The equation for the grain size is expressed as the equality: Nm(M/100)^2 = 2^(n-1) where Nm = number of grains per square inch at magnification M. M = Magnification n = ASTM grain size number
Let's solve for n, then substitute the known values and calculate. Nm(M/100)^2 = 2^(n-1)
(log(33) + 2*log(270/100))/log(2) + 1 = n (1.51851394 + 2*0.431363764)/0.301029996 + 1 = n (1.51851394 + 0.862727528)/0.301029996 + 1 = n 2.381241468/0.301029996 + 1 = n 7.910312934 + 1 = n 8.910312934 = n
So the ASTM grain size number is 8.9
If you want to calculate the number of grains per square inch, you'd use the same formula with M equal to 1. So: Nm(M/100)^2 = 2^(n-1) Nm(1/100)^2 = 2^(8.9-1) Nm(1/10000) = 2^7.9 Nm(1/10000) = 238.8564458 Nm = 2388564.458