Conduit fill calculations live in Chapter 9 of the NEC, specifically Tables 1 through 4, and Annex C if you want pre-calculated fill tables. The basic rule: you can fill a conduit to 40% of its cross-sectional area when running 3 or more conductors (53% for 1 conductor, 31% for 2). Chapter 9, Table 1 gives you the percentages; Table 4 gives you the conduit area; Table 5 gives you the conductor area.
The math: add up the cross-sectional areas of all your conductors (from Table 5), then check that against 40% of the conduit’s total area (from Table 4). If you’re under 40%, you’re good. If not, go up a conduit size. Annex C tables do this math for you for common scenarios, but only for single-size conductors. Mixed sizes, you do it by hand.
Pro tip: when you’re mixing conductors of different sizes in a conduit, add 15-20% to your calculated fill to account for real-world jamming issues, especially on long runs. The code number is theoretical; the actual pull is not. A conduit at 38% fill with mixed wire sizes is a nightmare pull compared to a uniform fill at 40%.