How this instrument works
True airspeed (TAS) is how fast an aircraft actually moves through the surrounding air mass, distinct from what the airspeed indicator shows in the cockpit. The gauge measures dynamic pressure — the force of air ramming into the pitot tube — and that pressure depends on both speed and air density. Calibrated airspeed (CAS) is that pressure reading translated into a speed using sea-level standard density, 1.225 kg/m³, regardless of how thin the actual air happens to be.
Divide CAS by the square root of the air density ratio, ρ ⁄ ρ₀, and the sea-level assumption falls away, leaving the true speed. A square root, not a plain ratio, appears because dynamic pressure scales with density times velocity squared: to hold that pressure fixed while density drops, velocity must climb by the inverse square root of the same factor. Climb into thinner air and the correction grows — a 250-knot CAS at a density ratio of 0.7385 becomes nearly 291 knots true.
The formula assumes incompressible flow, which holds well for propeller aircraft and most light-jet cruise speeds but breaks down as true airspeed approaches the transonic range, where air compresses ahead of the pitot tube and skews the pressure reading. It also has nothing to say about wind: true airspeed is a property of the aircraft relative to the air mass, and converting it to a groundspeed or a heading correction is a separate step that needs the wind vector as well.
- Enter Calibrated airspeed (CAS) — the indicated reading after correcting for instrument and position error, not the raw needle value.
- Enter the Air density ratio (ρ ⁄ ρ₀) for your altitude, pulled from a standard atmosphere table or your aircraft's performance charts.
- Read True airspeed (TAS), the aircraft's actual speed through the air mass at that altitude and density.
- Switch the CAS or TAS unit menu between knots and mph to match your flight plan or logbook.
Worked example — 250 knots CAS at 10,000 feet
A pilot levels off at 10,000 feet on a standard day, where the air density ratio ρ ⁄ ρ₀ works out to about 0.7385 — roughly three-quarters of the density at sea level. The airspeed indicator, already corrected for instrument and position error, reads a calibrated airspeed of 250 kn. Dividing by the square root of the density ratio: TAS = 250 ⁄ √0.7385 = 250 ⁄ 0.8594 ≈ 290.9 kn.
That 40.9-knot gap between CAS and TAS is not instrument error, it is the physics of thin air: at 10,000 feet the aircraft must move through the air markedly faster to generate the same dynamic pressure that a sea-level flight produces at 250 kn. Planning a three-hour cruise leg on the indicated 250 kn instead of the true 290.9 kn would understate the distance covered by well over a hundred nautical miles, which is exactly the error a proper flight-planning correction exists to catch.
Questions
Why is true airspeed higher than calibrated airspeed at altitude?
Because the airspeed indicator senses dynamic pressure, not actual speed, and dynamic pressure depends on air density as well as velocity. As density falls with altitude, the aircraft must move faster through the thinner air to produce the same pressure reading. At 10,000 feet, where the density ratio is about 0.7385, a 250-knot CAS corresponds to roughly 291 knots true — the aircraft is genuinely covering more distance through the air than the indicated speed alone suggests.
What's the difference between CAS and raw indicated airspeed?
Indicated airspeed (IAS) is the unadjusted needle reading; calibrated airspeed (CAS) is IAS corrected for instrument error and pitot-static position error, which changes with aircraft attitude and configuration. Most flight manuals include an IAS-to-CAS correction table or graph near the airspeed limitations section. Enter that corrected figure here — feeding in raw IAS carries an uncorrected error straight through the density calculation and into the true airspeed result.
Where do I find the air density ratio for a given altitude?
From a standard atmosphere table, an electronic flight computer, or the performance charts in the aircraft's flight manual, all of which tabulate ρ ⁄ ρ₀ against altitude and temperature. On a standard ISA day at 10,000 feet it is about 0.7385; on a hotter day at the same pressure altitude it will be lower still, because air density falls as temperature rises even when pressure altitude has not changed — density altitude, not pressure altitude alone, sets this ratio.
Is true airspeed the same thing as groundspeed?
No. True airspeed is the aircraft's speed relative to the surrounding air mass; groundspeed is its speed relative to the ground, and the two differ by whatever the wind is doing. Groundspeed comes from adding a wind vector to the true airspeed vector, a separate step this instrument does not perform. TAS is an input to that wind-correction calculation, not a substitute for it.
Does this formula hold at jet cruise speeds?
Not precisely once true airspeed climbs past roughly 250 to 300 knots or the aircraft nears the tropopause, because the formula assumes incompressible airflow. At higher Mach numbers, air compresses ahead of the pitot tube and the pressure reading runs higher than incompressible theory predicts, so the CAS-to-TAS conversion needs an added compressibility correction. Piston and light turboprop cruise speeds sit comfortably inside the range where the plain square-root relationship holds.
Why does the formula use a square root instead of the density ratio directly?
Because dynamic pressure, the quantity the pitot-static system actually senses, is proportional to density multiplied by velocity squared, not to velocity alone. Holding that pressure fixed while density falls means velocity has to scale by the inverse square root of the density ratio to keep the product constant. That is why a fairly large density change, like the 0.7385 ratio at 10,000 feet, produces a comparatively modest correction of about 16 percent rather than a one-for-one jump.