SizingKitThe machine, and its die
Press brake tonnage calculator
Air-bending force goes with the square of the thickness and inversely with the die opening, and this page returns it in US tons, kilonewtons and tonnes-force at once, free and with no signup. It runs the calculation twice — the US 575 chart and the metric 1.42 formulation — because the two published coefficients disagree by about 11% and choosing one silently would be the wrong kind of confidence. It also reports what the die you picked does to the part: the inside radius it will produce and the shortest flange it can hold.
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- Tons, kN and tonnes
- Both coefficients shown
- Die effects reported
The bend, and the tooling it runs in
Force goes with the square of thickness and inversely with the die opening, so those two fields matter more than the other four put together.
Squared in the answer, so 5% of error here is 10% of the tonnage.
The rule suggests 1.0000 in for this thickness. Choosing another is fine — it changes the radius as well as the force.
Along the brake. Force is proportional to it, so a full-bed bend is the worst case.
Typical for commercial-quality cold-rolled sheet. Lower than the 60,000 psi the chart assumes, so the chart is conservative here.
Prefilled from the material above and editable. Tonnage scales straight off this: the chart is normalized to 60,000 psi. Real cold-rolled mild steel runs 45,000–60,000 psi and hot-rolled A36 has a 58,000 psi minimum with a 58,000–80,000 psi band, so a chart reading for 'mild steel' can be 25% high or 30% low against the coil actually on the machine. If the mill certificate is to hand, use its number.
The standard air-bend rule for mild steel: the inside radius produced is approximately 16% of the vee die opening, independent of the punch nose radius. Material-dependent and the reason a flat pattern calculated for a nominal radius comes out wrong. Stainless produces a larger radius than mild steel in the same die (commonly quoted near 20–21% for 304) and soft aluminum a smaller one (near 14%). Measure a coupon before committing a production run.
Used only to report a percentage. A brake's rating is for a load spread across the bed; a short bend concentrated in one place can exceed the ram and table limits per inch long before the total is reached.
Start from a gauge number instead
11 ga Steel (uncoated) — Manufacturers' Standard Gauge for Sheet Steel. Manufacturers' Standard Gauge, which defines each gauge number by a weight per square foot and converts it at 41.82 lb/ft² per inch of thickness — the accepted rolling weight of sheet steel. 16 ga is 2.5 lb/ft², hence 2.5 ÷ 41.82 = 0.0598 in. Adopted by the US Bureau of Standards and used for hot- and cold-rolled carbon sheet.
US tons of force
29.9
Kilonewtons · tonnes-force
266 · 27.2
Nothing is binding hard: 8.0× thickness sits inside the range the 8× rule covers, the force is 29.9 tons against 60 available, and the die will give a 0.1600 in inside radius. The flange has to be at least 0.7071 in for the part to stay on the die.
| US chart, tons per foot of bend575 × t² ÷ V, scaled by tensile strength | 7.49 |
|---|---|
| US chart, totaltons per foot × the bend length | 29.9 tons |
| Metric formulation, total1.42 × Rm × t² ÷ V, in newtons per mm, converted back to US tons | 26.6 tons |
| Disagreement between themthe two coefficients are empirical and do not match; size against the higher | 11.1% |
| Die opening as a multiple of thicknessthe rule of thumb is 8× in the middle of the range | 8.0 × t |
| Inside radius this die will producein air bending the opening sets the radius, not the punch nose | 0.1600 in · 4.06 mm |
| Shortest flange this die can hold0.707 × the opening, from the geometry of the shoulders | 0.7071 in · 17.96 mm |
| Share of the machinerating is for a distributed load, not a short bend in one spot | 50% |
The constant of the standard US air-bending tonnage chart, which is normalized to mild steel of 60,000 psi ultimate tensile strength: tons/ft = 575 × thickness² ÷ die opening, in inches. Empirical, and handbooks differ. Metric formulations of the same relation are commonly written F = 1.42 × Rm × t² ÷ V and land some 10–15% below this one for the same bend. Both are estimates of a force that also depends on punch radius, die angle, lubrication and the friction of the material sliding over the die shoulders. Size a machine with margin.
Minimum inside bend radius, before it cracks
The die you picked will produce 1.3× thickness. Anything below the multiple in this table is where the outer fiber runs out of elongation.
| Material | Minimum R | What it does |
|---|---|---|
| Mild steel, cold-rolled (1008/1010) | 0.5–1tthis die clears it | Forgiving. Many shops bend CRS to a sharp 0.5t or even to the tool radius on thin gauge without trouble. |
| Hot-rolled structural steel (A36) | 1.5–2tcheck against this die | Needs a more generous radius than cold-rolled sheet — the mill scale and the coarser grain both promote cracking on the outer fiber. |
| Stainless 304 / 316, annealed | 0.5–1tthis die clears it | Bends readily when annealed, but work-hardens hard while doing it, so springback is large and a second bend in the same place will crack. Cold-worked or 1/4-hard stainless needs 1t–2t. |
| Aluminum 1100-O / 3003-H14 | 0–1tthis die clears it | The most formable common aluminum; thin dead-soft sheet takes a sharp bend. |
| Aluminum 5052-H32 | 0.5–1.5tcheck against this die | The usual choice when a part in aluminum has to be bent — the 5000 series keeps its formability at useful strength. |
| Aluminum 6061-T4 | 1–2tcheck against this die | T4 is the temper to bend 6061 in. Bend in T4, then age to T6 if the strength is needed. |
| Aluminum 6061-T6 | 3–5tcheck against this die | The classic cracked bracket. 6061-T6 has little formability left and cracks on the outside of a tight bend; if the design needs T6 strength and a tight radius, bend it in O or T4 temper and heat-treat afterwards. |
| Aluminum 2024-T3 / 7075-T6 | 4–8tcheck against this die | Aerospace alloys, and effectively not bendable in the hard temper at any radius a shop would want. Formed in O or W temper and aged after. Treat the range as a warning rather than a target. |
| Copper and brass, annealed | 0–0.5tthis die clears it | Very formable annealed. Half-hard and hard tempers need 1t–2t and crack readily along the grain. |
| Titanium, commercially pure | 2–3tcheck against this die | Springs back severely — enough that the bend has to be overbent by a large and material-specific amount, or bent warm. |
Representative minimum inside bend radii as multiples of thickness, consistent with the bend-radius guidance published by the Aluminum Association for the wrought aluminum alloys and with standard sheet-metal practice for the ferrous ones.
Every one of these is a range, and thickness moves it: published bend-radius tables give a larger multiple for thicker sheet of the same alloy and temper, so a figure taken here for 16 ga is optimistic for 1/4 in plate. Grain direction moves it too — bending with the bend line across the rolling direction is easier than along it, and a part with bends in two directions must be laid out to the harder of the two. These are minima for a bend that does not crack, not recommendations: a larger radius is always safer, and the radius the tool actually produces in air bending is set by the die opening rather than by the punch nose.
How to pick a vee die and find out what it costs you
One choice sets three things at once, which is why die selection is the whole job.
Start from the thickness and let the rule suggest an opening
Eight times the material thickness is the middle of the range: a 0.125 in sheet goes into a 1 in vee. Below about a sixteenth the ratio grows — six times is common, and very thin gauge is often run in a fixed small die — and above about a half inch it grows the other way to ten or twelve times, because at eight the force would exceed what the machine or the die can take. Type a thickness and the page prints the opening the rule suggests, then change it if the tooling on hand says otherwise.
Set the material to what is actually on the machine, not to what it is called
Force scales directly with ultimate tensile strength, and the chart is normalized to 60,000 psi. Cold-rolled mild steel typically runs below that and annealed stainless well above it, so the same bend that takes 29.9 tons in 50,000 psi cold-rolled takes 50.9 tons in 85,000 psi stainless. The material picker fills the tensile field with a figure from the governing product specification and then gets out of the way — if you have the mill certificate for the coil, its number beats the table.
Read the two answers, then read what the die did to the part
The US chart and the metric formulation come back about 11% apart, so treat the pair as a band and size the machine against the top of it rather than the middle. Then look further down: the opening you chose also fixed the inside radius the bend will have, near 16% of the opening in mild steel, and the shortest flange the die can hold, which is 0.707 times the opening. Both of those change the flat pattern, and both are easy to discover after the blanks are already cut.
Technical specifications
| US chart evaluated | Tons per foot = 575 × thickness² ÷ die opening, in inches, normalized to mild steel at 60,000 psi ultimate tensile and scaled linearly for anything else. 1/8 in mild steel in a 1 in vee returns 8.98 tons per foot against the 9 the printed chart shows. |
|---|---|
| The second answer, and why it is here | F = 1.42 × Rm × t² ÷ V, in newtons per millimeter with Rm in N/mm². It returns 7.99 tons per foot for the same bend — 11.1% below the US chart. Both coefficients are empirical, neither is derived, and the page prints both rather than picking. |
| Worked example | 0.125 in cold-rolled mild steel at 50,000 psi, 1 in vee, 48 in of bend: 7.49 tons per foot, 29.9 US tons, 266 kN, 27.2 tonnes-force. The metric formulation gives 26.6 tons for the same setup. |
| Die opening rule | 8 × thickness through the middle of the range, roughly 0.050 to 0.500 in; 6 × below that, 10 × or 12 × above it. Prefilled from the thickness and editable, because the tooling you own decides this and not the rule. |
| Radius the opening produces | 16% of the die opening for mild steel, prefilled and editable — near 20 to 21% for 304 stainless and near 14% for soft aluminum. In air bending the punch nose does not set the radius, which is why the number is here at all. |
| Shortest flange the die can hold | 0.707 × the opening, derived from the die geometry rather than quoted: the flange has to still reach the shoulder when it has rotated to 45°. A 1 in vee cannot hold a flange under 0.7071 in, and published shop minimums of 0.7 to 0.75 × V are this figure plus a working margin. |
| Bottoming and coining | Entered as multipliers on the air-bend force, because no standard fixes them and no equation exists. Prefilled at 4 × for bottoming and 7 × for coining, the middles of published bands of 3 to 5 and 5 to 10. A 10 ft bend that takes 74.9 tons in air takes 299 at 4 ×. |
| Where it runs | In this browser tab. Thicknesses, tooling, materials and your machine rating are never uploaded, logged or kept. |
Frequently asked questions
You give me two tonnage figures. Which one do I use?
Treat them as the ends of a band and size the machine against the higher one. The 575 in the US chart and the 1.42 in the metric formulation are both empirical constants that fold die friction, punch radius and the geometry of the bend into a single number, and they were fitted by different people to different test data — which is why they land about 11% apart and why neither can be shown to be the right one. What that spread is really telling you is the honest precision of the whole method: bending force is not a quantity anybody predicts to three significant figures. If the two figures straddle your machine's rating, the answer is not to pick the convenient one, it is to open the die or shorten the bend.
Why does opening the vee a little drop the tonnage so much?
Because force is inversely proportional to the opening, so going from a 1 in vee to a 1.5 in vee takes a third off it straight away. That looks like a free win and it is not, because the same opening is also setting the inside radius: a 1 in vee gives about 0.16 in of inside radius in mild steel and a 1.5 in vee gives about 0.24 in. A flat pattern calculated for the first will be wrong for the second by the difference in bend deduction, and it will be wrong on every bend in the part. Change the die to make a job fit the machine by all means, then recalculate the blank before cutting.
How much more tonnage does stainless need than mild steel?
Directly in proportion to ultimate tensile strength, which for annealed 304 or 316 against typical cold-rolled mild steel is about 70% more: the 48 in worked example goes from 29.9 tons to 50.9. Aluminum goes the other way — 5052-H32 at 33,000 psi needs 39% of what 85,000 psi stainless does for the same bend, because the ratio of the tensile strengths is the whole of it. The wider trap is inside a single specification rather than between them: ASTM A36 permits 58,000 to 80,000 psi, so two coils both correctly certified as A36 can differ by 38% in the force they take, and a job that fits the machine on one will not on the other.
My brake is rated 60 tons and this says 45. Does that mean it will make the bend?
It means the total force is inside the total rating, which is one of several questions and not the decisive one. A press brake rating is for a load spread across the bed, and the ram and the table both have a limit per inch of bed length that a short bend concentrated in the middle can exceed while the total is still comfortable — the machine's own manual gives that limit and this page does not know it. Off-center loading is a second question, tooling rating a third, and whether the ram has enough stroke and daylight for the part a fourth. This page reports arithmetic on published coefficients; whether a particular bend is safe on a particular machine is a decision for the machine's documentation and the person running it.
Why can I not bend a short flange in a big die?
Because the flange has to still be resting on the die shoulder when it has rotated, and geometry sets the limit. The sheet spans the vee with a shoulder at half the opening on each side. As the flange swings through a 90° bend it passes 45°, and at that point the material between the bend and the shoulder measures the half-opening divided by the cosine of 45 — which works out at 0.707 times the full opening. Anything shorter and the end of the flange comes off the shoulder, the workpiece pivots on the punch, and the bend ends up neither square nor where the backgauge put it. Shop minimums of 0.7 to 0.75 times the opening are this floor with a margin on top.
How much extra force does bottoming or coining actually take?
Nobody publishes a standard for it, and this page says so rather than inventing one. What is in circulation are multiples of the air-bend force: about 3 to 5 times for bottoming, about 5 to 10 for coining, with some sources quoting considerably more for a full coin in heavy material. The page prefills the middle of each band and lets you replace it, and the number worth replacing it with comes from the tooling maker's own chart for the die on your machine. The reason the spread is so wide is that both operations depend on how closely the tool matches the finished part and on how much material is being displaced, neither of which the air-bend variables describe. The practical consequence is easy to see: the 10 ft bend that takes 75 tons in air wants 299 tons bottomed, which is why almost nothing wide gets bottomed.
The radius on the finished part is not the one the drawing called for.
In air bending it never was going to be, because the drawing does not control it — the die opening does. The sheet bridges the two shoulders and takes a radius from that span whatever punch is in the holder, around 16% of the opening in mild steel, nearer 20% in stainless and nearer 14% in soft aluminum. So a 1/2 in vee gives roughly 0.080 in of inside radius on mild steel and a 1 in vee gives 0.16 in, and a drawing calling for 1/16 in is describing something the tooling cannot produce without bottoming. Fix it at the setup stage by choosing the die that gives the radius you need, then calculate the flat pattern for that radius, or bottom the bend so the punch nose takes over.
About air bending, and why the die opening decides everything
Air bending won the shop floor because it is the method where one set of tools makes every angle. The punch presses the sheet down between two shoulders and stops before the metal reaches the bottom of the vee, so how far the ram travels is what sets the angle, and a single die makes 30°, 90° and 120° parts without a tool change. Bottoming closes the sheet onto the faces of the vee and coining drives the punch nose into it, and both buy consistency — less springback, a radius that is the tool's rather than the die's — at a price in force that is several times the air-bend figure and in tooling that only makes the angle it was ground for. That price is why the tonnage question is nearly always an air-bending question, and why a page that quietly answered it with a bottoming number would send somebody shopping for a machine four times bigger than the job needs.
The consequence people underestimate is that die selection is not a force decision with side effects, it is three decisions taken simultaneously. Opening the vee reduces the force in inverse proportion, which is the reason the eight-times rule exists at all — it is the ratio that keeps the tonnage sensible through the middle of the thickness range, and it stretches to six times on thin material and ten or twelve on heavy plate for the same reason. But that same opening fixes the inside radius, because in air bending nothing is touching the punch nose, and it fixes the shortest flange the die can hold, because the metal has to stay on the shoulders while it rotates. A shop that changes the die to fit a job onto the machine and does not re-cut the blanks has changed the geometry the bend allowance and the bend deduction were calculated for, and will find out at assembly. The K-factor moves with it as well, which is why a measured K belongs to a tooling setup rather than to a material — the K-factor calculator is where that gets pinned down.
The last thing worth being honest about is the constant. The US chart's 575 reproduces the printed tonnage tables that shops have used for decades, and the metric formulation with 1.42 reproduces the ones European tooling makers print, and for the same bend they land 11% apart. Neither is derived from anything; both are curve fits to bending trials, wrapping friction at the shoulders, the punch radius and the exact geometry of the bend into one coefficient. The useful reading is that bending force is known to roughly a tenth, so a machine chosen with no headroom is chosen on a number that does not have that precision. Two inputs to all of this come from elsewhere: the thickness usually begins as a gauge number in one of four standards, and the tensile strength depends on the alloy and temper in front of you — the stainless and aluminum pages keep the grades apart rather than averaging them, and the metal weight calculator turns the blank into what the operator has to lift. The ram doing the pressing is a hydraulic cylinder like any other, and the hydraulic cylinder force calculator works out what bore and pressure it takes to make the tonnage above.
Where the machine details go
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
The tooling inventory and machine capacity a shop types into a page like this describe its capability to anyone collecting them. Nothing here is collected: the arithmetic and the tables both ship inside the page and run in the tab.