There is no direct conversion because the use of calibers does not measure up to exact sizes such as a .38 spl is actually a .357 caliber. Using the above conversion chart is as close as you can get with a formula , however it is not exactly correct either as a 9mm is actually a .355 caliber, and the conversion states that the bullet would be a .354 with a string of decimal points. Look into your reloading manuals for the best way to find out exactly what each barrel will be... and a hell of a lot easier than using the conversion , even though I use the conversion all the time.
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mm conversion to caliber size
Linear Mode
