Change the altitude and see the temperature, pressure, air density and speed of sound from the International Standard Atmosphere (ISA) model update in real time. Inspect the troposphere lapse rate and the isothermal stratosphere on the charts, and apply an ISA temperature deviation to model the real atmosphere.
Parameters
Altitude h
m
Height above sea level. Troposphere / stratosphere switch at 11 km
Sea-level temperature (baseline) T₀
°C
15 degC in the standard. The sea-level starting point
Sea-level pressure P₀
kPa
101.325 kPa (one atmosphere) in the standard
ISA temperature deviation ΔISA
°C
How much warmer / colder than standard. E.g. ISA+15 means +15
Results
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Temperature (°C)
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Pressure (kPa)
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Air density (kg/m³)
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Speed of sound (m/s)
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Density ratio (vs sea level)
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Atmospheric layer
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Atmosphere column profile — altitude marker
A column of air from sea level to 30 km — warm and dense at the bottom, cold and thin at the top. The 11 km tropopause separates the troposphere (falling temperature) from the stratosphere (isothermal). The aircraft marker shows the current altitude.
Troposphere (0–11 km) temperature T and pressure P. T₀: sea-level temperature (K), L: lapse rate 0.0065 K/m, h: altitude (m). Temperature falls at 6.5 degC/km.
Lower-stratosphere (11 km and above) pressure. Temperature is held at the 11 km value (isothermal) and pressure decays exponentially from the 11 km pressure P₁₁. g = 9.80665 m/s², R = 287.05 J/(kg·K).
Air density ρ from the ideal-gas law; speed of sound a depends on temperature only with γ = 1.4. The real-atmosphere temperature is the ISA temperature plus the deviation ΔISA.
What is the International Standard Atmosphere?
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I have heard of the "International Standard Atmosphere"... but air conditions are different everywhere and every day, right? Why do we even need a "standard"?
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Good question — that is exactly the point. The real atmosphere keeps changing with weather, season, latitude and time of day. Even at the same 10,000 metres, the air over the equator in summer is nothing like the air over the Arctic in winter. But to design an aircraft, calibrate an instrument or compare engine performance, you need one fixed atmosphere that everyone agrees to use as a baseline. That is the International Standard Atmosphere, the ISA. Starting from 15 degC and 101.325 kPa at sea level, it fixes temperature, pressure and density at every altitude by international agreement.
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So it is a common yardstick. I sort of get that temperature keeps falling as you climb — but when I push the slider past 11 km, the temperature stops and stays flat. What is that?
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Nicely spotted. The lower ISA splits into two layers. From 0 to 11 km is the "troposphere", where the temperature drops by a tidy 6.5 degC for every kilometre you climb. That is why mountain tops and cruising altitudes are so cold. But at 11 km the temperature reaches about -56.5 degC and then stops falling — it stays constant. That is the lower "stratosphere", and because the temperature does not change it is called "isothermal". The exact point where the fall stops, around 11 km, is the "tropopause".
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If the temperature is constant, I would expect the pressure to be constant too... does the pressure still fall in the stratosphere?
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That is the interesting bit. Pressure is just "the weight of the air sitting above you". Even if the temperature is constant, the higher you go the less air is left above you, so the pressure keeps dropping. In the troposphere it follows a more complex formula where temperature falls as pressure drops; in the stratosphere it follows a simple exponential decay at constant temperature. Look at the pressure profile chart below and you will see the pressure fall smoothly through both layers. The 100 kPa at sea level becomes about 22 kPa at 11 km — nearly a fifth of the value.
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Is thin air a good thing for an aircraft, or a bad thing?
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Both. Thin air — low density — means less drag, so you can fly fast and fuel-efficiently. That is why airliners deliberately cruise high. But thin air also produces less lift and less engine thrust. Try pushing the "ISA temperature deviation" slider to the positive side. Simulating a hot day drops the density even further, and the take-off run gets longer. Pilots compute performance as a deviation from standard, like "ISA+15". The standard atmosphere is the shared starting point for all of that.
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The speed of sound changes with altitude too. What does that affect?
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The speed of sound depends on temperature alone, so it is slower in the cold air up high — about 340 m/s at sea level, down to about 295 m/s at 11 km. It matters because an aircraft's Mach number is speed divided by the speed of sound. At the same ground speed, a lower speed of sound up high gives a higher Mach number, and shock-wave effects appear sooner. Choosing a cruising altitude is inseparable from this change in the speed of sound. The standard atmosphere is the common foundation that makes flight — including that change — work consistently.
Frequently Asked Questions
The International Standard Atmosphere (ISA) is an idealised, averaged reference model that specifies, by international agreement, exactly how air temperature, pressure and density vary with altitude. The real atmosphere changes constantly with weather, season, latitude and time of day, but designing aircraft, calibrating instruments and comparing performance all need one fixed reference. The ISA starts from a sea-level baseline of 15 degC and 101.325 kPa, uses a 6.5 degC/km lapse rate in the troposphere (0 to 11 km) and an isothermal lower stratosphere above it.
In the troposphere (below 11 km) the temperature falls at a constant lapse rate, so T = T0 - L*h and the pressure follows P = P0*(1 - L*h/T0)^5.2561. In the lower stratosphere (11 km and above) the temperature is constant (isothermal), so it is fixed at the tropopause value and the pressure decays exponentially from the 11 km pressure: P = P11*exp(-g*(h - 11000)/(R*T)). This tool switches automatically between the two formulas at 11 km.
Because the real atmosphere never matches the standard exactly, the difference is expressed as the ISA deviation. For example, ISA+15 means 15 degC warmer than standard. A hot day lowers air density, which cuts lift and engine thrust, lengthens the take-off run and reduces climb performance. Pilots and engineers enter this ISA deviation into performance calculations. The ISA temperature deviation slider in this tool plays exactly that role and feeds into the density, speed of sound and density ratio.
An aircraft pressure altimeter is calibrated to the ISA pressure-altitude relationship. The instrument measures pressure and converts it to an altitude using the ISA formula, giving the pressure altitude. When the real atmosphere differs from the ISA, pressure altitude drifts away from true geometric altitude. That is exactly why every aircraft reading the same ISA reference keeps a consistent relative separation, preserving safe vertical spacing. Engine and aerodynamic performance are also quoted at ISA conditions so different aircraft can be compared fairly.
Real-World Applications
Aircraft performance design and operations: Lift, drag and engine thrust all depend on air density. Designers compute take-off performance, climb rate and cruise fuel burn at ISA conditions, and during operations they correct for the day's temperature and pressure as an ISA deviation. On a hot day or at a high-elevation airport the density is lower, so the same aircraft needs a much longer take-off run and the maximum take-off weight may have to be restricted.
Altimeter calibration and air traffic control: A pressure altimeter has the ISA pressure-altitude relationship built in. With every aircraft reading altitude against the same ISA reference, the relative height difference between aircraft is preserved even when the real atmosphere differs from the ISA, so vertical separation (collision avoidance by altitude difference) holds up. This is also why cruising altitudes are managed as "flight levels", which are pressure altitudes.
Rockets, missiles and meteorological observation: A launch vehicle climbs rapidly from the troposphere through the stratosphere and beyond, so the change of dynamic pressure (density times velocity squared) with altitude is central to its structural loads. Weather balloons and drone flight planning also use the ISA as the reference for temperature, pressure and density at each altitude.
Reference conditions for wind-tunnel tests and CFD: When comparing or scaling wind-tunnel and computational fluid dynamics (CFD) results, the ISA serves as the reference atmospheric condition. Reynolds number and Mach number depend on density, viscosity and the speed of sound, so unifying conditions on the ISA lets results from different facilities and different analyses be handled consistently.
Common Misconceptions and Pitfalls
The biggest misconception is assuming the ISA represents the real atmosphere itself. The ISA is only an idealised, averaged model; it does not represent the atmosphere of any particular day or place. The real tropopause altitude varies a great deal — about 16 to 18 km over the equator but only about 8 km at the poles — and the lapse rate can even reverse, producing an inversion layer where temperature rises with height. This tool uses the standard fixed 11 km, 6.5 degC/km model, so it cannot be used to forecast actual weather. Understand that the "common design and comparison reference" and "the real weather" are two different things.
Next, the confusion that pressure altitude equals true altitude. Pressure altitude is the value obtained by converting pressure to altitude with the ISA formula, and it drifts away from true geometric altitude whenever the real atmosphere differs from the ISA. On a hot day (ISA+) you are actually higher than the same indicated pressure altitude suggests, and on a cold day (ISA-) you are actually lower. When flying low over mountainous terrain on a cold day, the "cold-temperature correction" — the fact that true terrain clearance is lower than the altimeter shows — is essential operational knowledge that, if missed, can lead to terrain impact.
Finally, the misconception that density and pressure fall in the same way. Density is set by both pressure and temperature (ρ = P/RT). As you climb, the pressure falls but so does the temperature, so density does not fall in the same proportion as pressure. In the stratosphere, where temperature is constant, density and pressure do fall in proportion in that layer — but not in the troposphere. For performance calculations, what usually matters is "density", not "pressure". Get into the habit of thinking in density ratio (relative to sea level) rather than pressure when you look at lift, drag and thrust, and the loss of performance on a hot day becomes intuitive.