1D NESTING

Miter Cut Length Optimizer with 45° Complementary Flip

Long-point lengths, 45°, 30° and 60° ends and the profile width in; trapezoid pieces, shared cuts and the flip OFF vs ON saving out.

Examples
Bars to buy5 bars
Material yield96.0%
Purchase cost$290.00
Saw cuts · kerf loss25 cuts · 88.4 mm
Offcuts ≥ threshold0 reusable
Lower bound: 5 barsOptimalExact search28800 mm of parts from 30000 mm of stock20 of 20 pieces placed

45° flipFlip OFF: 6 bars · 80.0% · 40 cuts | Flip ON: 5 bars · 96.0% · 25 cutsSaves 1 bar · 15 cuts · $58.00

PieceKerfReusable offcutScrap, trim, miter wedgeStop mark

6063-T5 window profile 60 mm5 bought · 0 from inventory · 96.0%

Bar 16000 mm96.0% yielddrop 155.9 mm · scrap
W2-1 · 1500 mm · 45°/45°W2-2 · 1500 mm · -45°/-45° · turned overW2-3 · 1500 mm · 45°/45°W2-4 · 1500 mm · -45°/-45° · turned over050010001500200025003000350040004500500055006000 mmW2-1W2-2W2-3W2-4

Stops 1510 · 2953.5 · 4397.1 · 5840.6 mm

Bar 26000 mm96.0% yielddrop 155.9 mm · scrap
W2-5 · 1500 mm · 45°/45°W2-6 · 1500 mm · -45°/-45° · turned overW2-7 · 1500 mm · 45°/45°W2-8 · 1500 mm · -45°/-45° · turned over050010001500200025003000350040004500500055006000 mmW2-5W2-6W2-7W2-8

Stops 1510 · 2953.5 · 4397.1 · 5840.6 mm

Bar 36000 mm96.0% yielddrop 155.9 mm · scrap
W2-9 · 1500 mm · 45°/45°W2-10 · 1500 mm · -45°/-45° · turned overW2-11 · 1500 mm · 45°/45°W2-12 · 1500 mm · -45°/-45° · turned over050010001500200025003000350040004500500055006000 mmW2-9W2-10W2-11W2-12

Stops 1510 · 2953.5 · 4397.1 · 5840.6 mm

Bar 46000 mm96.0% yielddrop 155.9 mm · scrap
W1-HS-1 · 1800 mm · 45°/45°W2-13 · 1500 mm · -45°/-45° · turned overW2-14 · 1500 mm · 45°/45°W1-J-1 · 1200 mm · -45°/-45° · turned over050010001500200025003000350040004500500055006000 mmW1-HS-1W2-13W2-14W1-J-1

Stops 1810 · 3253.5 · 4697.1 · 5840.6 mm

Bar 56000 mm96.0% yielddrop 155.9 mm · scrap
W1-HS-2 · 1800 mm · 45°/45°W2-15 · 1500 mm · -45°/-45° · turned overW2-16 · 1500 mm · 45°/45°W1-J-2 · 1200 mm · -45°/-45° · turned over050010001500200025003000350040004500500055006000 mmW1-HS-2W2-15W2-16W1-J-2

Stops 1810 · 3253.5 · 4697.1 · 5840.6 mm

Buy list

  • 5 × 6000 mm · $290.00

Drops (offcuts)

  • Bar 1 · 155.9 mm · scrap
  • Bar 2 · 155.9 mm · scrap
  • Bar 3 · 155.9 mm · scrap
  • Bar 4 · 155.9 mm · scrap
  • Bar 5 · 155.9 mm · scrap

Free proof files

Check it, share a proof

Shop-floor files PRO7 days · $4.99

Examples

Mitered jobs to start from

Window frames, a three-size picture frame batch and truss braces with 60° and 30° ends.

Aluminum window & picture frame 45° miter job

20 mitered pieces, W 60 mm, flip ON. Buy 5 × 6000 mm.

Bars
5
Yield
96.0%
Cost
$290.00
Cuts
25

Picture frame moulding batch

8×10, 11×14, 16×20 on 8 ft moulding. Buy 4 × 8 ft.

Bars
4
Yield
92.4%
Cost
$110.00
Cuts
28

Truss diagonal braces with 60°/30° ends

2" tube, 24 ft, 60° and 30° ends. Buy 5 × 24 ft.

Bars
5
Yield
82.5%
Cost
$520.00
Cuts
35

How to use it

Nest mitered pieces in five steps

  1. Enter the profile width W W is the face width the saw cuts through, measured across the fence face. It sets how far a mitered end reaches: d = W · cot a.
  2. Type long-point lengths Measure tip to tip on the fence face. For a frame, that is the outside dimension of each side.
  3. Choose both end angles 90 is square. 45 makes a frame corner; 60 and 30 lean less and more. A negative angle leans the other way for parallelogram braces.
  4. Decide on flip Flip ON lets the planner turn pieces over so neighbours share one cut. Only for profiles that look the same from both faces.
  5. Read the comparison strip Above the canvas, Flip OFF vs Flip ON shows bars, yield and cuts for the same list, so you see what the switch is worth.

Geometry

Long point, short point and centerline

long point L = 1800 mm (fence face)short point = L − 2d = 1680 mmcenterline = L − d = 1740 mmd = W · cot 45° = 60 mmW 6045°
Window head piece: 1800 mm long point, profile 60 mm wide, 45° at both ends, fence face up.

A mitered piece has three lengths. The long point is what you measure on the fence face and what this tool asks for. The short point is the far face, shorter by one end offset d at each angled end. The centerline sits halfway and is the length counted in yield.

d = W · cot a  ·  centerline = L − (dleft + dright) / 2

For a 60 mm profile at 45°, d is 60 mm, so the 1800 mm head has a 1740 mm centerline and a 1680 mm short point. At 60° d shrinks to 34.6 mm; at 30° it grows to 103.9 mm.

Kerf on angles

Along-axis kerf: k / sin a

End angle aFactor 1 / sin a3 mm blade1/8" bladeEnd offset d, W 60 mm
90° (square)1.0003.00 mm0.125 in0.0 mm
60°1.1553.46 mm0.144 in34.6 mm
45°1.4144.24 mm0.177 in60.0 mm
30°2.0006.00 mm0.250 in103.9 mm
Plane geometry: a slot of width k crossing the bar at angle a is k / sin a long along the axis.

The window preset uses a 2.5 mm blade. With flip OFF its 40 cuts lose 141.4 mm; with flip ON the 25 cuts lose 88.4 mm, because each shared junction replaces two angled cuts with one.

Worked example

Window frames: 15 shared junctions, one bar saved

ΔL = W · tan 45° = 60 mm per shared junction  ·  15 × 60 mm = 900 mm

20 pieces, 45°/45°, 6000 mm barsFlip OFFFlip ON
Bars65
Saw cuts4025
Yield80.0%96.0%
Cost at $58 per bar$348.00$290.00
Reusable drops40

Every 1500 mm casement side fits four to a bar when its neighbours share cuts. Without flipping, each junction wastes a 60 mm triangle plus an extra cut, and the fourth piece no longer fits. The engine reports this as Saves 1 bar · 15 cuts · $58.00.

Picture frames

Flip on a three-size frame batch

Flip OFF: 5 sticks · 48 cuts · 74.0%

Bar 1 8 ft · 6 pieces · 88.3% · drop 11/16" scrap

F16S-1 · 19 1/8" · 45°/45°F16S-2 · 19 1/8" · 45°/45°F11L-1 · 17 1/8" · 45°/45°F11S-1 · 14 1/8" · 45°/45°F8L-1 · 13 1/8" · 45°/45°F8S-1 · 11 1/8" · 45°/45°01'2'3'4'5'6'7'8 ftF16S-1F16S-2F11L-1F11S-1F8L-1F8S-1

Flip ON: 4 sticks · 28 cuts · 92.4%

Bar 1 8 ft · 8 pieces · 95.8% · drop 9/16" scrap

F11S-1 · 14 1/8" · 45°/45°F11S-2 · 14 1/8" · -45°/-45° · turned overF11S-3 · 14 1/8" · 45°/45°F8L-1 · 13 1/8" · -45°/-45° · turned overF8L-2 · 13 1/8" · 45°/45°F8L-3 · 13 1/8" · -45°/-45° · turned overF8S-1 · 11 1/8" · 45°/45°F8S-2 · 11 1/8" · -45°/-45° · turned over01'2'3'4'5'6'7'8 ftF11S-1F11S-2F11S-3F8L-1F8L-2F8L-3F8S-1F8S-2
8 × 10, 11 × 14 and 16 × 20 frames, four of each side, on 8 ft walnut moulding 1 1/2" wide. First stick of each plan.

The saving only applies to stock that is symmetric across its width, such as flat cap moulding or reversible strip. A rabbeted moulding must keep its back edge on the long point of every piece, so neighbours cannot share a cut: turn flip off for it, and the OFF plan above is the real one.

Limits

30° and 60° ends, and when not to flip

Steeper ends reach further. A 30° end on a 2 inch tube reaches 3.46 inches along the bar, so truss diagonals and stair braces interlock well when flipped. On the truss preset the bar count stays at 5, yet flipping still removes 24 cuts, which is saw time and blade wear.

Do not flip profiles whose faces differ: thermal-break windows, one-side-painted or laminated bars, sections with a glazing bead groove on one side. Leave the switch off, and the planner keeps every piece fence face up.

Where it fits

Jobs with angled ends

Picture and display frames

Four 45° sides per frame on 8 ft stock; on symmetric strip, flipping saved a whole stick on the three-size batch.

Aluminum windows and doors

Head, sill and jambs at 45°. Keep flip off for thermally broken or one-side-painted sections.

Aluminum profile calculator

Truss webs and knee braces

Square tube with 60° and 30° ends, where shared cuts mostly save saw time rather than bars.

Fractions and stop marks

Handrail and guard frames

Steel tube frames with mitered corners and square posts in the same list.

Steel bar nesting

FAQ

Miter and flip questions

Do I enter the long point or the short point?

The long point, measured tip to tip along the fence face. For a frame side that is the outside dimension. The planner derives the centerline (L − d for two 45° ends) and the short point (L − 2d) from W and the angles, so do not subtract anything yourself.

Which number is the angle: 45 or what my saw scale says?

The angle here is between the cut face and the bar's long edge, so 90 is a square cut. A saw scale usually reads degrees away from square: if the scale says 30, enter 60; if it says 60, enter 30; 45 is 45 either way. The planner offers 90, 60, 45 and 30, the angles frames, braces and trusses use most.

What does a negative angle mean?

It sets the lean direction. Positive ends lean so the fence face is the longest edge, the classic frame trapezoid. A negative end leans the other way. +45 on one end with −45 on the other gives a parallelogram, as used for stair stringer braces.

How much does one shared cut save?

One end offset, d = W · cot a, plus one kerf. At 45° that is W · tan 45° = W, so 60 mm per shared junction on a 60 mm profile. The window preset shares 15 junctions, which is 900 mm, enough to drop from 6 bars to 5.

When should I not flip pieces?

When the two faces differ. Thermally broken window sections, profiles painted or laminated on one side, bead grooves, and asymmetric T-slot covers must stay face up, so turning them over would put the wrong face outside. Leave Complementary miter flip off for those.

Why does an angled cut lose more kerf than a square one?

The blade still removes k across its own width, but along the bar axis the slot is k / sin a wide. A 3 mm blade takes 3.00 mm at 90°, 4.24 mm at 45° and 6.00 mm at 30°. The planner uses the along-axis value for every angled cut.

Same engine, six tools

Pick the cut planner for your material