What size chain is typically used when hanging a porch swing?
A standard double loop chain is often used for porch swings. 

Assuming three hefty occupants (~250 lbs each) and a 100 lb swing, you're up to a load of 850 lbs. If you use 4 lengths of chain to connect the swing, that's 212.5 lbs per chain. So you need at least 2/0 chain, which is rated to a working load of 255 lbs and an UTS of 1020 lbs.

EDIT: If you're a nerd/engineer like me, you can get more technical and take into account angle of the chains from vertical and normal acceleration from swinging. Then your equation comes to:

4*T*cos(Θ)-m*g=m*a where a=v^2/(l*cos(Θ))


or

T=m*((v^2/(l*cos(Θ)))+g)/(4*cos(Θ))


where 

T is the tension per chain length using a total of 4 chains,
m is the total mass of the system,
a is normal acceleration, 
l is the chain length, 
v is maximum horizontal velocity you'll be reaching, and
Θ is the angle of the chains from the vertical 


which will be a bit more than 255 lbs if you're swinging very fast, or have very short chains or a very wide swing. In that case, you may want to go with 3/0 chain.

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