Every press brake operation has a tonnage requirement — the minimum force the machine must deliver to complete the bend without stalling. Run too close to the machine’s limit and you get inconsistent bends from ram pressure fluctuations. Exceed the machine’s rated capacity and you risk damaging the frame, tooling, and ram guidance. The calculation is straightforward once you understand the variables, and it applies to every combination of material, thickness, and die geometry on the shop floor.
The Air-Bend Force Formula
For V-die air bending — the dominant method in CNC press brake operations — the required bending force is:
F = (1.42 × σ_y × b × t²) / V
Where:
- F = bending force (kN or tonnes; divide kN by 9.81 for tonnes)
- σ_y = material yield strength (MPa)
- b = bend length (mm)
- t = material thickness (mm)
- V = V-die opening width (mm)
- 1.42 = empirical constant for standard V-die air bending
The formula assumes a V-die opening of approximately 6–10× material thickness, which is the standard range. Narrower dies produce a proportionally higher force; wider dies lower it. The 1.42 factor also assumes 90° bending — for other angles, the force changes, but 90° is the standard specification condition.
Worked Examples
Example 1: 3 mm mild steel (A36), 1,000 mm bend, 24 mm V-die
A36 yield strength: 250 MPa
F = (1.42 × 250 × 1,000 × 9) / 24 = 133 kN = 13.6 tonnes
A 25-tonne press brake handles this with comfortable margin. Note that the V-die at 24 mm is 8× the material thickness (3 mm) — within the standard 6–10t range.
Example 2: 5 mm 304 stainless, 800 mm bend, 40 mm V-die
304 stainless yield strength: 310 MPa (annealed)
F = (1.42 × 310 × 800 × 25) / 40 = 220 kN = 22.4 tonnes
The V-die at 40 mm is 8× the 5 mm material. For stainless, it is common practice to use a V-opening of 8–10t rather than the 6–8t typical for mild steel, which reduces the required force and avoids marking the material surface.
Example 3: 8 mm A572 Grade 50 HSLA, 600 mm bend, 64 mm V-die
A572 Gr.50 yield strength: 345 MPa
F = (1.42 × 345 × 600 × 64) / 64 = 187 kN = 19.1 tonnes
The V = 64 mm (8t). Even at this thickness and moderate yield strength, a 25-tonne machine handles the 600 mm bend. Scale to a 2,000 mm bend and the force becomes 635 kN (64.8 tonnes) — now a 100-tonne machine is the minimum.
Key Variables and Their Effect on Required Tonnage
Material yield strength
Yield strength appears directly in the numerator — doubling it doubles the required force. This is why HSLA and AHSS grades require significantly more tonnage than mild steel at the same thickness, even before considering the tighter minimum bend radii those grades impose.
Common yield strengths for press brake work:
| Material | Yield strength (MPa) | Relative force vs. A36 |
|---|---|---|
| Mild steel (A36) | 250 | 1.0× |
| 304 stainless (annealed) | 310 | 1.24× |
| A572 Gr.50 HSLA | 345 | 1.38× |
| 6061-T6 aluminum | 276 | 1.10× |
| DP590 (dual-phase steel) | 390 | 1.56× |
| DP780 | 500 | 2.0× |
| A514 (T1 steel) | 690 | 2.76× |
| DP980 | 700 | 2.80× |
A shop that upgrades from mild steel to DP980 for an automotive structural part needs roughly 2.8× more tonnage — often requiring a press brake upgrade or a redesign to reduce bend length.
Material thickness
Thickness appears squared in the formula. Doubling thickness quadruples the required bending force at the same die width. This is the steepest scaling relationship in the formula — thickness matters more than any other variable.
At constant V/t ratio (same die proportions):
- 2 mm → 4 mm: force increases 4× if V also doubles (force ∝ t²/V, and V ∝ t, so net ∝ t)
- But if the same die is used: force increases 4× (t² in numerator, V unchanged)
In practice, V is typically scaled with t (8t rule of thumb), making the effective scaling approximately linear in t. But whenever a fixed die is used across a thickness range, the t² dependence becomes the dominant effect.
Die opening (V)
V appears in the denominator — a narrower die requires more force. The standard V-die selection rule: V = 6–8t for mild steel; V = 8–10t for stainless and aluminum. These ranges balance the achievable bend radius (narrower V → tighter radius), required force, and surface marking risk.
Choosing a V that is too narrow increases tonnage requirements, risks tool and machine damage on heavy gauges, and produces a tighter inside radius than the material’s minimum may support. Choosing a V that is too wide produces a large inside radius and, at extreme ratios, an unstable bend where the sheet rocks on the die edges.
Bend length
Force scales linearly with bend length. A 2,000 mm bend requires exactly twice the force of a 1,000 mm bend on the same material, thickness, and die. This linearity means that for long bends on thick material, the required tonnage can exceed any machine in the shop — the correct response is to either break the bend into multiple passes (on a machine long enough for the part) or to split the part into sub-assemblies.
Safety Factor and Machine Selection
The calculated force is the theoretical minimum under ideal conditions — uniform material, correct die alignment, clean tool contact. In production, apply a 20% safety margin: the machine should be rated for at least 1.2× the calculated force.
Reasons for the margin:
- Material yield strength varies within the specification range (A36 can be 250–345 MPa)
- Die misalignment concentrates load
- Cold or thick material at the start of a shift before warm-up
- Corner bending on short flanges requires higher force than the formula predicts
Machine selection rule: Select the press brake so that the required bending force is no more than 80% of the machine’s rated tonnage for sustained production.
Bottom Bending and Coining: Force Multipliers
The formula above applies to air bending. Bottom bending (allowing the punch to contact the die at bottom of stroke, coining the material) requires significantly more force:
- Bottom bending: approximately 3–5× the air-bend force
- Coining: approximately 5–10× the air-bend force
For the Example 1 scenario (3 mm A36, 1,000 mm, 24 mm V-die):
- Air bend: 13.6 tonnes
- Bottom bend: 40–68 tonnes
- Coining: 68–136 tonnes
Bottom bending and coining produce tighter angle tolerances and smaller springback variation, but the force requirements jump dramatically. A machine that handles air bending of a specific part may not safely handle coining the same part — this must be verified before changing the forming mode.
Punch Tip Load Check
Beyond the total machine tonnage, verify that the punch tip cross-section can handle the force without yielding. The maximum allowable load on a standard punch tip is approximately:
F_max (kN) = σ_y_punch × A_tip / 1,000
For a D2 tool steel punch at HRC 60 (compressive yield ~2,000 MPa) with a 100 mm × 3 mm tip cross-section:
F_max = 2,000 × (100 × 3) / 1,000 = 600 kN
For the same punch over a 1,000 mm bend length, the allowable load per 100 mm segment must be confirmed — the force is distributed along the punch length, but stress concentrations at the tip require this check for short flanges and deep bends.
Frequently Asked Questions
What formula calculates press brake tonnage?
F = (1.42 × σ_y × b × t²) / V, where σ_y is yield strength in MPa, b is bend length in mm, t is thickness in mm, and V is V-die opening in mm. The result is in kN; divide by 9.81 for tonnes.
Why does thickness have such a large effect on bending force?
Thickness appears squared in the numerator. Doubling the material thickness at the same die width quadruples the required force. This is why heavy-gauge work demands significantly larger press brakes than comparable thin-sheet work even at the same bend length.
How much safety margin should I apply to the calculated tonnage?
Run the machine at no more than 80% of its rated capacity for sustained production. Apply a 20% margin above the calculated force when selecting the machine to allow for material yield strength variation, die alignment, and other production variables.
References
- Oberg, E., et al., Machinery’s Handbook, 31st Edition. Industrial Press, 2020. (V-die air bending force formula, V-die selection, tonnage tables for standard materials.)
- Budynas, R.G., and Nisbett, J.K., Shigley’s Mechanical Engineering Design, 11th Edition. McGraw-Hill, 2020. (Bending stress, plastic deformation mechanics, punch tip load analysis.)
- ASM Handbook, Volume 14B: Metalworking — Sheet Forming. ASM International, 2006. (Bottom bending and coining force multipliers, HSLA and AHSS formability.)
- ASTM A36/A36M, A572/A572M, A514/A514M — current editions. (Yield strength values for mild steel, HSLA, and high-strength structural steel used in all worked examples.)
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