Need a Formula
How do I figure out gpm with pressure? How do I set this formula up?

The simplest way is to check tables for pipe flow. The actual mathematics to compute the flow through a pipe or out of a nozzle is too complex to present in a post like this. If you wish to pursue the math angle, check on the web for "orifice flow" and "pipe flow". You will find that the flow through a pipe depends on the diameter of the pipe, roughness of the pipe, length of the pipe, and head loss through the pipe. Computation of head loss is the most difficult, requiring careful mathematical computation, unless of course you use tables.

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Bucket test. put 1 gallon bucket under pipe, turn on valve. Time until bucket is full

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Do search for HazenWilliams.
Why do you need this information. What is your project? You are not doing calcs for a fire sprinkler system, fire sprinklers do not use 1/2 pipe. Is this for a potable water supply? If so is this gravity flow or pressure fed? 
A 1/2" bore will discharge 46 GPM at 40 PSI. The 40 PSI is measured at the discharge. How much pressure you need to apply at the source to reach 40 PSI discharge will depend on type of supply piping, length of run, number of fittings, plus or minus elevation, etc.

If you must have a formula, here it is. Manning's equation for flow through an open channel, can also be used for closed pipes.
Q = (1.49/n)*A*R^(2/3)*S^.5 where Q is the flow in cubic feet per second, n is Manning's n (the roughness coefficient), A is the area of the pipe in square feet, R is the hydraulic radius of the pipe, and S is the slope of the hydraulic grade line. If some of these terms are unfamiliar to you, you can Google them and learn all about hydraulics.When used with a closed pipe, the slope of the hydraulic grade line is measured as the total head loss in feet divided by the length of the pipe in feet. 
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