Springback / Overbend Calculator

What Is Springback and How Do You Compensate for It?

When a sheet-metal part is bent, only the outer fibers yield plastically; the material near the neutral axis stays elastic. When the tool is released, that stored elastic strain recovers and the bend opens up slightly — the part "springs back" to a larger radius and a smaller bend angle than the tool formed.

Springback grows with yield strength and bend radius, and shrinks with elastic modulus and thickness. That is why aluminum (low E) springs back far more than steel, and why a tight radius over thin stock barely springs back at all. The dimensionless group that governs it is x = σy·R / (E·t).

To hit a target angle you overbend: form the part past the target by the springback amount so it relaxes onto the specification. This calculator returns the overbend angle to set on the press brake, the springback angle it will recover, and the final (relaxed) radius.

Formula: x = σy · R / (E · t) Ks = R_i / R_f = 4x³ − 3x + 1 Overbend angle = target angle / Ks

Example Calculation

Aluminum 6061-T6 (σy 276 MPa, E 69 GPa), 1 mm thick, 10 mm inside radius, 90° target. x = 276·10/(69000·1) = 0.04, so Ks = 4(0.04)³ − 3(0.04) + 1 ≈ 0.880. Overbend to 90/0.880 ≈ 102.2°, giving about 12.2° of springback and a final radius near 11.4 mm.

When to Use This Calculator

• Setting up a press brake for a new material/thickness and needing the overbend angle to hit the target after the part springs back
• Switching an existing part from steel to aluminum or a high-strength alloy — springback rises sharply as the yield-to-modulus ratio grows, so the old overbend setting overshoots
• Air bending at large radius-to-thickness ratios (r/t > 5) where springback is significant and cannot be ignored
• Compensating the tool radius so the final formed radius matches the drawing after elastic recovery
• Diagnosing parts that consistently open past the target angle and quantifying exactly how much to overbend

Common Mistakes to Avoid

• Ignoring material grade — aluminum 6061-T6 (E≈69 GPa) springs back roughly 3× more than mild steel (E≈200 GPa) at the same geometry; a steel overbend leaves an aluminum part far open
• Confusing overbend angle with springback angle — you bend TO the overbend angle (the larger value) so the part relaxes TO the target; the springback is the difference, not the setpoint
• Applying the model below r/t = 2 — the Ks = 4x³ − 3x + 1 relation assumes elastic-dominated bending and loses accuracy for tight radii where the neutral axis shifts inward
• Assuming springback is a fixed angle across all bends — the overbend compensation scales with the target angle, so a 90° and a 30° bend need different absolute overbend
• Using nominal yield strength for cold-worked or tempered stock — work hardening raises the effective yield and increases springback beyond the handbook value

How to Interpret Results

• The overbend angle is the press-brake setpoint — bend to this angle and the part relaxes to your target; confirm with a first-article and adjust the material yield if it lands off
• The springback angle quantifies elastic recovery — larger values (high-strength or low-modulus materials, large radii) demand more overbend and tighter process control
• The springback factor Ks (0–1) is the ratio of final to loaded angle — Ks near 1 means little springback (thick, small-radius, low-strength); Ks well below 1 signals aggressive springback
• The final radius is always larger than the tooling radius because the part springs open — compensate the punch/die radius by 1/Ks when the drawing calls out a specific formed radius
• An "overbend exceeds 180°" warning means the target cannot be reached in a single bend — plan a multi-stage forming or a bottoming/coining operation instead

Related Standards & References

• ASM Handbook Vol. 14B — Metalworking: Sheet Forming (springback ratio and Ks model)
• DIN 6935 — Cold bending of flat steel products
• ISO 7438 — Metallic materials — Bend test
• Machinery's Handbook — Springback and overbend compensation reference

Frequently Asked Questions

Why does aluminum spring back more than steel?

Springback scales with σy/E. Aluminum alloys have a much lower elastic modulus (~69 GPa vs ~200 GPa for steel) but comparable yield strength, so they store and recover more elastic strain. Expect roughly 2–3× the springback of mild steel for the same geometry — always overbend aluminum more.

Does a tighter bend radius reduce springback?

Yes. Springback is proportional to R/t, so a smaller inside radius (or thicker stock) yields a stiffer bend with less elastic recovery. Very tight radii near the minimum bend radius spring back only a fraction of a degree, while large-radius bends in thin sheet can spring back several degrees.

Is this exact enough for production?

The 4x³ − 3x + 1 model is the standard first-order estimate and is accurate for elastic-plastic bending of common sheet alloys. Real springback also depends on tooling, friction, strain hardening, and material lot variation, so use the overbend angle as a starting setpoint and fine-tune with a first-article bend.