ISA Deviation Calculator
Find the standard (ISA) temperature at any flight level or altitude, and how much warmer or colder the real air is: ISA+10, ISA−5 and so on.
Altimeter reading with 1013 hPa / 29.92 inHg set. You can also type "FL350" or "10668 m".
The real (static) air temperature at that level, from the flight deck, a forecast or a sounding.
For true airspeed and the probe's ram rise. Needed for TAT.
1.0 for a jet's TAT probe. Simple OAT probes recover about 0.7–0.9 of the heating.
How your ISA deviation is worked out
Find the standard temperature for your level, compare it with the real air, and see what the difference does to the air's density.
- 1
Standard at your level
FL350 · 35,000 ft
ISA −54.3 °C - 2
Your outside air
OAT measured
−44.0 °C - 3
The difference
−44.0 − (−54.3)
= +10.3 °C
ISA+10 - 4
Thinner or thicker air
σ = 0.296
DA 36,170 ft
Read more: the formula, a worked example and the ISA table
The International Standard Atmosphere (ISA) is the made-up "average day" that altimeters, airspeed indicators and performance charts are built on: 15 °C and 1013.25 hPa at sea level, cooling at a fixed rate as you climb. Real air is almost never exactly standard, so pilots say how far off it is: ISA+10 means 10 °C warmer than standard at that level, ISA−5 means 5 °C colder. Performance charts, cruise tables and the flight management computer all use this number.
The formula
height in metres h = pressure altitude (ft) × 0.3048
ISA temperature, up to 11,000 m (36,089 ft) = 15 − 0.0065 × h (°C)
ISA temperature, 11,000 to 20,000 m = −56.5 °C
ISA temperature, 20,000 to 32,000 m = −56.5 + 0.001 × (h − 20,000)
ISA deviation = outside air temperature − ISA temperature
outside air temperature = ISA temperature + deviation
quick rule: ISA ≈ 15 − 2 × (altitude in thousands of ft), not below −56.5
SAT (K) = TAT (K) ÷ (1 + 0.2 × recovery factor × Mach²)
pressure, up to 11,000 m = 1013.25 × (1 − 0.0065 × h ÷ 288.15)^5.2559 hPa
speed of sound = 661.48 kt × √(temperature in K ÷ 288.15)
TAS = Mach × speed of sound
density ratio σ = (pressure ÷ 1013.25) ÷ (temperature in K ÷ 288.15)
Density altitude is the standard-atmosphere height that has the same density ratio σ. The calculator works it out layer by layer, so it stays right above the tropopause too. The freezing level assumes the air keeps the same ISA deviation all the way down, which real air often doesn't: treat it as a rough guide and use the cloud base and freezing level calculator or the forecast for icing decisions.
Worked example
You are at FL350 and the outside air temperature is −44 °C.
- FL350 is a pressure altitude of 35,000 ft. In metres: 35,000 × 0.3048 = 10,668 m, below the tropopause.
- ISA temperature = 15 − 0.0065 × 10,668 = 15 − 69.342 = −54.3 °C.
- ISA deviation = −44 − (−54.342) = +10.3 °C, so the air is ISA+10.
- Quick rule: 15 − 2 × 35 = −55 °C, which would make it ISA+11. The rule is 0.7 °C too cold at this level.
- Pressure = 1013.25 × (1 − 0.0065 × 10,668 ÷ 288.15)^5.2559 = 1013.25 × 0.23530 = 238.4 hPa (7.04 inHg).
- Temperature ratio θ = (−44 + 273.15) ÷ 288.15 = 229.15 ÷ 288.15 = 0.79525. Density ratio σ = 0.23530 ÷ 0.79525 = 0.2959, so the density altitude is about 36,170 ft, some 1,170 ft above the pressure altitude.
- Speed of sound = 661.48 × √0.79525 = 661.48 × 0.89177 = 589.9 kt. At Mach 0.78 that is a TAS of 0.78 × 589.9 = 460 kt.
- Freezing level in the same air mass: (15 + 10.342) ÷ 1.9812 × 1,000 = about 12,790 ft.
ISA temperature and pressure by flight level
| Level | ISA temperature | Quick rule | Pressure | Speed of sound |
|---|---|---|---|---|
| Sea level | 15.0 °C | 15 °C | 1013.3 hPa | 661 kt |
| FL050 | 5.1 °C | 5 °C | 843.1 hPa | 650 kt |
| FL100 | −4.8 °C | −5 °C | 696.8 hPa | 638 kt |
| FL180 | −20.7 °C | −21 °C | 506.0 hPa | 619 kt |
| FL250 | −34.5 °C | −35 °C | 376.0 hPa | 602 kt |
| FL300 | −44.4 °C | −45 °C | 300.9 hPa | 589 kt |
| FL350 | −54.3 °C | −55 °C | 238.4 hPa | 576 kt |
| 36,089 ft (tropopause) | −56.5 °C | −56.5 °C | 226.3 hPa | 574 kt |
| FL390 | −56.5 °C | −56.5 °C | 196.8 hPa | 574 kt |
| FL450 | −56.5 °C | −56.5 °C | 147.5 hPa | 574 kt |
Why it matters
- Performance: warmer than ISA means thinner air, so engines make less thrust and wings less lift. Take-off, climb and maximum altitude charts are read by ISA deviation. The density altitude calculator covers this near the ground, with humidity.
- Altimeters: in air colder than ISA you are lower than the altimeter shows; in warmer air you are higher. For approach altitudes use the cold temperature correction calculator, and for pressure altitude from QNH the pressure altitude calculator.
- Speed: the same Mach gives a higher true airspeed in warmer air, because the speed of sound rises with temperature. The true airspeed calculator converts IAS, CAS, EAS, TAS and Mach.
Uses the ICAO Standard Atmosphere (ICAO Doc 7488/3; identical to the US Standard Atmosphere 1976 up to 32 km): 15 °C, 1013.25 hPa and 1.225 kg/m³ at sea level, 6.5 °C per km to 11 km, −56.5 °C from 11 to 20 km, +1 °C per km from 20 to 32 km, dry air (R = 287.053 J/kg·K, γ = 1.4), and Sutherland's law for viscosity. The 2 °C (3.5 °F) per 1,000 ft rule is the one in the FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25), chapter 4. Pressure altitude is treated as geopotential height, as altimeters do.
Common questions
How do you calculate ISA deviation?
Work out the standard (ISA) temperature for your pressure altitude, then take it away from the real outside air temperature. ISA is 15 °C at sea level and falls 1.98 °C per 1,000 ft up to 36,089 ft. At FL350 ISA is −54.3 °C, so an outside air temperature of −44 °C is 10.3 °C warmer: ISA+10.
What is the ISA temperature at FL350?
At FL350 (35,000 ft pressure altitude) the ISA temperature is −54.3 °C. Worked out exactly: 35,000 ft is 10,668 m, and 15 − 0.0065 × 10,668 = −54.342 °C. The quick 2 °C per 1,000 ft rule gives −55 °C, close enough for a mental check.
What does ISA+10 mean?
ISA+10 means the outside air is 10 °C warmer than the standard atmosphere at that level. Warmer air is less dense, so the density altitude is higher than the pressure altitude, engines and wings work less well, and performance charts give a longer take-off run and a lower climb rate.
What is the ISA temperature above the tropopause?
In the standard atmosphere the temperature stops falling at the tropopause, 11,000 m or 36,089 ft, and stays at −56.5 °C up to 20,000 m (65,617 ft). Above that it warms by 1 °C per 1,000 m. So at FL390 and FL410, ISA is still −56.5 °C.
How do I get the outside air temperature from TAT?
A TAT probe reads warmer than the real air because the air heats up as it rams into it. Divide the TAT in kelvin by 1 + 0.2 × Mach² (times the probe recovery factor). At Mach 0.78 a TAT of −17 °C works out at a static air temperature of −44.8 °C, about 28 °C cooler.
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