You are all providing interesting rules of thumb, but there are a lot of factors involved to come up with an accurate answer for all speeds and altitudes. As someone else mentioned, use an E6B. Here is the correct method found on this website of aviation formulas:
Mach numbers, true vs calibrated airspeeds etc.
Mach Number (M) = TAS/CS
CS = sound speed= 38.967854*sqrt(T+273.15) where T is the OAT in celsius.
TAS is true airspeed in knots.
Because of compressibility, the measured IAT (indicated air temperature) is higher than the actual true OAT. Approximately:
The recovery factor K, depends on installation, and is usually in the range 0.95 to 1.0, but can be as low as 0.7. Temperatures are Celsius, TAS in knots.
OAT = (IAT + 273.15) / (1 + 0.2*K*M^2) - 273.15
The airspeed indicator measures the differential pressure, DP, between the pitot tube and the static port, the resulting indicated airspeed (IAS), when corrected for calibration and installation error is called "calibrated airspeed" (CAS).
For low-speed (M<0.3) airplanes the true airspeed can be obtained from CAS and the density altitude, DA.
TAS = CAS*(rho_0/rho)^0.5=CAS/(1-6.8755856*10^-6 * DA)^2.127940 (DA<36,089.24ft)
Roughly, TAS increases by 1.5% per 1000ft.
When compressibility is taken into account, the calculation of the TAS is more elaborate:
M=(5*( (DP/P+1)^(2/7) -1) )^0.5
P_0 is is (standard) sea-level pressure, CS_0 is the speed of sound at sea-level, CS is the speed of sound at altitude, and P is the pressure at altitude.
These are given by earlier formulae:
P_0= 29.92126 "Hg = 1013.25 mB = 2116.2166 lbs/ft^2
P= P_0*(1-6.8755856*10^-6*PA)^5.2558797, pressure altitude, PA<36,089.24ft
CS= 38.967854*sqrt(T+273.15) where T is the (static/true) OAT in Celsius.
[Example: CAS=250 knots, PA=10000ft, IAT=2C, recovery factor=0.8
DP=29.92126*((1+0.2*(250/661.4786)^2)^3.5 -1)= 3.1001 "
P=29.92126*(1-6.8755856*10^-6 *10000)^5.2558797= 20.577 "
M= (5*( (3.1001/20.577 +1)^(2/7) -1) )^0.5= 0.4523 Mach
OAT=(2+273.15)/(1 + 0.2*0.8*0.4523^2) - 273.15= -6.72C
CS= 38.967854*sqrt(-6.7+273.15)=636.08 knots
In the reverse direction, given Mach number M and pressure altitude PA, we can find the IAS with:
ias=661.4786*(5*((1 + x*((1 + M^2/5)^3.5 - 1))^(2/7.) - 1))^0.5
Have fun trying to figure this out!