In short: in air bending the force is roughly 1.42 × Rm × t² / V, in newtons per millimetre of bend length. Thickness is squared: going from 2 to 4 mm quadruples the requirement. Widening the V divides it. Coining in the bottom of the die needs three to five times more. Check the tonnage before you cut, not after.
The formula, and what each term means
F ≈ 1.42 × Rm × t² / V
F is in newtons per millimetre of bend length. For tonnes on a whole part, multiply by the length in millimetres and divide by 9,810.
- Rm, the tensile strength of the material, in N/mm². About 400 for mild steel, 520 for S355, 600 for 304 stainless, 220 for 5754 aluminium.
- t, the thickness, squared. This is the term that dominates everything else.
- V, the die width. It is in the denominator: a wider V needs less force.
- 1.42, an empirical air bending coefficient, commonly accepted on the shop floor.
Our bend radius chart applies this formula for thicknesses from 1 to 10 mm across four materials, with bend length as a parameter. Faster than working it out by hand between two parts.
Thickness squared, the one thing to remember
This is the intuition most often missing, and the one that costs the most.
Mild steel at 2 mm on a 16 mm V needs about 14 tonnes per metre. The same steel at 4 mm, on a 32 mm V, needs about 28 tonnes per metre. But if you keep the 16 mm V because that is what is in the machine, you jump to 57 tonnes per metre.
In other words: doubling the thickness without changing the die does not double the requirement, it quadruples it. That is how a 100-tonne press that handled the previous run without complaint stalls on the next one.
Three mistakes that cost a sheet
Quoting on the ideal V, bending on the available one. The quote assumes a 32 mm V, the workshop has a 16 mm V fitted, and nobody changes tooling for six parts. The force doubles, the press struggles, the angle drifts.
Forgetting the length. Tonnage is counted per metre. A three-metre part needs three times the force of a one-metre part, and most presses do not deliver their rated tonnage across the whole bed: past a certain span the bed deflects and the angle varies from one end of the bend to the other.
Confusing air bending with coining. A customer demanding an angle within half a degree forces coining in the bottom of the die. The formula above no longer applies: allow three to five times more. A part that went fine in air on your press can become unmakeable with the same geometry and a tighter tolerance.
What it changes on the quote
Force is not only a machine constraint, it is a cost line. Three direct consequences.
The V choice becomes a commercial decision. Widening the V reduces the force, so the part bends on a smaller press, which frees the big one. But it increases the radius produced, which the customer may not have agreed to. See our article on the minimum bend radius.
Bend length enters the cycle time. A long part needs two operators or a sheet follower. That is not the same minute as the same part at 500 mm.
A tight tolerance changes machine. And therefore hourly cost. If your rate card does not separate air bending from coining, you are selling the second at the price of the first.
Check before cutting, not after
The worst moment to discover a tonnage problem is when the sheet is already cut. The material is consumed, the lead time is committed, and only bad options remain: subcontract in a hurry, widen the V and renegotiate the radius, or remake the part.
The check is three questions, asked at quoting time:
- What is the force per metre for this material, this thickness and this V?
- What is the longest bend on the part?
- Does the product of the two fit the press that will actually be free that day?
Three questions, two minutes, and nearly every unpleasant surprise disappears.
Why automating this check is worth it
This is exactly the kind of verification a person does well the first time, less well the tenth, and not at all when twelve quotes are waiting.
Koventor knows your presses, your dies and your materials. A part whose tonnage exceeds your capacity is flagged at entry, with the V that would make it feasible. The customer does not get a quote for a part you cannot produce, and you do not learn about the problem on bending day.
The bend allowance calculator and the bend radius chart do the same thing by hand, free. Use them: it is the best way to check that our figures are your figures before going further.