When will the value of indicated airspeed equal the aircraft's true airspeed?

The value of indicated airspeed equals true airspeed when the air density at the aircraft’s altitude is equal to that at sea level, particularly under standard atmospheric conditions.

Indicated airspeed is derived from the measurement of dynamic pressure, which is influenced by the surrounding air density. True airspeed accounts for the actual velocity of the aircraft through the air, adjusting for the effects of pressure and temperature changes with altitude. When air density at altitude matches that at sea level, the correction factors for air density disappear, and both indicated airspeed and true airspeed present the same numerical value.

At altitudes where air density is equal to sea level standards, the computed values from instruments reflect actual performance without the need for any adjustments. Under any conditions other than this, variations in density due to altitude would lead to a difference between indicated airspeed and true airspeed. Thus, the condition of matching air densities is crucial for these two speeds to align numerically.