True Airspeed Calculator

Convert indicated airspeed to true airspeed using pressure altitude and outside air temperature.

Physics and EnergyUpdated 2026-10-214 min read

True Airspeed Calculator

True airspeed

...

Density altitude...

Density ratio...

Deviation from standard temperature...

What it does

An airspeed indicator does not measure the speed of the aircraft through the air. It measures the speed through a pitot tube and reacts to the pressure of the air around it, so its reading changes with the density of the air and not only with the motion. The Pilot's Handbook of Aeronautical Knowledge calls this out when it lists the airspeed definitions, and every pilot learns the same table: indicated airspeed, calibrated airspeed, equivalent airspeed and true airspeed.

True airspeed is the speed of the aircraft relative to the surrounding air mass, and it is the number that matters for performance, because thin air lets a propeller or a jet fly faster for the same indicated reading. The relationship comes from matching the dynamic pressure on both sides, which gives true airspeed as equivalent airspeed divided by the square root of the density ratio.

The density ratio comes from the standard atmosphere: the pressure at the altitude you are at, which depends on the pressure altitude, and the actual temperature of that air. The standard atmosphere falls 1.9812 °C for every 1,000 ft, so at 5,000 ft the standard temperature is 5.1 °C and the standard density ratio is 0.86167.

Density altitude is the altitude in the standard atmosphere with the same density as the air you are actually in. On a standard day it equals the pressure altitude. When the temperature is above standard the air is thinner, the density altitude rises, and the aircraft performs as if it were at a higher altitude than the altimeter says.

This tool uses the troposphere model, so it is valid up to about 11,000 m, where the standard atmosphere stops bending the way the formula assumes. It also assumes dry air, and it treats indicated airspeed as equivalent airspeed, so instrument, position and compressibility errors are not part of the answer.

How to use

Pick imperial or metric units.
Enter the indicated airspeed from the airspeed indicator.
Enter the pressure altitude, which is the altitude set in the altimeter.
Enter the outside air temperature.
Read the true airspeed, which is the speed of the aircraft through the air mass.
Check the density altitude against the height of the obstacles, because a high density altitude means a longer takeoff roll and a poorer climb.

Formula

True airspeed = indicated airspeed / sqrt(sigma). Sigma = (1 - 0.0065 x h / 288.15)^5.2559 x 288.15 / T, with h in metres, T in kelvin and 288.15 K the standard sea level temperature. Density altitude = (288.15 / 0.0065) x (1 - sigma^(1/4.2559)).

IAS: Indicated airspeed read from the instrument.
TAS: True airspeed, the speed through the air mass.
sigma: Density ratio, the density of the air at the conditions divided by 1.225 kg per cubic meter.
h: Pressure altitude in metres.
T: Outside air temperature in kelvin.
DA: Density altitude, the altitude in standard air with the same density.

The constants are the standard atmosphere values: 288.15 K, 1013.25 hPa and 1.225 kg per cubic meter at sea level, with the troposphere temperature falling 0.0065 K per metre. The relation between true and equivalent airspeed is exact for the low speeds of a light aircraft, and the approximation gets worse above about 10,000 feet where compressibility starts to matter, which is why a high speed aircraft also needs a compressibility correction.

Worked example

Example: 100 kt at 5,000 ft with 15 °C outside

Defaults: imperial units, 100 kt indicated, 5,000 ft pressure altitude and 59 °F, which is 15 °C.

Pressure altitude in metres: 5,000 x 0.3048 = 1,524 m.
Standard temperature at that height: 288.15 - 0.0065 x 1,524 = 278.24 K, which is 5.1 °C.
Actual temperature: 15 °C = 288.15 K, so the temperature ratio is 1.
Pressure ratio: (1 - 0.0065 x 1,524 / 288.15)^5.2559 = 0.83205, which is the density ratio.
True airspeed: 100 / sqrt(0.83205) = 109.6 kt.
Density altitude: 1,874 m, which is 6,150 ft, about 1,150 ft above the pressure altitude.
The tool shows 109.6 kt, 6,150 ft, a density ratio of 0.83205 and a deviation of +9.9 degrees C.

Reference table

What 100 kt of indicated airspeed is worth on a standard day
Pressure altitude	Standard temperature	Density ratio	True airspeed
0 ft	15.0 °C	1.00000	100.0 kt
2,000 ft	11.0 °C	0.94277	103.0 kt
5,000 ft	5.1 °C	0.86167	107.7 kt
8,000 ft	-0.8 °C	0.78602	112.8 kt
10,000 ft	-4.8 °C	0.73848	116.4 kt
15,000 ft	-14.7 °C	0.62924	126.1 kt

Limits

Uses the troposphere model, so it does not cover the tropopause or the stratosphere above about 11,000 m.
Assumes dry air, so humid air is treated as if it had the same density as dry air.
Treats indicated airspeed as equivalent airspeed, so instrument, position and compressibility errors are not included.
Ignores wind, which changes the groundspeed but not the true airspeed.

Common mistakes

Using the true airspeed as if it were the indicated airspeed in a performance calculation, which reverses the error.
Entering the outside temperature in Fahrenheit without converting, which throws the density ratio off badly.
Using the geometric altitude instead of the pressure altitude, which differ whenever the altimeter is not set to standard.
Forgetting that a warm day raises the density altitude as well as the true airspeed.
Assuming the 2% per 1,000 ft rule of thumb is exact, since it ignores the temperature.

Try it yourself

Quick checks. Answers sit tucked under each question.

An aircraft cruises at 120 kt indicated at 3,000 ft on a standard day. What is the true airspeed?

At 3,000 ft the standard temperature is 9.1 °C and the density ratio is 0.91512, so the true airspeed is 120 / sqrt(0.91512) = 125.4 kt.

At 5,000 ft with 25 °C, what does 100 kt of indicated airspeed read as?

The density ratio falls to 0.80414, so the true airspeed is 100 / sqrt(0.80414) = 111.5 kt, and the density altitude rises to 7,262 ft.

What is the true airspeed on a standard day at sea level?

Exactly the indicated airspeed, because the density ratio is 1. At 100 kt indicated the true airspeed is 100.0 kt and the density altitude is 0 ft.

Questions

What is the difference between indicated and true airspeed?

The indicated number comes from an instrument that reacts to air pressure, so it changes with density. The true number is the actual speed through the air, and it grows as the air thins with altitude and heat.

Why does the FAA handbook mention adding 2% per 1,000 feet?

That is a rule of thumb for mental maths that assumes standard temperature. The calculator does the real density calculation, which also accounts for the temperature, and the two agree closely on a standard day.

What is density altitude used for?

Performance planning. A high density altitude means a longer takeoff roll, a weaker climb and a longer landing roll, because the wings and the propeller have less air to work with.

Does humidity change the answer?

Slightly. Humid air is less dense than dry air at the same temperature, so a humid day gives a slightly lower density ratio and a slightly lower true airspeed than this dry air model shows.

Can I use this above 11,000 m?

Not with confidence. The standard atmosphere changes shape above the tropopause, and the temperature stops falling at the same rate, so the formula in this page no longer describes the air.

What about groundspeed?

Groundspeed is true airspeed plus or minus the wind component along the track. The wind does not change the true airspeed, it changes how fast you cover the ground.

Sources

How this page was checked. The formula above was matched against the cited sources, and the worked example was run through the tool on this page before publishing. If you spot an error, contact us so we can fix it and note the correction.