What sets the force in a press brake bend
A press brake does not wrap sheet around a punch. In air bending, the only three points touching the metal are the punch nose and the two die shoulders, and the sheet spans between them like a very short beam. That is why the die opening dominates the force: widening the V lengthens the span, and a longer span needs less force to produce the same bending moment.
Four quantities set the tonnage. Thickness enters squared, because the section modulus of the strip goes as the square of thickness — doubling thickness quadruples the force. Bend length enters linearly, since each inch of bend needs the same force per inch. Tensile strength enters linearly, so stainless takes roughly a third more force than mild steel of the same gauge, and 5052 aluminium takes about half. Die opening enters in the denominator.
The number this page returns is what the ram has to deliver. It is not what the machine can safely deliver at every station: a brake rated for 60 tons is rated with the load spread along the bed, and a short bend concentrated at one end of the ram can damage the machine well below the plate rating. Treat the rating as a ceiling that only applies to full-length work, and check your machine's load-distribution chart for short bends.
The formula and where its constant comes from
The working equation is F = 1.42 × UTS × T² × L / V in pounds, divided by 2,000 for short tons. The 1.42 is an empirical coefficient that folds together the geometry of three-point bending, the plastic section modulus of a rectangular strip and the friction at the die shoulders. It is the form used in press brake tooling literature, and it is what tonnage charts are generated from.
You will also see the shorthand tons per foot = 575 × T² / V for mild steel. That is the same equation with the numbers already substituted: 1.42 × UTS × 12 / 2,000 equals 575 when UTS is about 67,500 psi. This calculator defaults mild steel to 65,000 psi, which gives 553 in place of 575 — a 4% difference, and a good illustration of how much the answer depends on an assumed material property rather than on the arithmetic. If your steel certificate quotes a tensile strength, use it.
Two geometry rules travel with the force calculation. The air-bend inside radius is about 16% of the die opening, written here as 0.156 × V; this is why you cannot choose radius and tonnage independently. The minimum flange follows from where the sheet touches the die shoulder: the contact point is V/2 from the centreline horizontally, and the sheet leaves at half the bend angle, so the flange must reach at least (V/2) / cos(A/2) measured along the material. At 90° that is V ÷ √2, or 0.707 × V. Shorter than that and the flange falls into the die instead of resting on the shoulder.
Bottoming and coining are different processes with different force. In bottoming the punch closes the material into the die angle, and in coining it drives into the metal to set the radius by plastic flow. Both need multiples of the air-bend force — commonly quoted as three to five times for bottoming and eight to ten for coining. Those are workshop rules of thumb, not standard values, and this calculator uses 4 and 8. Confirm them against your tooling supplier before running a machine near its rating.
Worked example: a 10 ft bend in 1/4 in mild steel
You need one 90° bend across a 10 ft length of 0.250 in mild steel with a tensile strength of 65,000 psi. Your tooling drawer has a 2 in V-die, which is eight times thickness — the standard starting point.
- Square the thickness. 0.250² = 0.0625 in².
- Multiply the constant by tensile strength. 1.42 × 65,000 = 92,300.
- Apply thickness and length. 92,300 × 0.0625 × 120 = 692,250.
- Divide by the die opening and by 2,000. 692,250 ÷ (2 × 2,000) = 173.06 tons.
- Convert to tons per foot. 173.06 × 12 ÷ 120 = 17.31 tons/ft, which is what a tonnage chart would list for 1/4 in steel in a 2 in die.
- Check the radius you will get. 0.156 × 2 = 0.312 in inside radius, about 1.25 times thickness.
- Check the shortest flange. (2 ÷ 2) ÷ cos(45°) = 1 ÷ 0.7071 = 1.414 in. Any flange shorter than that will not sit on both die shoulders.
A 200 ton brake handles this at 87% of rating, provided the bend is centred. Move to a 3 in die and the force drops to 173.06 × 2/3 = 115.4 tons, but the inside radius grows to 0.468 in and the minimum flange to 2.12 in. That trade — force down, radius and minimum flange up, all in exact proportion to V — is the whole art of die selection.
Air-bend tonnage per foot for mild steel at V = 8 × T
| Material | Thickness (in) | V-die (in) | Tons per foot | Inside radius (in) | Min flange (in) |
|---|---|---|---|---|---|
| 20 ga | 0.0359 | 0.287 | 2.49 | 0.045 | 0.203 |
| 18 ga | 0.0478 | 0.382 | 3.31 | 0.060 | 0.270 |
| 16 ga | 0.0598 | 0.478 | 4.14 | 0.075 | 0.338 |
| 14 ga | 0.0747 | 0.598 | 5.17 | 0.093 | 0.423 |
| 12 ga | 0.1046 | 0.837 | 7.24 | 0.131 | 0.592 |
| 1/8 in | 0.1250 | 1.000 | 8.65 | 0.156 | 0.707 |
| 3/16 in | 0.1875 | 1.500 | 12.98 | 0.234 | 1.061 |
| 1/4 in | 0.2500 | 2.000 | 17.31 | 0.312 | 1.414 |
| 3/8 in | 0.3750 | 3.000 | 25.96 | 0.468 | 2.121 |
| 1/2 in | 0.5000 | 4.000 | 34.61 | 0.624 | 2.828 |
Air bending only, 90 degrees, mild steel at 65 ksi. Multiply by the tensile ratio for other alloys: 85/65 for 304 stainless, 33/65 for 5052 aluminium.
Mistakes that damage tooling or the machine
- Reading a rated tonnage as available everywhere on the bed. Machine ratings assume a distributed load. A short bend at one end of the ram concentrates force into a few inches of frame and can deflect or crack it far below the plate figure.
- Using a die narrower than six thicknesses. Force climbs as 1/V, the sheet marks at the shoulders, and on thick plate the die itself can split. Six to twelve times thickness is the working band.
- Forgetting the material multiplier. Running the mild steel number on 304 stainless understates the force by about 30%, which is enough to stall a brake mid-stroke.
- Applying an air-bend number to a coined bend. Coining can need eight times the force. Tooling rated in tons per inch will fail long before the machine does.
- Ignoring the minimum flange. A flange shorter than (V/2)/cos(A/2) drops into the die, bends unpredictably and can eject. Change to a narrower die or add material and trim after bending.
- Assuming the punch sets the radius. In air bending the radius comes from the die opening. A sharp punch in a 3 in V still produces roughly a 0.47 in inside radius, which changes your flat pattern.
Why typing into the custom tensile field alone changes nothing
The tensile strength that drives the whole calculation comes from the Material dropdown, not from the custom tensile field on its own. The custom box only feeds the formula when Material is set to Custom tensile strength - for every other setting, the dropdown's fixed value is what gets used, and the number sitting in the custom field is ignored, whether or not you have typed something into it.
This produces a specific, silent error: you know your certified tensile strength - say your steel is actually 304 stainless at 85 ksi - so you type 85000 into the custom field, but Material is still showing the default Mild steel (65 ksi UTS) from when the page loaded. The tonnage returned is still built on 65,000 psi, not 85,000. Since force scales linearly with tensile strength, that is a straight (85,000 − 65,000) ÷ 65,000 = 30.8% understatement of the tonnage the bend actually needs - the same ratio the calculator's own aluminium test vector demonstrates in reverse, where switching the preset from 65 ksi to 33 ksi drops the required tonnage by the matching 65/33 factor.
The fix is procedural: always confirm the dropdown reads Custom tensile strength before trusting a typed value, and afterwards check the result against a known point - the reference table above shows 1/4 in mild steel in a 2 in die needing 17.31 tons per foot, so if your material and die match that row and the tonnage does not, the dropdown is the first thing to check.
Tonnage per inch of tooling is a separate limit
Punches and dies carry their own rating, usually quoted in tons per inch of length. A 60 ton bend spread over 48 in is 1.25 tons per inch and harmless; the same 60 tons over 4 in is 15 tons per inch and will crush a standard punch. Check the tooling rating and the machine rating separately, and take the lower of the two.
How tonnage fits with the rest of the bend calculation
Tonnage tells you whether the bend can be made; it does not tell you how long to cut the blank. Once the die opening is chosen, the inside radius follows, and that radius is an input to the bend allowance calculator. Get the sequence right: pick the die from the force and radius you need, read the achievable radius, then compute the allowance. Choosing a radius first and discovering afterwards that no die in the shop produces it is the usual way parts end up mis-sized. For a multi-bend part, carry all of that into the sheet metal flat pattern calculator.
The tensile strength this calculation needs is the same number a materials certificate reports, and it is closely tracked by hardness — the hardness conversion calculator estimates tensile strength from a Brinell or Rockwell reading if you have a hardness tester but no certificate. That is a practical route when a customer supplies unlabelled stock.
Two related limits sit outside this page. The minimum bend radius for an alloy and temper is a formability limit, usually quoted as a multiple of thickness and dependent on whether the bend line runs with or across the rolling direction; exceed it and the outer fibre cracks regardless of available tonnage. And springback, which decides how far past the target angle you must overbend, scales with the ratio of yield strength to elastic modulus — the reason 6061-T6 springs back much more than mild steel of the same thickness. Neither changes the force; both change whether the part is acceptable.
If you are sizing a machine rather than a job, work from the heaviest bend you expect to run, add the tooling limit, and compare with the plate weight of the blanks you will be handling — on heavy plate the handling equipment often becomes the real constraint before the ram does.