Let's break down the pull box calculation for an angle pull and see if your logic holds.

Understanding the Code (NEC - National Electrical Code) 314.28(A)(2) Angle or U Pulls, or Splices

This section covers the requirements for pull boxes used for angle or U pulls. The minimum dimension of the pull box in the direction of the pull must be at least six times the trade diameter of the largest raceway plus the sum of the trade diameters of the other raceways on the same row or same wall.

Your Scenario

You have two 3" conduits entering the pull box for an angle pull.

Calculations


Largest Raceway

The largest raceway is 3".2.

Six Times Largest Raceway

6 3" = 18"3.

Other Raceways on the Same Wall/Row

You have one other 3" conduit on the same wall/row. So, you have 3".4.

Minimum Dimension

18" + 3" = 21"

Therefore, the minimum dimension of the pull box in the direction of the pull must be 21 inches.Your Assumption

Your initial calculation of 13" x 13" is incorrect. You likely were figuring for straight pulls, not the angle pull that is mentioned.16"x16" is too small. You will need a larger pull box to fit this requirement.Selecting a Standard Size

You need at least 21" x 21" inches. Since pull box dimensions are in standard increments, you'd typically round up to the next common size. 24"x24" would be a good choice to exceed the code minimums.

Important Considerations



Trade Size vs. Actual Dimensions

Remember that "3-inch conduit" is a trade size. The actual outside diameter of the conduit will be larger. This is typically already accounted for in the calculations.

Deflection

Always ensure there's enough space within the pull box for proper conductor bending radii as per NEC requirements.*

Working Space

Consider the required working space around the pull box for installation and maintenance.

In Conclusion:

Your calculation of a 13" x 13" pull box is incorrect for an angle pull using (2) 3" conduits. You need at least 21" in the direction of the pull. Rounding up to the next standard size, 24" x 24" is a more appropriate choice. Always consult the NEC and local regulations for specific requirements. Flag for review