This process can be broken down into two steps:
1.) Determining the Average Application Rate.
(Hose-end Sprinklers Only)2.) Using catch cans to determine uniformity of sprinkler application.
(Optional for Hose-end Sprinklers, but Required for Underground sprinkler systems)
Step #1 - Determining the Average Application Rate (Required for Hose-end Sprinklers)

This step involves placing your sprinkler
over a know volume container and tracking the time it takes to fill the
container. Repeat this step three times and take an average of your
findings. For our test, it took an average of 30 seconds to
fill this five gallon bucket. That equates to 10 gallons per minute.
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After you know the flow rate of your sprinkler you need to determine the area in which it covers. Run the sprinkler on a concrete or asphalt surface to see the size of the pattern it creates. It is not necessary to place your sprinkler on a concrete or asphalt surface, but it makes it easier to see the extent to which the sprinkler reaches.

After you have wetted the concrete determine
the area that the sprinkler covers.
Circular Patterns:
Measure the distance between the sprinkler
and the edge of the pattern to determine the radius.
Area (ft2) = 3.14 x radius2(ft)
Square patterns:
If your sprinkler makes a square pattern you need to measure the total width and total length to determine the area you sprinkler covers.
Area (ft2) = Length (ft) x Width (ft)
If you know your sprinkler pressure is between 40 - 50 psi the manufactures may have the flow rates and coverage areas already calculated.
Our sprinkler was a circular pattern with a radius of 17 feet. Using the above equation we determined that the area that the sprinkler covered was 907 ft2.
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To get the average application of your sprinkler, use the following formula:
Application Rate (in/hr) = [Flow rate (gpm) / Area covered (ft2)] x 96.26
For our test:
Application Rate (in/hr) = [10 / 907] x 96.26 = 1.06 in/hr
Our sprinkler is applying an average of 1.06 inches per hour over the applied area. Therefore to only apply the required 0.6 inches to fill the soil to satisfy the grass' water requirement, the sprinkler would need to be moved every 37 minutes. This value is obtained by the following formula:
Set time (minutes) = ([0.6 / Application Rate (in/hr)] x 60)/.9
(Note: the .9 is a safety factor to account for the margin of error
when you water your lawn)
This will give you an estimate that you can work with. However, most sprinklers are not uniform in their distribution over the whole area that they cover. Therefore for a more accurate process must be undertaken to greater understand the water distribution of your sprinkler.
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Step #2 - Determining the Distribution Uniformity (Optional for Hose-end sprinklers, but Required for Underground sprinkler systems)
This step will help you better understand the distribution of your sprinkler and more accurately apply only the amount of water that you need. This step will show you how you should overlap your sprinkler between sets in order to get the amount of water needed applied.
As before, set you sprinkler up during
the typical time of day that you will be watering and ideally on a non
windy day. You will need to obtain three to four straight walled
containers such as soup cans to catch water under the sprinkler.
They must be vertical sides without a lip in order to accurately measure
the amount of water the sprinkler is
applying.

Then you will need to place these cups under the sprinkler's pattern at various distances from the sprinkler.

In our test we placed our cans under our sprinkler as the picture below indicates.

Two cans were fairly close to the center of the sprinkler and the other two were placed toward the outer edge of the pattern. We ran our sprinkler initially for a few minutes to determine where the outer reaches of the sprinkler pattern was reaching. After the sprinkler ran for an hour we measured the depth of water in the containers to determine the application rate and distribution of our sprinkler. This process should be repeated up to three times and the results averaged to get the most accurate value.
We found that as expected the sprinkler
did not have a uniform pattern, but looked more
like this side view:

It was applying almost twice as much water at the center as it was at the edges. This is useful when determining how to overlap your sprinkler to get the correct application. Therefore, with a nearly 50% difference between the inside and outside of the pattern roughly 50% will need to be overlapped. However, for application purposes, the inside (or larger value) is used to determine how much water to apply. Our sprinkler was putting out about 1.5 in/hr in the center and .85 in/hr on the outside edge. Therefore with a 50% overlap, the outer portion of the pattern will receive more water than is needed, but this cannot be avoided due to the sprinkler pattern.

The application rate closest to the sprinkler
(1.5 inches per hour), which receives no overlap, is used to determine
the set times.
Set time (minutes) = [0.6 / Application Rate (in/hr)] x 60
So from the formula above, the set time is 24 minutes, to only apply the 0.6 inches needed to bring the root zone back to capacity, while overlapping the sprinkler by 50%.
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Since sprinkler location in an underground system is fixed the catch can method of calibrating your sprinkler is the method that is required for determining your sprinkler output. Distribute cans similar to the ones used in Step #2 of the sprinkler calibration process throughout your lawn. Ideally you are in search of the lowest application area in your lawn. Run your sprinklers during the normal time they will be running and measure the amount that they are applying. Then enter the value directly into the application rate calculator instead of just clicking on it. You do not need to use step one and two, go directly to step three. Make sure to choose the lowest application result as your base for calculations to ensure that you get at least the 0.6 inches on the driest area of your lawn.