The Calibrated Air Speed (CAS) is obtained from the Indicated Air Speed (IAS) correcting the latter for position, instrument and manoeuvre errors. The aircraft manual usually contains the information which allows to obtain CAS from IAS since the errors mentioned above are very much aircraft specific.
The Equivalent Air Speed (EAS) can be derived from CAS accounting for the air compressibility. For speeds up to 1/3 of the local speed of sound, air compressibility can be neglected and EAS ≈ CAS.
The True Air Speed (TAS) can be determined from EAS by considering the effect of the air density.
The Mach number is equal to the TAS divided by the local speed of sound.
The mobile application allows you to calculate the various airspeeds for a given altitude. Have fun!