Here is a formula (ready?)
Sigma =SQRT(LN(1/(1-EXP(-B24/1000000))^2))-(2.55155+0.802853*SQRT(LN(1/(1-EXP(-B24/1000000))^2))+0.010328*SQRT(LN(1/(1-EXP(-B24/1000000))^2))^2)/(1+1.432788*SQRT(LN(1/(1-EXP(-B24/1000000 ))^2))+0.189269*SQRT(LN(1/(1-EXP(-B24/1000000))^2))^2+0.001308*SQRT(LN(1/(1-EXP(-B24/1000000))^2))^3)+1.5
where B24 is DPMO
This formula is accurate to two decimal places between Sigma = 3.2 - 9.0, and one decimal between 2.5 & 3.2, and shouldn't be used for Sigma < 2.5
If you're using Excel you can use:
Sigma =NORMINV(1-B24/1000000,1.5,1)
The Excel function is accurate to 2 decimal places between Sigma = 1.4 - 5.7, and to 1 decimal place for Sigma = 5.7 - 6.1