Cable tray bend formulas: 90, 45 and any angle
All the maths the calculator uses, for a 90 degree bend, a 45, or anything in between. The formulas are simple — a phone calculator is enough. Below: where they come from, worked examples, and a one-page cheat sheet you can print or save as a PDF in one tap — no sign-up.
Where the cut-out formula comes from
When tray is bent, the outer edge keeps its length while the inner edge has to get shorter — otherwise the metal has nowhere to go. That difference is the cut. Geometrically, a wedge whose apex angle equals the turn angle sits on the tray width: half the opening is to the width as the tangent of half the angle. That gives the main formula.
Why the angle is halved
The wedge is symmetrical about the bend line: half goes left, half goes right. Each half is a right triangle with one leg equal to the tray width and an angle equal to half the turn. The tangent of that angle gives the other leg — the cut on one side.
The allowance on offsets
For an offset, the spacing between notches is not the plain diagonal. Each notch removes a wedge, and as it folds the bend line draws inward by exactly one cut. So the cut is added to the diagonal — otherwise the second turn lands short and the run never reaches the line you planned.
Symbols
- W
- tray width, mm
- H
- side height, mm
- θ
- turn or bend angle, degrees
- L
- cut each way from the bend line, mm
- O
- sideways offset, mm
- ΔH
- change in height, mm
- R
- arc radius at the centre of the run, mm
- n
- number of notches on the arc
Horizontal turn
Cut in the base, each way from the bend line. Full opening is 2L.
300 mm tray at 45°: L = 300 · tan(22.5°) = 300 · 0.4142 = 124 mm
Vertical bend
Same again, but the side height sets the size. Both sides are cut.
60 mm side at 45°: L = 60 · 0.4142 = 25 mm
Sideways offset
D is the diagonal. The cut is added to it as the allowance for removed metal.
250 mm offset at 45° on 300 mm tray: D = 250 / 0.7071 = 354 mm, centres 354 + 124 = 478 mm
Change between levels
The horizontal reach is ΔH / tan θ.
250 mm rise at 45°: length = 250 / 0.7071 = 354 mm
Arc from segments
Φ is the full arc angle. Deviation from a true circle: (R + W/2) · (1 − cos(θ/2)).
Ø2000, 300 mm tray, 90° in 6 notches: θ = 15°, L = 39 mm, pitch = 300 mm, deviation 10 mm
Tangent of half the angle — for working it out by hand
Multiply the tray width by the number from the table to get the cut on one side.
| Angle | tan(θ/2) | 100 | 200 | 300 | 400 |
|---|---|---|---|---|---|
| 15° | 0.1317 | 13 | 26 | 39 | 53 |
| 22.5° | 0.1989 | 20 | 40 | 60 | 80 |
| 30° | 0.2679 | 27 | 54 | 80 | 107 |
| 45° | 0.4142 | 41 | 83 | 124 | 166 |
| 60° | 0.5774 | 58 | 115 | 173 | 231 |
| 90° | 1.0000 | 100 | 200 | 300 | 400 |