Key Takeaways
- Air-bending tonnage formula: T (t/m) = (t² × Rm) / (8 × V) — multiply by length in metres for total tons.
- V-die opening = 8× material thickness for standard air bending.
- Stainless 304 needs ~1.5× the tonnage of mild steel; aluminium 5052 needs ~0.56×.
- Always add a 20% safety margin and never exceed 80% of machine rated capacity.
- Use the free calculator to skip the arithmetic.
The Tonnage Formula Explained
Press brake tonnage for air bending (the dominant mode on all modern CNC press brakes) follows this relationship:
Where:
- T = required tonnage per metre of bend length (metric tons/m)
- t = material thickness (mm)
- Rm = tensile strength of the material (MPa or N/mm²)
- V = V-die opening width (mm)
To get total tonnage, multiply T by the bend length in metres and add 20%:
This formula is derived from simple beam bending theory applied to sheet metal. The 8 in the denominator comes from the bending moment of a simply supported beam: M = (F × L) / 4, combined with the punch-V geometry. It applies to air bending only — bottoming and coining use 3–8× higher tonnage and follow different mechanics.
Worked Example
Problem: Bend 2,500 mm of 3 mm mild steel (Rm = 410 MPa) with a 24 mm V-die. What tonnage is required?
Step 1 — Calculate T per metre:
T = (3² × 410) / (8 × 24) = (9 × 410) / 192 = 3,690 / 192 = 19.2 t/m
Step 2 — Multiply by bend length (2.5 m):
T_bend = 19.2 × 2.5 = 48.0 tonnes
Step 3 — Add 20% safety margin:
T_safe = 48.0 × 1.20 = 57.6 tonnes → use an 80-tonne or larger press brake
Material Tensile Strengths
Rm values vary by grade and heat treatment. Use these mid-range representative values for initial calculations — always confirm against the mill certificate for critical applications.
| Material | Grade | Rm (MPa) | Relative Tonnage vs Mild Steel |
|---|---|---|---|
| Mild Steel | S235 / A36 | 360–510 (use 410) | 1.00× |
| High-Strength Steel | S355 / A572 Gr50 | 490–630 (use 550) | 1.34× |
| Stainless | 304 | 515–720 (use 620) | 1.51× |
| Stainless | 316 | 485–680 (use 580) | 1.41× |
| Duplex Stainless | 2205 | 620–820 (use 720) | 1.76× |
| Aluminium | 5052-H32 | 215–265 (use 230) | 0.56× |
| Aluminium | 6061-T6 | 260–310 (use 310) | 0.76× |
| Copper | C11000 | 200–250 (use 220) | 0.54× |
| Brass | C26000 | 320–380 (use 340) | 0.83× |
Mild Steel Tonnage Reference Chart
The table below shows required tonnage per metre for mild steel (Rm = 410 MPa) using the standard 8× V-die rule. Values shown are calculated — apply your 20% safety margin before selecting a machine.
| Thickness (mm) | V-Die (mm) | Tonnes/metre | 1,000 mm bend (t) | 2,000 mm bend (t) | 3,000 mm bend (t) |
|---|---|---|---|---|---|
| 0.5 | 4 | 3.2 | 3.2 | 6.4 | 9.6 |
| 0.8 | 6 | 4.4 | 4.4 | 8.7 | 13.1 |
| 1.0 | 8 | 5.1 | 5.1 | 10.2 | 15.4 |
| 1.5 | 12 | 7.7 | 7.7 | 15.4 | 23.0 |
| 2.0 | 16 | 10.3 | 10.3 | 20.5 | 30.8 |
| 3.0 | 24 | 19.2 | 19.2 | 38.4 | 57.7 |
| 4.0 | 32 | 20.5 | 20.5 | 41.0 | 61.6 |
| 5.0 | 40 | 32.1 | 32.1 | 64.1 | 96.2 |
| 6.0 | 48 | 38.4 | 38.4 | 76.9 | 115.3 |
| 8.0 | 64 | 51.3 | 51.3 | 102.5 | 153.8 |
| 10.0 | 80 | 64.1 | 64.1 | 128.2 | 192.3 |
| 12.0 | 96 | 76.9 | 76.9 | 153.8 | 230.8 |
Calculated values (Rm = 410 MPa, V = 8t). Add 20% safety margin before selecting machine capacity.
V-Die Sizing Rules
The V-die opening is not fixed — it has significant effects on bend quality, tonnage, and inside radius:
| V-Die Opening | Effect on Tonnage | Inside Radius | Springback | Risk |
|---|---|---|---|---|
| Narrow (4–6×t) | Higher (+25–50%) | Sharper | Less | Tooling/part damage |
| Standard (8×t) | Baseline | ~0.16×V | Normal | Correct for most work |
| Wide (10–12×t) | Lower (−20–30%) | Larger | More | Marking soft metals |
The inside bend radius in air bending is approximately 16% of the V-die opening (Ri ≈ 0.16 × V). To achieve a sharper inside radius you must either use a narrower V-die (and accept higher tonnage) or switch to bottoming mode.
Safety rule: Never operate a press brake above 80% of its rated tonnage. The machine rating is the maximum safe load — not a target. Tooling and ram damage from overloading is expensive and can be dangerous.
Safety Margin: Why 20%?
The 20% safety margin compensates for:
- Material variation — mill certificates allow ±15% on Rm for most structural grades
- Batch variation — hardness can vary within a coil
- Tooling wear — worn punch tips increase bending force
- Measurement errors — stated thickness is nominal; actual gauge may be slightly thicker
For safety-critical applications or hard-to-source materials, some fabricators use a 30% margin. For production work with certified mill certs and calibrated material thickness, 15% can be acceptable if your machine is regularly serviced.
Use the Free Calculator
Skip the arithmetic — our Press Brake Tonnage Calculator handles the formula, material selection, V-die sizing, and safety margin automatically. Enter your material, thickness, bend length, and die opening to get the answer in seconds.
Frequently Asked Questions
What is the press brake tonnage formula?
T (t/m) = (t² × Rm) / (8 × V) — where t is thickness in mm, Rm is tensile strength in MPa, and V is V-die opening in mm. Multiply by bend length in metres for total tonnage, then add 20%.
What V-die opening should I use?
The standard rule for air bending is V = 8 × material thickness. For 3 mm mild steel use a 24 mm V-die. Narrower V sharpens inside radius and increases tonnage; wider V does the opposite.
How much more tonnage does stainless need vs mild steel?
304 stainless has an Rm of ~620 MPa vs ~410 MPa for mild steel — so you need approximately 1.51× (51% more) tonnage for the same thickness and die opening. 316 stainless is similar at ~1.41×.
Does this formula apply to bottoming and coining?
No. This formula is for air bending only. Bottoming requires approximately 3–5× air bending tonnage; coining requires 5–8×. These modes are rarely used on modern CNC press brakes because air bending with angle correction achieves equal precision at much lower force.