KCAS/KIAS to KTAS -- how to convert accurately?

[Chr017]

Good morning,

Someone had recommended that I use this formula to convert KCAS/KIAS to KTAS:

https://www.experimentalaircraft.info/flight-planning/aircraft-navigation-speed.php

If you scroll down to "True Airspeed, TAS," you will see this formula:

=KIAS*SQRT(SEA LEVEL AIR DENSITY/AIR DENSITY OF DESIRED ALT)

So, entered into an Excel spreadsheet cell, the formula would look like this:

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=100*SQRT(1.225/0.905)

100 is the KIAS, 1.255 is air density at sea level, and 0.905 is air density at 10,000 feet.

This formula gives us 116 knots for KTAS.
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This formula works for low airspeeds, but as airspeeds get higher, the KTAS that is given is not accurate. As I have learned, this formula does not take into account "compressibility," and therefore the KTAS will not be accurate at higher airspeeds.

I am interested in a formula that I can enter into my Excel spreadsheet that will give an accurate KTAS for all airspeeds up to Mach 3, and altitudes up to 100,000 feet.

Is there one particular formula that will work?

Thank you very much,

Chris