1. Introduction
Sizing a press brake is one of the first — and most expensive to get wrong — engineering decisions in a sheet metal shop. The consequences of an error are not symmetrical.
A machine that is undersized for the parts you actually run means working at or above its rated tonnage. The result is accelerated tool wear and cracked punches, bend angles that will not repeat, permanent deflection of the ram and frame, and in extreme cases a failure that puts the operator directly at risk.
A badly oversized machine costs more to buy, draws more power, takes more floor space, and — with short parts bent on a long bed — forces you to watch load distribution so you do not overload the ram at a single point.
Sizing correctly does not stop at one formula. It means gathering data on the material, the part geometry, the bending method and the tooling on hand — then checking the result against three independent limits: the machine’s rated tonnage, the allowable load per foot, and the capacity of the tooling.
IN ONE LINE
The formula gives you a minimum. Sizing a machine is the formula plus the checklist in Section 8.
2. Units — tons, tonnes and kilonewtons
US press brakes are rated in tons, meaning short tons of force at 2,000 lbf each. Imported machines and most European tooling catalogs are rated in metric tonnes-force or in kilonewtons. The two “tons” are not the same thing, and the gap is about 10%:
1 metric tonne-force = 2,205 lbf = 9.81 kN = 1.10 US tons
1 kN = 225 lbf = 0.112 US tons
110 ton
220,000 lbf ≈ 979 kN
175 ton
350,000 lbf ≈ 1,557 kN
350 ton
700,000 lbf ≈ 3,114 kN
WATCH THE NAMEPLATE
A European builder’s “100 ton” machine is 100 metric tonnes — about 110 US tons. Read the unit before you compare quotes, and do not assume a 100 US-ton machine satisfies a 100-tonne requirement. Separately, commercial designations always carry two numbers, such as “175 ton × 12 ft”. The second is bed length, not the length you can bend at full tonnage — more on that in Section 8.
3. Inputs
Before you calculate anything, you need to know:
WHAT YOU NEED BEFORE YOU CALCULATE
- L — bend length [in],
- T — material thickness [in] (actual, not nominal — rolling tolerance can add a few percent to the force),
- UTS — ultimate tensile strength [psi] for the specific grade and condition,
- V — die opening [in],
- bending method — air bending, bottoming or coining,
- geometry — required inside bend radius and minimum flange length,
- bend angle and the repeatability you have to hold.
4. The bending force formula
The basic formula for the force required in air bending:
=
k · UTS · L · T²
V
where:
- F — bending force [lbf],
- k — die factor (empirical, typically 1.33–1.42),
- UTS — ultimate tensile strength [psi = lbf/in²],
- L — bend length [in],
- T — material thickness [in],
- V — die opening [in].
The result comes out in pounds of force. To convert to tons, divide by 2,000.
CRITICAL CAVEAT
This formula applies to air bending only. Bottoming and coining take several times the force — see the table in Section 8.1.
4.1. The die factor k — what it is not
The die factor k in the force formula gets confused with the K-factor used in CAD. They are two completely different quantities, and it is worth separating them once and for all:
| Quantity | Die factor k | K-factor |
|---|---|---|
| Typical value | 1.33 – 1.42 | 0.30 – 0.50 |
| What it is for | calculating bending force | calculating the flat pattern |
| What it describes | friction and the punch–die geometry | position of the neutral axis in the section |
| Where it is used | press brake sizing | CAD/CAM, laser nesting |
For a conservative check, use k = 1.42. With UTS = 65,000 psi — a reasonable working figure for mild steel — that collapses into a shop rule of thumb:
with T and V in inches. Published tonnage charts commonly show a figure closer to 575, which reflects a slightly higher assumed die factor or tensile strength — either way, the point of the rule is a fast sanity check, not a final number.
4.2. Ultimate tensile strength
UTS is not a universal value. It depends on chemistry, production route, heat treatment, thickness and delivery condition. “Mild steel” is a shop term, not a material specification — in practice it covers hot-rolled structural carbon grades, most often A36 or A572 Gr. 50, and the difference in bending force between the two runs 20–25%.
Below are specification ranges and the values normally used for a sizing check. European grade designations are given with their closest US counterparts, since imported material and imported tooling data are both common on US shop floors:
| Grade | Spec range [ksi] | Use for sizing [ksi] |
|---|---|---|
| S235JR (≈ A36) | 52 – 74 | 65 |
| S275JR (≈ A529 Gr. 50) | 60 – 81 | 72 |
| S355JR (≈ A572 Gr. 50) | 68 – 91 | 80 |
| 1.4301 / AISI 304 | 75 – 104 | 87 |
| 1.4404 / AISI 316L | 71 – 100 | 87 |
| Aluminum EN AW-5754 H22 (≈ 5052-H32) | 32 – 39 | 36 |
| Aluminum EN AW-6082 T6 (≈ 6061-T6) | 42 – 49 | 45 |
| Brass CuZn37 (≈ C27200, per temper) | 44 – 73 | 51 |
| Copper Cu-DHP, soft (≈ C12200) | 29 – 36 | 33 |
| High-strength steels (S700MC, Strenx, Hardox) | 110 – 230 | per mill test report |
NOTE
For high-strength and hard-to-bend steels, never work from table values. Take UTS from the mill test report for the specific heat, and take the minimum bend radius and minimum die opening from the steel producer’s technical data sheet.
5. Choosing the die opening V
The die opening is the only variable in the formula you actually control on the shop floor — and the one with the largest effect on the answer. Force is inversely proportional to V: moving from a 2 in die to a 3 in die cuts the required force by a third.
5.1. The basic rule
Contrary to a widespread shortcut, the die-opening multiplier depends first on material thickness and only second on the material itself:
| Thickness T [in] | Recommended V | Notes |
|---|---|---|
| up to 1/8 (11 ga and lighter) | 6 × T (up to 8 × T) | standard for light mild steel |
| 1/8 – 5/16 | 8 × T | the most common working range |
| 5/16 – 3/8 | 10 × T | protects tooling and the ram |
| over 3/8 | 12 × T | plate bending |
| UTS > 100 ksi | 12 – 15 × T and up | strictly per the steel producer’s data sheet |
Material corrections are applied within those bands:
- Stainless steel — top of the band, or one die opening wider (higher UTS and noticeably more springback).
- Aluminum in a hardened temper — top of the band, because of the risk of cracking on the outside of the bend.
- A tight inside radius requirement — bottom of the band, but go there deliberately: dropping from 8 × T to 6 × T raises the force by about 30%.
RULE OF THUMB
Round the calculated V to the nearest opening you actually have in the die. If an opening matches the calculated width exactly, use it. If not, take the next one wider — a narrower opening means higher force and a real risk of overloading the tooling.
5.2. What the force formula doesn’t show
Changing the die opening is not a neutral move. Three things change along with V, and you need to clear all three with the designer before you move a part to a different die:
Inside bend radius
In air bending mild steel, the inside radius is a function of the die, not the punch: Ri ≈ V / 6.3, roughly 16% of the die opening.
Minimum flange length
The flange has to be longer than half the die opening so the part does not drop into the die. In practice, figure a minimum of about 0.63 × V.
Flat pattern
A different radius means a different neutral axis position, so a different flat pattern. A blank cut for a 2 in die and bent in a 3 in die will come out off-dimension.
Short version: you can change the die to fit the job inside the machine’s tonnage, but that is always an engineering change to the part, not just a process change.
5.3. Die types and the cost of getting V wrong
The industry runs many die types: multi-V (universal, Amada style), four-way, channel dies, Wila style, plus a whole family of special tooling. Die openings are called out in inches in the US and in millimeters on imported tooling.
The wrong die opening produces problems you see on the floor immediately:
- overloaded and cracked punches,
- permanent surface damage on the part (die shoulder marking),
- wrong, non-repeatable bend angles,
- accelerated tool wear,
- the punch shearing into the material when the opening is too narrow,
- cracking on the outside of the bend when the radius is too tight,
- an unstable process with no dimensional repeatability.
Fig. 1. A four-way universal die. One tool gives you four die openings, so you can match V to material thickness without a tooling change — and with it control the required force, the inside radius and the minimum flange length.
6. K-factor
The K-factor is not used to calculate tonnage — it is used to calculate the flat pattern. It belongs here because it depends directly on the die you pick, which means it depends on a decision made while sizing the force.
During bending the outside of the arc is stretched and the inside is compressed. Between them lies a neutral layer — the neutral axis — where there is neither tension nor compression. The neutral axis does not sit exactly at mid-thickness; it shifts toward the inside surface.
- K — the K-factor,
- t — distance from the inside bend surface to the neutral axis [in],
- T — material thickness [in].
K falls between 0 and 0.5. What drives it is primarily the ratio of inside radius to thickness (Ri/T), not thickness on its own:
| Ri / T | K | Character of the bend |
|---|---|---|
| below 1 | 0.30 – 0.38 | sharp bend, narrow die |
| 1 – 3 | 0.38 – 0.43 | typical air bending |
| above 3 | 0.43 – 0.50 | large radius, wide die |
The trends worth remembering:
- larger bend radius (wider die) → K rises, approaching 0.5,
- tighter radius (narrower die, sharp bending) → K drops,
- bottoming and coining → tighter radius, so lower K than air bending,
- material is a secondary effect — geometry dominates; material shows up mainly through springback.
IN PRACTICE
For typical mild steel work, K ≈ 0.40 is the usual starting point. A table value is always an approximation — the only reliable method is to run samples on your machine, your tooling and your material, measure the flat pattern, and build your own bend deduction table. In a modern CAD/CAM system a BD table is more accurate than any single K value.
7. Worked example
INPUTS
- material: mild steel A36, UTS for sizing 65,000 psi,
- bend length L = 10 ft (120 in),
- thickness T = 1/4 in (0.250 in),
- air bending, 90°,
- die factor k = 1.42.
7.1. Case A — 2 in die opening
Pick the die. 1/4 in falls in the 1/8 – 5/16 in band, so V = 8 × 0.250 = 2.0 in. A 2 in opening is standard in multi-V tooling.
Bending force.
Safety margin. Add 10–20% for thickness tolerance, UTS scatter, friction and tool wear.
So the job calls for a 225-ton machine — the next standard size up.
Load per foot. 346,125 lbf / 10 ft ≈ 34,600 lbf/ft, about 17 tons per foot. Typical segmented tooling is rated near 30 tons per foot, so there is plenty of margin.
Part geometry. Inside radius Ri ≈ 2.0 / 6.3 ≈ 0.32 in, minimum flange ≈ 0.63 × 2.0 ≈ 1.26 in.
CONCLUSION
This part needs a machine in the 225-ton class. Do not run it on a 175-ton press in this configuration — 173 tons is the rated figure with no margin whatsoever.
7.2. Case B — the same bend on a 175-ton press
If a 175-ton machine is all you have, the only variable left to work with is the die opening. Move to V = 3.0 in (12 × T — the top of the allowable band for this thickness):
2 in die opening
3 in die opening
Same material, same bend length — moving to a wider die alone takes a third off the required force.
With a 20% margin that comes to about 139 tons, so a 175-ton press handles the bend safely. The price of that change is concrete, though, and you have to accept it knowingly:
| Parameter | V = 2 in | V = 3 in |
|---|---|---|
| Required force | ≈ 173 tons | ≈ 115 tons |
| Inside radius Ri | ≈ 0.32 in | ≈ 0.48 in |
| Minimum flange length | ≈ 1.26 in | ≈ 1.89 in |
| Flat pattern | per K for Ri/T ≈ 1.3 | recalculate — different K |
| Springback | less | more |
If the print allows a 0.48 in radius and the shortest flange on the part is at least 1.89 in, the bend is workable. If not, you are back to a higher-tonnage machine. Either way, the flat pattern has to be recalculated from scratch.
ON PRECISION
The realistic accuracy of this formula is ±10%. Reporting a result as “115.3750000 tons” is false precision — the practical answer is “about 115 tons”.
8. What the formula doesn’t cover — a checklist
The formula result is a starting point. Before you call the sizing done, work through the list below.
8.1. Bending method
This is the single most common source of serious sizing errors. The formula covers air bending. The other methods take several times the force:
| Method | Force multiplier | Characteristics |
|---|---|---|
| Air bending | × 1 | angle set by ram position |
| Bottoming | × 2 – 4 | tighter radius, less springback |
| Coining | × 5 – 10 | realistically thin material only |
A 175-ton press air bending can turn into a 500-ton requirement for the same part bottomed.
8.2. Load per foot
The machine and the tooling have not just a total force limit but a limit on force per foot of bend length. Typical segmented tooling is rated near 30 tons per foot; the ram has its own limit, published by the builder. Load per foot is:
Which is exactly the 550 rule from Section 4.1 — and note that it is independent of bend length. It depends only on material, thickness and die opening. The problem shows up on thick and high-strength material: 5/16 in Hardox 450 (roughly 200 ksi) in a 4.5 in die works out to about 37 tons per foot, above the capacity of standard tooling no matter how large the press is.
8.3. Short parts and off-center bends
A press brake reaches its rated tonnage under a symmetric load spread over an appropriate length of the bed. A short bend taking full force at a single point — and especially a bend run close to one end of the machine — twists the ram and can deflect it permanently. The allowable force for concentrated and off-center loading is published in the machine manual, and it is not a number to skip.
8.4. Springback and grain direction
The formula says nothing about the angle you will actually get. Once the load comes off, the material springs back — the higher the UTS and the larger the radius, the more it moves. Stainless and high-strength steels spring back noticeably harder than A36. Separately: bending across the rolling direction is safer than bending along it; with aluminum and high-strength steels, bending along the grain frequently ends in a crack.
8.5. Crowning
On long bends the ram and bed deflect in the middle, which opens the angle at the center and closes it at the ends. A crowning system — hydraulic or mechanical — compensates for that. If you are buying a machine for parts close to full bed length, crowning is mandatory equipment, not an option.
8.6. Beyond tonnage
Sizing a press brake does not end with force. Also check:
- Bed length against your longest bent part.
- Open height (daylight) and ram stroke — they determine whether a closed profile can be lifted out.
- Throat depth — critical for U-shapes and box parts.
- Back gauge axis count and configuration.
- Tool clamping system and compatibility with the tooling you already own.
- Approach, bending and return speeds — in production work these drive throughput.
8.7. Data sources and standards
Treat the formula as a quick check. The basis for sizing remains the tonnage charts published by machine and tooling makers (Amada, Trumpf, Bystronic, Wila, Wilson Tool, Mate, Rolleri), the calculator built into the press brake’s CNC control, and the steel producer’s technical data sheets. On the safety side, press brakes in the US fall under ANSI B11.3 together with OSHA’s general machine guarding requirements; imported CE-marked machines are built to the harmonized European standard EN 12622. ISO 6909, covering hydraulic and servo-driven press brakes, was published in 2026.
9. Summary
Sizing a press brake comes down to three steps and one verification.
THREE STEPS AND ONE CHECK
Step 1. Establish the material, thickness, bend length and bending method.
Step 2. Pick the die opening from the band appropriate to the thickness, and confirm that the resulting inside radius and minimum flange length meet what the print requires.
Step 3. Run the force calculation, add a 10–20% margin, and round up to an available tonnage.
Verify. Check load per foot against the capacity of the tooling and the ram, apply the multiplier if you are bottoming, and for short or off-center bends, check the allowable concentrated load in the machine manual.
A press brake is only as capable as the whole system around it: the machine, the tooling, knowledge of the material, a correctly calculated flat pattern, and the operator’s experience. The formula gives you the minimum force — the rest determines whether the part comes out on dimension, on angle, and repeatably across the entire run.