True Airspeed (TAS) Calculator
Calculate true airspeed from indicated airspeed, pressure altitude, and outside air temperature. Essential for flight planning and navigation.
About this calculator
Your airspeed indicator reads indicated airspeed, but that reading only matches your actual speed through the air at sea level in standard conditions — climb into thinner air and the same dynamic pressure corresponds to a faster true speed. This calculator treats indicated airspeed as calibrated airspeed directly (a reasonable simplification for most light aircraft in normal cruise, since position error is usually small — check your POH if you need a precise correction). It then computes the air density ratio (sigma) as the ratio of a pressure ratio, derived from the standard barometric formula at your pressure altitude, to a temperature ratio between your entered OAT and the ISA reference temperature of 288.15 K. True airspeed follows from CAS divided by the square root of that density ratio — thinner, warmer air pushes TAS further above CAS for the same indicated reading.
The calculator also reports Mach number, computed from the local speed of sound (which depends only on temperature, not altitude, via 38.967 × √T in kelvin), useful for checking against Mmo limits at higher altitudes. Feed the resulting TAS into a wind triangle calculation to get ground speed and course corrections for flight planning. The main thing to keep straight: pressure altitude (altimeter set to 29.92) is not the same as your actual indicated altitude, so look it up separately if your altimeter is set to local pressure.
Inputs
Light aircraft cruise: 90–180 kt
VFR cruise: 3,000–12,000 ft
At 8,000 ft ISA: ~1°C
Results
True Airspeed (TAS)
136 kt
How to Use This Calculator
- Read your indicated airspeed (IAS) from the airspeed indicator.
- Enter your pressure altitude (set altimeter to 29.92 inHg and read altitude).
- Enter the outside air temperature (OAT) in Celsius.
- Use the resulting TAS for wind triangle and flight planning calculations.
How the result changes across these scenarios
| Scenario | True Airspeed (TAS) |
|---|---|
| Low & Slow (Pattern) | 92 kt |
| VFR Cruise 8,000 ft | 136 kt |
| IFR High Cruise FL180 | 212 kt |
What each input means
- Indicated Airspeed (IAS)
- Airspeed shown on the airspeed indicator in the cockpit.
- Pressure Altitude
- Altitude with altimeter set to 29.92 inHg. Use the Pressure Altitude calculator if needed.
- Outside Air Temperature (OAT)
- Current outside air temperature at your altitude. Read from the OAT gauge or METAR temps aloft.
What each result means
- True Airspeed (TAS)
- Your actual speed through the air — use for flight planning ground speed calculations.
- Mach Number
- Speed as a fraction of the speed of sound at your temperature.
- Speed of Sound
- Local speed of sound at the given OAT.
- Density Ratio (σ)
- Ratio of air density to sea-level standard. Lower = thinner air.
- ISA Deviation
- Difference between actual OAT and ISA standard temperature.
How this is calculated
Worked example, using the default values
- Calibrated Airspeed (CAS)CAS ≈ IAS (assuming zero position error)IAS = 120 kt = 120 kt
- Density Ratio (σ)σ = Pressure Ratio ÷ Temperature Ratio0.7428 ÷ 0.9479 = 0.7836
- True Airspeed (TAS)TAS = CAS ÷ √σ120 ÷ √0.7836 = 136 kt
- Mach NumberMach = TAS ÷ Speed of Sound136 ÷ 644 = Mach 0.210
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the calculator treat IAS as calibrated airspeed with no correction?
For most light aircraft in normal cruise configuration, the gap between indicated and calibrated airspeed (position error) is small enough to ignore for flight-planning purposes, so the engine sets CAS equal to your entered IAS directly. If you need a precise correction — near stall speed or with flaps extended, for example — check your POH's IAS-to-CAS conversion table.
What is the density ratio (σ) and why does it matter?
Density ratio is the ratio of actual air density to sea-level standard density, computed here as a pressure ratio from the standard barometric formula at your pressure altitude, divided by a temperature ratio between your OAT in Kelvin and the 288.15 K ISA reference. TAS equals CAS divided by the square root of this ratio, so a lower density ratio — from higher altitude or warmer temperature — always widens the gap between TAS and CAS.
Why is Mach number based only on temperature, not altitude?
The speed of sound depends solely on air temperature (38.967 × √T in Kelvin), not directly on pressure or altitude, so the calculator computes it from your entered OAT alone. Two aircraft at different altitudes but the same OAT would share the same local speed of sound and, for a given TAS, the same Mach number.
Why does the same pressure altitude produce a bigger IAS-to-TAS gap on a hot day than a cold one?
Warmer air at a given pressure altitude is less dense, which lowers the density ratio and widens the gap between CAS and TAS since TAS equals CAS divided by the square root of that ratio. This is the same physical effect behind density altitude — hot air needs a higher true speed to generate the dynamic pressure your airspeed indicator reads.
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
Airspeed Converter
Convert between all airspeed types: IAS, CAS, TAS, Mach.
Aviation & Pilot ToolsPressure Altitude Calculator
Field elevation corrected for non-standard pressure.
Aviation & Pilot ToolsDensity Altitude Calculator
Calculate density altitude for flight performance planning.
More in Aviation, Marine & Transport.