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The size of your die will often determine the type of press you will need and the tonnage, but it also determines the ultimate cost per piece of the product you are cutting. In the die cutting world, everything is driven by cost per piece. If you have a press with a 19 x 24 cutting head and you are cutting out 9" circles, you can cut 4 circles with every stroke providing the press is strong enough to cut 4 circles depending on the material you are cutting.
But, it takes nearly the same labor to cut 4 circles with a swing arm press as it does to cut 21 circles with a 30 x 64" Beam Press. Once you have paid for a press, your highest cost will be labor. The more you can cut per stroke the less your cost per piece will be. As a rule, you're always better to buy the biggest press you can afford, which is a onetime purchase, than to bear the expense of labor forever.
Just remember that the larger your die, the more pressure you will need to complete the cut.
This is what causes a lot of uncertainty with prospective buyers. They have no idea how many tons they will need to cut a specific die with a given material. Everyone hopes for a formula so they can measure the linear inches of steel rule and enter in a factor for the material they are cutting. Not quite this simple.
Everything eventually gets down to cost per piece you can live with and the production requirement. IF you can go slow, a smaller press may work, but if you need high output and the cheapest price possible you'll need a larger press and perhaps a full automatic press.
That being said, we're back to the size of your die. First consider the dimensions of the item you are cutting and then determine how many you can get on a die based on the size press that fits your budget.
Swing Arm Presses start between 10 and 27 tons with a cutting head from 11" x 14.5 to 24" x 24".