Perimeter, not area
Punching cuts a wall of material whose height is the thickness and whose length is the outline of the hole. That wall is what fails in shear, so the force is perimeter times thickness times shear strength, and the area of the hole never appears. It catches people out because a half inch round hole and a half inch square hole feel like the same job. The round one has a perimeter of 1.571 inches, the square one has 2.000, so the square costs 27 percent more force for the same nominal size.
The practical consequence is that a slotted hole is expensive relative to what it looks like, and that a part with a lot of small holes can need more force than the same part with one large one. Ten quarter inch holes have 7.85 inches of perimeter between them. One two inch hole has 6.28.
| Hole | Perimeter (in) | Force in 0.125 in mild steel at 50,000 psi |
|---|---|---|
| 1/4 in round | 0.785 | 4,909 lb — 2.45 tons |
| 1/2 in round | 1.571 | 9,817 lb — 4.91 tons |
| 1/2 in square | 2.000 | 12,500 lb — 6.25 tons |
| 1/2 x 1 in slot | 2.571 | 16,067 lb — 8.03 tons |
| 1 in round | 3.142 | 19,635 lb — 9.82 tons |
Shear strength is the number to argue about
Everything on this page scales linearly with the shear strength you put in, and it is the figure least likely to be right. Shear strength is not a fixed property of a name like mild steel. It moves with the heat, with how much cold work the sheet has taken, with temper in the case of aluminum, and it drops when the material is warm. The starting figures behind the material selector are the middle of the usual range for the family, offered so the page does something before you have looked anything up. The number that belongs in the field is the one on the supplier data sheet for the material actually on the bench.
If you only have tensile strength to hand, shear strength for most of these materials lands somewhere around two thirds to three quarters of it. That is a relationship worth knowing and not worth trusting to three figures.
Clearance is the whole quality story
Clearance is the gap between punch and die on each side, expressed as a percentage of material thickness. It decides what the hole looks like in section. Too little and the fracture from the punch side and the fracture from the die side do not meet, so the material tears twice and leaves a secondary burnished band with a ragged step between. Too much and the material rolls over the die edge before it cuts, giving a big dished entry and a heavy burr. In between, the two fractures meet cleanly and the hole has one burnished band, one fracture zone and a modest burr.
Because clearance is a percentage of thickness, the absolute gap for thin sheet is tiny. At six percent per side, 22 gauge sheet wants about 0.0018 inches, which is inside the tolerance most people would ignore on a drawing. Thick plate at the same percentage wants ten times that. Getting a clean hole in thin stainless is largely a question of whether the tooling can hold a gap that small.
Which member carries the print size flips depending on what you are keeping. When the hole is the part, the punch sets the size and the die is larger. When the slug is the part, which is blanking, the die sets the size and the punch is smaller. Getting that backwards puts the whole clearance on the wrong side and makes every part a full clearance out of tolerance.
Stripping, rake and where the tonnage really goes
Punching force is the peak on the way down. On the way back up the punch has to be pulled out of a hole that has sprung shut on it, and that stripping force is real work the machine or the stripper spring has to supply. Five to twenty percent of punching force is the range usually quoted, sitting near the bottom for thin sheet with plenty of clearance and near the top for thick, gummy or work-hardening material and for punches that have gone dull.
Rake solves a different problem. Tilt the blade of a shear so that only a short length is cutting at any instant and the peak force stops depending on the length of the cut altogether. It becomes thickness squared times shear strength divided by twice the tangent of the rake angle. A degree and a half of rake on eighth inch plate means about 4.8 inches of blade engaged at once, so a 48 inch cut is made by a machine that only ever cuts 4.8 inches. The bill for that is stroke length and a twist in the offcut, which is why long narrow strips come off a raked shear with a bow in them. Cutting force per foot of cut on a press brake works the other way and is covered by the press brake tonnage calculator.
What this cannot tell you
It gives the demand. It says nothing about supply. Whether a given press, ironworker or turret has the tonnage, whether the tooling is rated for the stroke rate, whether the punch is thick enough not to buckle in a hole smaller than the material, and whether the frame deflects enough to spoil the clearance are all questions for the machine plate, the tooling maker and the manufacturer. A calculated ten tons and a machine plate that says twenty is not an argument that finishes here.
Related material weight and cost work through the metal weight calculator, and the gauge to thickness step through the sheet metal gauge chart.
Questions people ask
What is the formula for punching force?
Force equals the perimeter of the cut multiplied by the material thickness multiplied by the shear strength of the material. In inches and psi that comes out in pounds, and dividing by 2000 gives short tons. There is no shape factor and no allowance for hole size, because the cut is a wall of material whose length is the outline and whose height is the thickness. That is also why a square hole costs more than a round one of the same width: it has more outline.
How much die clearance should I use?
The clearance belongs to the tooling supplier and to the material, and this page takes it as an input rather than handing you one. The general shape of the answer is that clearance is expressed per side as a percentage of thickness, that thin soft material wants less and thick or hard material wants more, and that the consequences of getting it wrong are visible in the hole. A hole with a doubled burnished band and a ragged step in the middle of the wall was cut too tight. A hole with a big rolled entry and a heavy burr was cut too loose.
Why does my punch press struggle on a hole the tonnage says it can do?
Several reasons that the force calculation does not see. A dull punch cuts by tearing rather than shearing and the load climbs. Material that is thicker than nominal, or harder than the family figure, scales the whole answer up. If several punches land on the same stroke the peak is their sum, which is why staggering the punch lengths so they enter at different moments is a standard trick. And the rating on the machine plate is the manufacturer figure for their test conditions; whether it applies to your setup is a question for them, not for arithmetic done here.
How do I work out the weight of the slugs a job drops?
Slug volume is the hole area times the thickness, and weight is that times the density of the alloy. Do it once for one slug and multiply by the number of holes over the whole run. It is worth doing on a job with a lot of piercing, because the scrap can be a surprising fraction of the sheet you bought and because the slugs have to physically go somewhere. A turret punching a few thousand quarter inch holes fills a drum, and the drum has to be emptied before it jams the machine.
Is there a minimum hole size for punching?
There is, and it comes from the punch maker rather than from this calculation. The limit is not the force but the punch itself, which acts as a slender column under the punching load and buckles if it is too thin for the thickness it is going through. Punch manufacturers publish minimum diameter against material thickness for each of their punch materials and coatings, and those figures differ enough between suppliers that quoting a general rule here would be misleading. Below the published minimum the usual answers are drilling, or a laser or plasma cut.