Flight Level represents the pressure altitude in hundreds of 100 feet.
So FL = Pressure altitude / 100.
So FL 300 = 30000 ft / 100, FL 10 = 1000 ft /100, and FL 0 = 0 ft / 100.
In the ISA the temperature decreases by approximately 2 degrees C per 1000 ft.
This means that for every increase of 10 in FL the temperature decreases by 2 degrees C.
So if we divide the FL by 10 then multiply by 2, we get the amount by which the local temperature is lower than ISA msl.
But at ISA msl the temperature is +15 degrees C, so we can predict the temperature (OAT) at any given FL by taking +15 and subtracting ((FL/10)x2)
This gives the equation OAT (at any given FL in the ISA) = +15 -((FL/10)x 2)
So for example we can predict that at 36000 ft (FL 360) in the ISA
The OAT = +15 -((36 / 100 x 2)
which is OAT = +15 -(36 x 2)
This is OAT at 36000 ft ISA = +15 - 72= -57
THIS CAN ALSO BE USED TO CALCULATE THE FL GIVEN THE OAT.
The equation OAT = +15 -((FL/10) x 2) can be rearranged to give the following:
(OAT -15) / 2 = -FL/10 So FL = 10(15 - OAT)/2) Or FL = 5(15 - OAT)
For example if the OAT is known to be -35 degrees C in the ISA then
FL = 5(15 -(-35))
Which is FL = 5(50) = 250.
So in the ISA if the OAT is -35 then the FL = 250
ACCOUNTING FOR TEMPERATURE DEVIATION
The actual OAT at msl in a real (non ISA) atmosphere is 15 degrees C plus the temperature deviation (Tdev).
Our original equation can therefore be adapted to non ISA conditions by adding Tdev to give the following.
OAT = (+15 + Tdev) - ((FL/10) x 2)
For example if the temperature deviation is known to be plus 2 then:
At msl (FL 0) the OAT = (+15 +2) - ((0/10) x 2) which is 17 degrees C.
And OAT at FL360 = (+15 +2) - ((360/10) x 2) which is - 55 degrees C.
This method can also be applied to give the following equations which take Tdev into account:
At any given OAT, the FL = 5(+15+Tdev - OAT)
and
At any given flight level the OAT = +15+Tdev - ((FL/5)