Sheet Metal Spring-Back Angle Calculator

Air-bend a sheet to ninety degrees, release the punch, and the part opens several degrees wider — that elastic recovery is spring-back. This calculator estimates how much a bend will open and the die angle you must over-bend to so the finished part holds the angle you actually want.

The springback ratio, defined

The change in bend radius on release is estimated from the elastic recovery of the outer fibre, using a standard relation between the radius before and after springback:

x      = (Ri × Sy) / (E × t)
Ri/Rf  = 4·x³ − 3·x + 1

Here Ri is the inside bend radius, Sy the yield strength, E Young’s modulus, and t the thickness. The factor Ri/Rf (the spring-back factor Ks) is always less than one. Because the bend angle measured from flat scales inversely with radius, the part bent to a given angle relaxes to that angle times Ks. To finish on the target bend the die must over-bend to target / Ks, and the difference is the spring-back you compensate for.

Worked examples

Example 1 — Mild steel, 90° bend

• Material: mild steel, Sy ≈ 250 MPa, E ≈ 200,000 MPa
• Sheet: 2.0 mm thick, 4 mm inside radius
• x = (4 × 250) / (200,000 × 2.0) = 1,000 / 400,000 = 0.0025
• Ks = 4·(0.0025)³ − 3·(0.0025) + 1 ≈ 0.9925
• Spring-back ≈ 90 × (1 − 0.9925) ≈ 0.67°
• Die angle to set: 90° / 0.9925 ≈ 90.7° — barely detectable, mild steel springs back very little.

Example 2 — 6061-T6 aluminum, 90° bend

• Material: 6061-T6 aluminum, Sy ≈ 275 MPa, E ≈ 69,000 MPa
• Sheet: 1.5 mm thick, 3 mm inside radius
• x = (3 × 275) / (69,000 × 1.5) = 825 / 103,500 ≈ 0.00797
• Ks ≈ 4·(0.00797)³ − 3·(0.00797) + 1 ≈ 0.976
• Spring-back ≈ 90 × (1 − 0.976) ≈ 2.2°
• Die angle to set: 90° / 0.976 ≈ 92.2°

The aluminum example spring-back is over three times larger than the mild steel case for similar geometry, confirming why aluminum press-brake work requires more careful over-bend setting.

Key variables and how they interact

Stainless 304 is the most challenging common material to hit a precise angle because it combines high yield strength with work-hardening during the bend itself, pushing the real Sy up during deformation. The tool uses nominal Sy; if you are pressing hard stainless, the actual spring-back will be larger than the estimate.

Practical guidance for the press brake floor

• Always run a test coupon first at the calculated over-bend before committing production material.
• Grain direction matters. Bending perpendicular to the rolling direction requires less force and typically shows slightly less spring-back than bending parallel to it.
• Temperature affects modulus slightly in aluminum; cold material in an unheated shop will spring back a touch more than the nominal calculation.
• If you are working with a spring-back factor very close to 1.0 (near-zero spring-back), double-check your yield strength input — very soft or annealed material can produce unrealistically small corrections.

Compensating on the press brake: three strategies

Knowing the springback angle is only useful if you counter it. Shops use three approaches, usually in this order:

1. Overbend. Bend past the target by the predicted springback so the part relaxes onto the correct angle — the cheapest fix, and the one this calculator directly supports.
2. Coining/bottoming. Press the punch fully into the die at high tonnage so the material yields through its thickness, cutting springback dramatically at the cost of tooling wear and higher press force.
3. Air-bend with angle correction. Modern brakes measure the achieved angle in-cycle and re-strike automatically; the predicted value here makes the first strike land close enough that one correction pass suffices.

The trade press documents these methods extensively — see the bending technique archives at The Fabricator — and tooling suppliers publish springback charts for their specific die widths.

Why material certs matter more than material names

“Stainless steel” spans a factor-of-two range in yield strength depending on grade and temper, and springback scales with yield strength over elastic modulus (σ_y / E). Two batches of the same alloy from different mills can spring back measurably differently. For production work, pull the yield strength off the material test certificate for the actual batch — reference values such as those in MatWeb’s material property database are fine for quoting and first articles, but the cert number is what keeps a 500-part run consistent. Always prove the first part with a protractor before committing the batch.