To find out how long the rod has to be, you need to draw a sketch of the star arch, according to the size you want it to be.
You can either draw it in real size (for example on your drive way), or a proportionately smaller one on a piece of paper.
Then take the measures from your sketch, and you'll know how long the rod needs to be.
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Walk Through Arch by: Margit
For a self-supporting walk through arch you will need at least 1/2" aluminium rod for the frame. If the frame has to be extra sturdy (e.g. for outdoor arches), I would even recommend using 1/2" conduit. It's more difficult to work with, but it will give your arch the sturdyness it needs.