A scarf splice is a long taper that joins two pieces end to end. Length along the board is thickness times the ratio you pick. The cut angle from that long edge is atan(1/ratio) in degrees. 8:1 is the usual shop scarf; 12:1 is the longer structural taper. Layout only — not a glue spec.
Use it when a part has to be longer than your stock — a gunwale, a long handrail, a curved stringer, a laminated spar — and you plan to splice two pieces end to end with a glued taper.
Enter the stock thickness and the slope ratio; the page gives the length of the taper and its angle, so you can lay out the cut or set a jig. Longer tapers such as 8:1 and 12:1 give more glue area and a stronger joint; short ones such as 4:1 suit trim and low-stress work.
Lay the board on its long axis. From one end, measure a distance equal to thickness times the ratio, then draw a line from that mark down to the far corner of the end grain. That line is the cut. The triangle is thickness (opposite) by scarf length (adjacent). This page reports the length along the board, not the hypotenuse of the cut face.
L = t × ratio
θ° = atan(1 / ratio) × 180 / π from the long edge
Complement from square = 90° − θ°
Face along the cut (hypotenuse) = t × √(ratio² + 1) — shown for marking, not as a glue area.
The angle does not depend on thickness: an 8:1 scarf is always about 7.1° from the long edge, whether the stock is ¾ in or 38 mm. Thickness only scales the length you mark. This is layout arithmetic. It does not choose a glue, a clamp pressure, a feathered tip, or a hook / keyed / plywood variant.
| Stock × ratio | Length | Angle from long edge |
|---|---|---|
| 1 in at 8:1 | 8 in | 7.1° |
| 1.5 in at 8:1 | 12 in | 7.1° |
| 1.5 in at 12:1 | 18 in | 4.8° |
| 0.75 in at 8:1 | 6 in | 7.1° |
| 25 mm at 8:1 | 200 mm | 7.1° |
| 20 mm at 8:1 | 160 mm | 7.1° |
Those rows come from L = t × ratio and θ = atan(1/ratio) × 180/π, then rounded to one decimal on the angle. 1.5 × 8 is exactly 12 in; atan(1/8) is 7.125…°, which displays as 7.1°. 12:1 is atan(1/12) = 4.764…° → 4.8°.
The joint is eight times as long as the stock is thick. On 1.5 in material that is a 12 in mark along the board and a 7.1° cut from the long edge. It is the usual shop ratio for furniture repairs, trim splices, and general solid-wood work. It is a starting layout, not a code minimum.
When the splice is asked to carry more load or to bend more like solid stock — beams, long rails, and similar shop glue-ups. This is not boat-spar engineering. Same thickness, longer glue line: 1.5 in stock becomes an 18 in scarf at 4.8°. This page will compute any custom N:1 you type. It still does not certify the joint.
Most miter saws and bevel gauges read 0° when the blade is square to the long edge. For an 8:1 scarf you swing or tilt 7.1° off that square stop. 82.9° is the complement (90 − θ), the angle of the cut relative to the end grain. Mixing those two numbers is how a scarf becomes a steep ramp. The calculator prints both.
Along the board — the adjacent side of the triangle, t × ratio. That is what you mark with a square and a tape. The cut face is a hair longer (the hypotenuse). On the 1.5 in / 8:1 check that face is 12.09 in. Use the board length to lay out; the face length is only there so the two numbers are not confused.
Out of scope. A hooked or keyed scarf adds a step or key after you have this taper. Plywood panel scarfs often use a jig on a circular saw or router and may run 8:1 or 12:1 across the sheet thickness. Mark those variants from a drawing once the basic L and θ are on the stock.
No. Species, adhesive, clamp pressure, feathered tips, and grain at the joint decide whether the splice holds. This calculator only sizes the taper. A longer ratio makes more face, which is why 12:1 shows up on structural work — that is still a layout choice, not a glue schedule.