BendMath / fabrication reference
Printable bend worksheet
Published November 5, 2026 · Single-bend calculations for shop planning
Use this sheet to document bend allowance (BA), neutral-axis location, and bend deduction (BD) before confirming your flat pattern with an actual test coupon. All lengths must use the same unit (in or mm).
1. Formula and angle convention
BA = (π / 180) × A × (r + K × t)
A is the bend rotation angle in degrees, not automatically the inside included angle. For a conventional bend drawing, A = 180° − included angle. r = inside radius; t = material thickness;K = fraction of thickness to the neutral axis from the inside face.
Neutral-axis offset = K × t; neutral-axis radius = r + K × t. For outside flange dimensions, OSSB = tan(A / 2) × (r + t); BD = 2 × OSSB − BA. Evaluate tan with angles converted to radians.
2. Worked checks — 16-gauge mild steel
The site’s mild-steel calculator preset is t = 0.0598 in, r = 0.0598 in and K = 0.42. These are illustrative defaults, not A36 grade-specific test measurements; verify the exact grade, material condition and tooling before production.
| Angle A | K × t | Neutral-axis radius | Bend allowance |
|---|---|---|---|
| 90° | 0.0251 in | 0.0849 in | 0.1334 in |
| 45° | 0.0251 in | 0.0849 in | 0.0667 in |
Calculations are rounded to four decimal places for display. Keep unrounded intermediate values when solving a production flat pattern.
3. Test-coupon verification
- Record the actual material grade, sheet thickness, grain direction, tooling/V-die, bend method, nominal angle and inside radius.
- Bend a representative coupon using the production tooling; measure final angle, radius and flange geometry after springback.
- From the measured coupon’s developed flat length and straight tangent lengths, determine the measured bend allowance. Confirm the same tangent/reference convention is used throughout.
- Back-calculate K = (BA / (A × π / 180) − r) / t using measured BA, measured angle and measured radius; reject implausible results and recheck measurement conventions.
- Recalculate BA and BD using the measured K, make another test bend, compare the resulting formed dimensions and adjust before cutting production blanks.
4. Shop worksheet — blank write-in rows
Write units alongside every measurement. Record the measured BD separately from the formula estimate.
| # | Material | Gauge / thickness | K | Inside r | Angle A | BA | BD |
|---|---|---|---|---|---|---|---|
| 1 | |||||||
| 2 | |||||||
| 3 | |||||||
| 4 | |||||||
| 5 | |||||||
| 6 |
5. Setup and measurement notes
Production caution
This worksheet is a planning aid, not a certified fabrication instruction. Material variation, tooling, grain direction, springback, machine capacity and load ratings must be checked independently. Validate both bend allowance and bend deduction with production-representative coupons.