How do I figure out how long the PVC needs to be?

I'll be making my first SFG this Spring and I'm figuring out the supplies I'll need. But I'm stuck trying to figure out how long the PVC pipes need to be to construct a hoop house over a 3 x 4 TT.

Is there a formula for figuring out how long they need to be if I want the hoop to be 4", or 6", or 12", etc., high?

I know someone out there can steer me to the correct math, and I thank you (ALL!!!) in advance!!!

I believe flexible PVC conduit comes in 10 foot lengths.
If it was me I would bring some home, stick one end into the box and just eyeball how tall I want. Draw a line on the pipe and cut it with a hack saw. Then cut the next one the same length.
Sorry, I cannot help with the math part,

Saw a film on GardenFork.TV and the final tally was for 10' lengths for a 4' wide bed. He clamped them along the inside of the lumber.

This guy, Eric Rochow, makes films on everything he tries and its fun to watch because he leaves in the errors and takes corrections from his wife during the video and you see his labradors retrievers at play all the time. Those dogs never rest. He has some good ideas though.

There's really no need to bother with fancy smancy formulas unless you really want to. PVC pipes won't bend alike anyway.
Simply get a piece 10' or 12' piece lay it on the ground or garage floor and bend it to the arc you need and mark a few pencil marks at the desired locations for the width and the height.
It's easy to use a cement wall to push against with one end of the PVC pipe to make the arc. Just be careful about the built up tension in the bending pipe should you loose you grip. Don't forget to add for some extra width. I have the width of my hoops to about 5 feet for a 4 foot wide box. The reasons for this is sometimes I add a few 1 gallons jugs of water to the inside of the hoop house for a little heat and it give the plants on the edges of the grow box a little extra room . Before you go and cut them all to length try one to see how it looks then you'll know for sure .Once you have the length you like it's easy to cut to all the same length with a wood saw. I use 3/4" PVC . Also it's important to secure the ends of the pipe with 1/2" diameter re-bar metal rods. I use 2' lengths , drive 1 foot into the ground and insert the PVC pipe into it.
Very Easy...

It's best to hold the tubes in a warm place for 24 hrs before you try and bend them for if they are cold they often collapse .

I used some stick that went inside the pipe and made a sort of bow ....as in bow an arrow .
Every now and again I shortened bow the string to get the arc of the bow sharper and as it was chuffing cold outside I did it inside where it was nice and warm

Unfortunately, the math sucks for ovals/ellipses. A rough estimate is as follows:

(I'm much too lazy to try to figure out how to type all those symbols and meanwhile make the equation look readable)

That the equation for the circumference of an ellipse with about a 5% margin of error - a & b are the width and height. Order doesn't matter. You'll want to chop that number in half and you probably don't want to see the real equation.

Assuming you want the hoops going across the 3' sides, here are some numbers using that formula:
3" - 6.6ft
6" - 6.7ft
1' - 7ft
2' - 8ft
4' - 11.2ft
6' - 14.9ft

Use these to gauge how much tubing you'll need, then use the eyeball method to decide where to cut.

For the extremely nerdy reply, see:

http://en.wikipedia.org/wiki/Catenary

Nothing I'll ever be able to figure out, but it's fun to look.

even the 1/2" low pressure PVC is not as bendy as you are thinking... I have a 4x4 and ended up crisscrossing 10ft sections - I tried to do 8 foot sections, but it put too much tension on the corners. The height at the center of beds is probably like 4ft tall....

you could try to build a 4 ft sq top our of 4 4ft sections with 3 way corner pieces and then you could put the length leg on it that you want... would also collapse down well for off season storage... hmmmm......

it was chuffing cold outside

This does not help the OP whatsoever but Plantoid I am at that comment.

Have not heard that one since living back in blighty.

You have a lot of stuff in here by members already. I would only add that the Gardenfork guy does a little math in the episode where he builds a hoophouse with a vent in it. He writes the math right there on the wood...lol.

Here....he starts the math at the 3 minute 12 second mark. https://www.youtube.com/watch?v=v6bWeYCV53A&feature=fvst

I watched the video following the video with the math in it by the gardenfork guy. He said in the next video that his math was wrong in the video about the vented hoop house. I don't know if he meant his formula or the way he applied the formula.

Gardenfork meant his original math on how to get there was wrong and that the 10' length worked for him.

just a tidbit...

page 74 of the ANSFG, Mel says:

"The arch over a four foot span has to be more than 5 feet long."

The width of the plastic covering should also be part of determining the length of the PVC. For instance, if you use a 10 foot length PVC over the top of the bed, then a 10 foot wide piece of plastic does not leave enough plastic on each side to weigh the edges of the plastic down. Next time I am going to cut the PVC down to at least 9 feet so I have a little plastic left on each side so I can put something on the plastic to keep the cold out better.