standard-atmosphere appendix cited below uses geopotential height. The following table includes the next 20โ32 km reference layer for context; its 25 and 32 km rows are outside this calculatorโs supported range.
| Altitude (m) | Altitude (ft) | ISA Temp (ยฐC) | ISA Temp (ยฐF) | Layer |
|---|---|---|---|---|
| 0 | 0 | 15.0 | 59.0 | Troposphere |
| 1,000 | 3,281 | 8.5 | 47.3 | Troposphere |
| 2,000 | 6,562 | 2.0 | 35.6 | Troposphere |
| 3,000 | 9,843 | -4.5 | 23.9 | Troposphere |
| 5,000 | 16,404 | -17.5 | 0.5 | Troposphere |
| 8,000 | 26,247 | -37.0 | -34.6 | Troposphere |
| 11,000 | 36,089 | -56.5 | -69.7 | Tropopause begins |
| 15,000 | 49,213 | -56.5 | -69.7 | Tropopause (isothermal) |
| 20,000 | 65,617 | -56.5 | -69.7 | Tropopause ends |
| 25,000 | 82,021 | -51.5 | -60.7 | Lower Stratosphere |
| 32,000 | 104,987 | -44.5 | -48.1 | Lower Stratosphere |
Actual tropopause height and temperature vary with location and weather. The fixed 11 km transition is a model boundary, not a measurement of the current tropopause, and latitude alone does not determine the temperature on a route.
Types of Atmospheric Lapse Rates
An environmental lapse rate describes the surrounding atmosphere. Dry and saturated adiabatic rates describe displaced air parcels. Stability depends on comparing the environmental profile with the relevant parcel behavior; a fixed 6.5 ยฐC/km threshold does not by itself establish stability, convection or precipitation.
| Lapse Rate Type | Rate (ยฐC/km) | Rate (ยฐF/1,000 ft) | Conditions |
|---|---|---|---|
| Dry Adiabatic (DALR) | 9.8 | 5.4 | Rising unsaturated air parcel, no condensation |
| Moist Adiabatic (MALR/SALR) | Variable | Variable | Saturated parcel rate depends on temperature and pressure; the toolโs 5 ยฐC/km value is illustrative. |
| Standard-profile gradient | 6.5 | 3.57 | Fixed lower-model gradient, not a measured local environmental lapse rate. |
| Super-adiabatic environment | >9.8 (approx.) | >5.4 (approx.) | Cooling faster than the dry parcel rate can favor instability; convection also depends on moisture, forcing and the vertical profile. |
| Stability comparison | Compare environmental and parcel rates | Use consistent difference units | No universal 6.5 ยฐC/km cutoff establishes stability. Compare the environment with the applicable dry or saturated parcel rate. |
The saturated adiabatic rate varies with parcel temperature and pressure because condensation releases latent heat. The calculatorโs fixed 5 ยฐC/km option is an illustrative straight-line assumption, not a universal moist rate or a measured environmental profile. Use an appropriate observed lapse rate for a custom layer when one is available.
Illustrative Temperature Differences from the Model
The standard profile is a fixed reference, not a real-time observation. The following table uses explicitly assumed temperatures for arithmetic examples; none is a verified annual, seasonal or summit climate average. Named places are scenario labels only. The listed heights are numeric geopotential inputs to the model, not an unannounced conversion of actual geometric city or summit elevations. A real comparison requires measured temperature, its observation period and a consistent height definition.
| Illustrative scenario label | Modeled geopotential height (m) | ISA Temp (ยฐC) | Assumed temperature (ยฐC), not an observed average | Assumed minus model (ยฐC) |
|---|---|---|---|---|
| Sea Level (ISA reference) | 0 | 15.0 | 15.0 (assumed) | 0.0 |
| Denver, Colorado | 1,609 | 4.5 | 9.6 (assumed) | +5.1 |
| Machu Picchu, Peru | 2,430 | -0.8 | 13.0 (assumed) | +13.8 |
| La Paz, Bolivia | 3,640 | -8.7 | 8.0 (assumed) | +16.7 |
| Mont Blanc, Alps | 4,808 | -16.3 | -14.0 (assumed) | +2.3 |
| Kilimanjaro Summit | 5,895 | -23.3 | -7.0 (assumed) | +16.3 |
| Mt. Everest Summit | 8,849 | -42.5 | -26.0 (assumed) | +16.5 |
| Commercial cruise (FL350) | 10,668 | -54.3 | -55.0 (assumed) | -0.7 |
| Tropopause (mid-latitude) | 11,000 | -56.5 | -65 to -50 (assumed) | -8.5 to +6.5 |
These assumed scenarios do not establish regional temperature patterns or observed ISA deviations. The difference column subtracts the unrounded model temperature from the chosen illustrative temperature, then rounds for display. Use current observations and forecasts for real conditions.
Temperature Inversions: When Altitude Warms Instead of Cools
A temperature inversion means temperature increases with height, corresponding to a negative lapse rate under this sign convention. Inversions occur in real atmospheric profiles; the retained custom model accepts only positive lapse rates and does not calculate them.
Inversions can be associated with near-surface radiational cooling, subsidence or frontal structure. Their strength, duration and effects depend on the actual weather profile. A positive constant-lapse assumption cannot represent these layers.
Inversions can limit vertical mixing and matter for air quality, wind profiles, frost and smoke dispersion. Their practical effects depend on moisture, wind, terrain and the evolving vertical profile. This calculator does not assess those hazards; use appropriate official observations, forecasts and guidance.
Applications in Aviation
Temperature relative to a standard profile is one input to aircraft performance assessment. This tool calculates only the selected temperature-height relation; it does not calculate air pressure, density altitude, thrust, lift, takeoff distance or climb performance. Use approved aircraft procedures and current weather for flight planning.
Cold conditions can require altimetry temperature corrections under applicable published procedures. This calculator does not perform those corrections, verify an aircraft systemโs behavior or establish terrain clearance.
Applications in Mountaineering and Outdoor Recreation
As a custom arithmetic example, 25 ยฐC at a 500 m reference and a constant 6.5 ยฐC/km lapse gives 25 โ 6.5 ร (3,000 โ 500) / 1,000 = 8.75 ยฐC at 3,000 m. That is a model assumption, not a summit forecast or a clothing recommendation. Wind, precipitation, radiation and actual temperature layers are not modeled.
To calculate a 0 ยฐC crossing in the selected model, choose Altitude from temperature and enter 0 ยฐC. The supported ISA-style profile gives approximately 2,307.69 geopotential meters; the custom solve uses the entered reference conditions and positive lapse. There is no separate Freezing Level tab. This calculation does not determine an observed freezing level, rain/snow type, icing or avalanche conditions.
Model references: NASA standard-atmosphere appendix, Table A1 and height definitions; NOAA/NWS adiabatic glossary; NWS guidance on environmental and parcel stability comparisons. These references support the model assumptions, not the illustrative tableโs chosen local temperatures or a weather/safety prediction.
