How this instrument works
Air near the ground is warmed chiefly by the ground itself: sunlight passes through the atmosphere largely unabsorbed and heats the surface, which then warms the air touching it by conduction and convection. Move away from that surface and you move away from the heat source, so the average temperature falls with height. In the standard atmosphere that fall is fixed at 0.0065°C per metre — 6.5°C for every kilometre climbed — and the formula is nothing more than that constant rate multiplied by height and subtracted from a known starting reading.
That 6.5°C/km figure is the environmental lapse rate built into the International Standard Atmosphere: an averaged profile fitted to decades of real soundings, not a number derived from a single physical law. It is often confused with the dry adiabatic lapse rate of about 9.8°C/km, which instead describes one parcel of unsaturated air cooling as it rises and expands into lower pressure, doing work as it goes. The environmental figure describes the resting atmosphere on an average day; the adiabatic figure describes a single rising bubble of air. The two get mixed up constantly, and they rarely match exactly.
The straight line holds only through the troposphere, roughly the lowest 11,000 m, and only on an average day. A temperature inversion — cold air trapped beneath a warmer layer, common on clear calm nights or in a fog-filled valley — reverses the trend entirely, and no linear formula can anticipate it. Pilots lean on this relationship anyway, because a single ground reading is often all that is available before takeoff, and an estimate built on a tested average beats no estimate when judging icing risk or engine performance at cruise height.
- Enter the Sea-level temperature — the reading at 0 m, in °C or °F.
- Enter the Altitude you want the estimate for, in metres, kilometres, or feet.
- Read Temperature at altitude, computed by multiplying height by the 0.0065°C/m lapse rate and subtracting it from your starting figure.
- Switch either temperature field to °F to work entirely in Fahrenheit — the conversion happens before the subtraction, not after.
Worked example — 1,000 m on a 15°C morning
Take a 15°C reading at the airfield, sea level, and climb to 1,000 m. The formula runs T = 15 − 0.0065 × 1000 = 15 − 6.5 = 8.5°C. That single multiplication, 0.0065 times a thousand, is exactly the 6.5°C-per-kilometre figure pilots and hikers carry in their heads and apply here to one clean kilometre of climb.
Push the same arithmetic further and the pattern holds: a 20°C surface day cools past freezing by 5,000 m, landing at −12.5°C, roughly where a small aircraft might cruise, and a fair reminder of why cabins need heating even when the ramp was warm. Every 1,000 m climbed costs another 6.5°C in either example, because the rate the formula applies never changes.
Questions
Why does temperature drop by exactly 6.5°C per kilometre?
It doesn't, exactly — 6.5°C/km is the International Standard Atmosphere's fitted average of real-world soundings, not a law derived from first principles. A single day's actual profile can run steeper, shallower, or even reverse in an inversion. The value stays useful because it is a well-tested average: aviation performance charts and forecasting rules of thumb lean on it as the best single number available without a live weather balloon.
How is this different from the adiabatic lapse rate?
The adiabatic lapse rate describes one parcel of air cooling as it rises and expands: about 9.8°C/km when dry, nearer 5°C/km when saturated with moisture, both derived from thermodynamics. This calculator's 6.5°C/km is the environmental lapse rate, the average vertical profile of the resting atmosphere mixing many such parcels together. They agree loosely but are not interchangeable, a common mix-up in introductory meteorology.
Does this formula work above the troposphere?
No. The linear relationship holds only through the troposphere, roughly the lowest 11,000 m. Above that, in the stratosphere, temperature stops falling and briefly holds near-constant before rising again, because ozone there absorbs solar ultraviolet radiation directly. A mountain height suits this calculator fine; a stratospheric cruise altitude will return a figure the real atmosphere will not match.
What happens during a temperature inversion?
The straight-line prediction fails. An inversion is a layer where temperature rises with height instead of falling, common on clear, calm nights when the ground radiates heat away faster than the air above it, or where warm air overruns a cold valley floor. This calculator cannot detect one; it always assumes the standard falling trend, so a sounding or pilot report beats the formula whenever an inversion is suspected.
Who actually uses this calculation?
Pilots use it before takeoff to estimate icing risk and engine performance at cruise altitude from a single ground reading. Hikers and mountaineers use it to judge how much colder a summit will feel than the trailhead. HVAC and structural engineers occasionally reference the same standard-atmosphere profile when a design temperature needs adjusting for a building's elevation.
Can I enter the sea-level temperature in Fahrenheit?
Yes. Both temperature fields carry a °C/°F unit menu, and the instrument converts to Celsius internally before applying the 0.0065°C/m lapse rate, then converts the answer back to whichever unit is selected for display. Altitude accepts metres, kilometres, or feet the same way, all converted before the arithmetic runs.