Both can be correct.
At 1/4 inch per foot of drop you are going to feel the slope, but at only 12 feet of run, it is not going to 'read' that much.
If you are using a material that has a lot of cleft ( irregular stone face cut ) a 1/4 inch per foot may be just the right amount of slope to adequately move the surface water in the prescribed direction.
If you have a nice clean smooth texture then 1/8 per foot of slope is perfectly fine.

There are a variety of other reasons why one might want to use 1/4 inch vs 1/8 inch such a soil composition, climate, location of patio, surface materials....
In your situation, with this limited amount of information, it looks like 1/8 might work just fine.

You can always split the difference and go 3/16 .

An illustration of the explanation... downward pitch is to the left. The smooth paving drains completely at slight pitch. At the same pitch, water catches in the surface imperfections of the textured paving. It would need to be pitched more to drain completely.

{{gwi:18812}}

Thanks for the info. I planned on getting a textured tile so I guess I'll be going with the 1/4".

At a 1/4" per foot grade there should be a 3" difference from one end to the other. Do I start the grading at the gravel base and make sand layer follow the same grading? Also, since the patio won't be touching the house, do I need to account for the grading when digging the site so there isn't one side that has the pavers 3" above ground or 3" below?

Do I start the grading at the gravel base and make sand layer follow the same grading? - yes.

do I need to account for the grading when digging the site so there isn't one side that has the pavers 3" above ground or 3" below? - yes.

we always start figuring out how to set the grade by noting the FF height ( finished floor ) at the house and then depending on the local code ( in my area there are two distinctly sets of written code covering this issue - the city is at odds with the county - keeps life interesting ) we figure the required code compliance of threshold drop and set our top grade at that point.

This is where grading and drainage converge and each solution is specifically designed to the site .

Find your FF.and mark it on an outside stake .
Research code for your threshold drop .
Set that elevation with a stake and string line.
Measure and appropriate slope along with any paths to the patio with stake and string line.
Do the same for your patio.
Lay it all out with stakes and string and if grade keeps you from laying it out due to topo, then do the math calculations on paper.
This will inform you how deep you will have to excavate and slope for proper drainage.

acharles, how thick are the "tiles"? For setting on sand, you need something that is brick thickness. So called 'patio tiles' do not hold up that well over the long haul. How do you plan to compact them on the sand layer?

I was looking to get 16" x 16"concrete stones. They are 2" thick. I was going to use a rubber hammer to level and tap the stones in place.

If you're talking about the standard big box patio "tiles" I'd bet the actual measurement is slightly less than 2" thickness. People make patios out of these tiles all the time, but don't expect them to stay "perfect" for too long. They will settle unevenly. Tapping them in with a rubber mallet is not sufficient to compact the sand tightly and "lock" the tiles in place. Over time, they'll tip various ways making your 1/8" or 1/4" pitch-to-drain a moot point. Concrete pavers would be a better solution (of the many available.)

We've set plenty of 1.5 - 2"' thick concrete tiles/ pavers on a compacted class II base with a leveling bed of sand and have had excellent luck. Run a viberplate over the pavers and you'll have good success. ( we place a piece of old carpet over the tiles and then run the viberplate over the carpet/ pavers )
If you have freeze/ thaw buckling, then pull out the paver in the summer and excavate into the scree and reset the paver.
{{gwi:18814}}From Before and After Projects

{{gwi:18816}}From Before and After Projects
{{gwi:18817}}From Paths
{{gwi:18818}}From Paths

The standard residential paver is 2 1/2" thickness. (Same as what's shown in photo above.) And true, compacting pavers with a machine will make a huge difference. A rubber mallet cannot achieve that.

I was looking to get these for the patio, OldCastle Pinnacle.

Thanks for the carpet suggestion. I thought of getting a compactor but I didn't want to cause any damage.

acharles,
Looks like a nice pattern. The old carpet trick works well with a variety of stones, bricks and pavers of various thicknesses.

Enjoy the building of your project, and if you have a chance post us some photos of your finished project.