I recommend vents, low and high. With venting, you shouldn’t need fans.

This sounds like a building code question rather that peoples opinions. While local, I believe the building code requires a certain number square inches of vent for every cubic foot of space. Of course it would all depend on the building code in the area you live.

krnuttle, I live in Silicon Valley, CA. The building codes for storage sheds are: x feet from property lines, x height, x mph roofing material, there are no code requirements for venting storage sheds.

What do you plan to keep in it? Anything temperature or humidity sensitive?

Elmer, there will be some tools, metal, some hardwood, and generic boxed goods from house.

ssewalk1, there will be a ridge vent, but it will vent the air space between the metal roof and the rigid foam. So, you propose to also leave the ridge open towards the inside of shed (by not adding self adhering membrane on the ridge)? I can do that. Would I still need eave vents, even though metal roof will be vented under it?

What I plan looks something like this: https://www.youtube.com/watch?v=DpxLi_Rm30s 

It is an overkill for a shed, but I am testing the theory on the shed before applying it to house.

I watched the video you posted and you're right it would be over kill for a shed. Not to mention expensive. It should work very, very well (how they show in the video). But due to the expense I could almost see people (roofing contractors) modifying the process to reduce costs. This could easily be 3 times the cost of a regular roof, maybe more.

So if not doing it yourself you should keep a close eye on contractors to make sure the roof is installed properly. That vent system they show in the video is a key part to making it work. It would be very tempting for a roofer to skip that part to reduce cost.

Once the roof is on how would you know if the vent system was installed?

So keep that in mind. Also if the metal roof is not sealed properly if the roof leaks you're talking one hell of mess to find a water leak with so many roofing layers. You definitely do not want to hire amateurs I can tell you that much.

In some areas metal roofing may not be allowed due to HOA so you want to consider that too.

Ylm , I reviewed the video , as advised by Austin a rather complex system in the video . I have seen foam applied to the interior surface of roofs by spray method , it works ! I do not like the system the video shows to many areas were a small error can cause extensive failures yrs later , also very costly . Definitely over kill for a simple storage shed . I have built 6 garages over the last 2 summers , all with steel roofs. Will not shingle another roof ever ! lol. For a shed leave the interior open , you can use it for overhead storage . The ridge vent is over 3/4 of the length of the roof line , so no other venting is required . 2 small 6 inch vents could be added on the bottom ends of the structure should any combustibles , paints gasoline or propane be stored within the structure. Eave vents are not mandatory in a cold storage application , however they do enhance the flow of hot air to the ridge vent .