Enter an altitude to get the temperature, pressure, density, speed of sound and viscosity of the U.S. Standard Atmosphere 1976, which matches the ICAO International Standard Atmosphere up to 32 km. Add an ISA deviation or the actual temperature for hot or cold days.
Last updated:
Altitude
From −5 km to 86 km (−16,404 ft to 282,152 ft)
Altitude type
Aircraft pressure altitude and ISA tables use geopotential altitude; the difference is under 0.5% below 30 km.
Temperature
Day type
e.g. 15 for ISA +15 (hot day), −10 for a cold day
Enter your values to see the result.
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How to use the Standard Atmosphere (ISA) Calculator
Enter the altitude and choose meters, feet or kilometers.
Choose the altitude type: geometric for true height above sea level, geopotential for pressure altitude as used in aviation and ISA tables.
Pick the day type: standard, an ISA deviation such as +15 °C, or the actual outside air temperature.
Press Calculate to see temperature, pressure, density, speed of sound and viscosity with the formulas used.
Scroll down for the temperature profile and a full atmosphere table that you can download as CSV.
Layers of the 1976 standard atmosphere
The model is built from layers in which temperature changes linearly with geopotential altitude. Pressure at the base of each layer follows from the hydrostatic equation and the ideal gas law.
Layer
Base geopotential altitude
Base geometric altitude
Base temperature
Lapse rate
Base pressure
Troposphere
0 m
0 m
288.15 K (15 °C)
−6.5 K/km
101,325 Pa
Tropopause
11,000 m
11,019 m
216.65 K (−56.5 °C)
0
22,632 Pa
Stratosphere
20,000 m
20,063 m
216.65 K (−56.5 °C)
+1.0 K/km
5,474.9 Pa
Stratosphere
32,000 m
32,162 m
228.65 K (−44.5 °C)
+2.8 K/km
868.02 Pa
Stratopause
47,000 m
47,350 m
270.65 K (−2.5 °C)
0
110.91 Pa
Mesosphere
51,000 m
51,412 m
270.65 K (−2.5 °C)
−2.8 K/km
66.939 Pa
Mesosphere
71,000 m
71,802 m
214.65 K (−58.5 °C)
−2.0 K/km
3.9564 Pa
Top of the lower model
84,852 m
86,000 m
186.87 K (−86.3 °C)
-
0.37338 Pa
Constants: g₀ = 9.80665 m/s², R = 287.05287 J/(kg·K), γ = 1.4, effective Earth radius r₀ = 6,356,766 m. Between 80 and 86 km the 1976 standard lowers the kinetic temperature slightly because the mean molecular weight starts to drop; the calculator includes that correction.
Quick reference by altitude (standard day)
Geometric altitude
Temperature
Pressure
Density
Speed of sound
0 km (0 ft)
15.0 °C
101,325 Pa
1.225 kg/m³
340.3 m/s
1 km (3,281 ft)
8.5 °C
89,876 Pa
1.112 kg/m³
336.4 m/s
2 km (6,562 ft)
2.0 °C
79,501 Pa
1.007 kg/m³
332.5 m/s
5 km (16,404 ft)
−17.5 °C
54,048 Pa
0.7364 kg/m³
320.5 m/s
10 km (32,808 ft)
−49.9 °C
26,500 Pa
0.4135 kg/m³
299.5 m/s
15 km (49,213 ft)
−56.5 °C
12,112 Pa
0.1948 kg/m³
295.1 m/s
20 km (65,617 ft)
−56.5 °C
5,529 Pa
0.08891 kg/m³
295.1 m/s
30 km (98,425 ft)
−46.6 °C
1,197 Pa
0.01841 kg/m³
301.7 m/s
50 km (164,042 ft)
−2.5 °C
79.78 Pa
0.001027 kg/m³
329.8 m/s
70 km (229,659 ft)
−53.6 °C
5.221 Pa
8.283 × 10⁻⁵ kg/m³
297.1 m/s
86 km (282,152 ft)
−86.3 °C
0.3734 Pa
6.958 × 10⁻⁶ kg/m³
274.1 m/s
Using ISA in practice
Pilots compare the actual temperature with the ISA value at their pressure altitude. Every degree above standard raises density altitude by roughly 120 ft.
Engineers use the density and viscosity to compute Reynolds numbers, drag and lift for drones, rockets and wind tunnel tests at a given altitude.
True airspeed is equivalent airspeed divided by √σ, so at 35,000 ft (σ ≈ 0.31) an aircraft flies almost twice as fast through the air as its indicated speed suggests.
Real weather differs. The standard atmosphere is an average; on any given day the actual tropopause height and temperatures can differ by several kilometers and tens of degrees, especially near the poles and the tropics.
Frequently asked questions
What is the International Standard Atmosphere (ISA)?
The ISA is a reference model of how temperature, pressure and density change with altitude in average mid-latitude conditions. At sea level it defines 15 °C, 1013.25 hPa and 1.225 kg/m³. Temperature falls by 6.5 °C per kilometer up to 11 km, then stays at −56.5 °C to 20 km before rising again in the stratosphere.
Is the US Standard Atmosphere 1976 the same as ISA?
Yes for practical purposes below 32 km (about 105,000 ft): the ICAO standard atmosphere and the U.S. Standard Atmosphere 1976 use the same constants and give the same values. The 1976 model also defines layers up to 86 km and a separate upper atmosphere to 1,000 km.
What is the difference between geometric and geopotential altitude?
Geometric altitude is the true height above sea level. Geopotential altitude accounts for gravity getting weaker with height, so a geopotential meter represents the same change in potential energy everywhere. The standard atmosphere is defined in geopotential altitude: H = r₀ · Z / (r₀ + Z) with r₀ = 6,356,766 m. At 11 km geometric the difference is about 19 m.
How is air pressure calculated at altitude?
In layers where temperature changes linearly, P = P_b · (T_b / T)^(g₀ / (R · L)). In isothermal layers, P = P_b · exp(−g₀ · (H − H_b) / (R · T_b)). Here P_b and T_b are the pressure and temperature at the base of the layer, L is the lapse rate, g₀ = 9.80665 m/s² and R = 287.05287 J/(kg·K).
What does ISA +15 mean?
ISA +15 means the air is 15 °C warmer than standard at that pressure altitude, for example 30 °C at sea level instead of 15 °C. The pressure is unchanged, so the air is less dense, aircraft perform worse and the density altitude is higher than the pressure altitude.
How is the speed of sound found from temperature?
For an ideal gas, a = √(γ · R · T), with γ = 1.4 for air. It depends only on temperature, so it is 340.29 m/s at sea level and 295.07 m/s in the isothermal layer between 11 and 20 km.
How is the viscosity of air calculated?
Dynamic viscosity uses Sutherland's law, μ = 1.458×10⁻⁶ · T^1.5 / (T + 110.4) Pa·s, which gives 1.7894×10⁻⁵ Pa·s at 15 °C. Kinematic viscosity is μ divided by density, so it rises quickly with altitude as the air thins.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.