Which is stronger?

[PAmizerman]

Is a 2x12 or a 3x10 stronger as a rafter?

[POSTON WIDEHEAD]

How long of a span?
I would say the 2x12

[Magicman]

I am sure that someone will speak up that has the formula, but personally I would spike together two factory 2X10's (3") to take advantage of the changing grain patterns/slopes.  Whatever I used whether 10's or a 12" they would be grade sawn "jacket" boards.
 
"Magic has a Brand New Sticker" but he has been busy getting ready for Colorado and has not had time to install it yet.  ;D

[CabinCreations]

Based on the second moment of area (moment of inertia), the 2x12 would be a stiffer rafter.

For future reference, the most simple way to compare beam strength is to use the equation b*h^3/12 - where b = the thickness of the beam/rafter and h = the height of the beam/rafter.

[PAmizerman]

20' span 
Thinking 2' centers and a 5/12 pitch with steel roofing

[PAmizerman]

I'm gonna price trusses tomorrow. It may be cheaper

[Magicman]

I figured that the formula would disprove my notion but as mentioned, trusses trump single stick construction.  ;D

[Brad_bb]

Don't forget the proper order of operations (example below):
2x12

2 =b
12=h

I = b*h^3/12
=(2*12^3)/12
=(2*12*12*12)/12
=(3456)/12
=288

[Greyman]

Actually the correct comparison is the section modulus: S = MOI / c, where c is the distance from the centroid to the edge and MOI = bh^3/12 as noted above.

2x12:  S = (2 x 12^3 / 12) / 6 = 48

3x10:  S = (3 x 10^3 / 12) / 5 = 50

Therefore the 3x10 is slightly stronger.  The stress due to bending is f = M / S

Being an aerospace structural engineer comes in handy once in a while...  lol

[Don P]

Which is "stronger" is an interesting question. Often it isn't strength that controls but deflection, stiffness. We do allow twice the deflection in a roof member as compared to a floor.
 
CabinCreations and Brad are describing stiffness where Greyman is describing bending strength. Both are answers to the question.
What Magicman was saying is also correct, you get a 15% bending strength increase by nailing 2 or more pieces together because of distribution of defects, deflection doesn't change.