How do I calculate density altitude by hand? I've seen the following equation for calculating density altitude on a dozen websites:

[ (OAT - ISA) * 120 ] + Pressure Altitude.


But it was never very clear what the units of measurement are supposed to be.

Question 1: Are OAT and ISA in Celsius?

Question 2:
So for example, if current true altitude is 6000 feet above sea level then:
ISA = 15 + (-2C * 6) because for each 1000 feet we lose 2 Celsius. Does this mean to make this calculation I just substitute field elevation for true altitude? So ISA is equal to 3.

If the outside air temp is 10C, then we have 10 - 3 = 7 multiplied by 120 = 840.

Question 3:
Pressure altitude confuses me a little bit, I read that it is the altimeter reading when the Kollsman window is set to 29.92" hg. So let's say I'm sitting in my airplane on the runway, I set my altimeter to 29.92 and it reads 6200 feet. In this case my final equation would be: 840 + 6200 = 7040 feet density altitude. 

What happens if I don't have access to my plane's barometer, is there another way to calculate pressure altitude?

Question 4:
How does this all change if I'm trying to figure out density altitude while flying the plane? OAT is the air around the plane. What about ISA? Do I calculate pressure altitude by resetting my Kollsman window in the middle of the flight to 29.92" hg? Is it normal to try to figure out density altitude while up in the air?

Question 5:
Does this entire equation change or become meaningless above a certain altitude threshold, such as 10,000 feet above sea level?
Density altitude is a value that directly correlates aircraft performance to atmospheric conditions.


  Density altitude is pressure altitude corrected for non-standard temperature.


Almost all temperatures in aviation is Celsius including this formula.



You will notice that all aircraft performance calculations require pressure altitude and temperature and in effect is calculating density altitude.

To calculate pressure altitude you will calculate 
$$ \left( 29.92 - \frac{\mathrm{current~altimeter~setting}}{\mathrm{inHg}} \right) \cdot 1000 \, \mathrm{ft} + \mathrm{current~field~elevation}$$

For example if the current altimeter is $30.12 \, \mathrm{inHg}$ and you are $ 6,400 \, \mathrm{ft} $ MSL, the pressure altitude is
$$ \left( 29.92 - 30.12 \right) \cdot 1000 \, \mathrm{ft} + 6,400 \, \mathrm{ft} = 6,200 \, \mathrm{ft}$$
pressure altitude.



Your formula to calculate density altitude is correct but is never required to be known to calculate aircraft performance as the "calculation" is being done in the background of the performance charts.

To calculate density altitude, you must first calculate pressure altitude and then apply it to your formula.

If you are at 10°C at $6400 \, \mathrm{ft}$ MSL with an altimeter setting of $30.12 \, \mathrm{inHg}$:
$$(10-2.6) \cdot 120 \, \mathrm{ft} + 6,200 \, \mathrm{ft} = 7,088 \, \mathrm{ft}$$ density altitude



I have never calculated density altitude once I got into the air.  I have calculated density altitude while determining if its a good idea to takeoff.  In higher elevation airports on a warm day, the airplane may not get out of ground effect due to the density altitude.

The formula for density altitude above is correct for any altitude, albeit a more simplistic formula.  Humidity also has an effect of density altitude and there are formulas that take humidity into account when calculating density altitude.