I have not looked at their site lately but in the past they would first ask the to and from zips and then (in some order) would ask the weight and the dimensions of your box. Then you would get to the rate page where they would list rates for flat rate and also for your dimension box. The rate is the same for all boxes between 1 and 2 pounds that go to the same zone as long as the box size is within or below the 12x12x12 total inches size. Make sure you choose that you have a box/package and not an envelope.
I was able to get a results for 3rd day priority by using custom size. (You often pay more these days using your own box instead of using the provided boxes and envelopes.) When you go to USPS choose Mail and ship, then Calculate a price. Add your details then click on Calculate based on size/shape. Add the weight and then click on Package or Large package...continue through to the end. The 3rd day non flat rate rate was the second result in the list. For the specs I added it was 42$ vs 20$ for 3rd day Large flat rate box. (The first result in the list was for 2nd day priority express non flate rate at 111$)