Cutting & joints
Mitre long point / short point
- where
- each end difference (mm)
- face width (mm)
- saw angle from square (°)
- long-edge length (mm)
- short-edge length (mm)
Explain this equation
Converts between the short-edge and long-edge length of a piece mitred at both ends, for example a frame member or architrave head.
S is the length along the short edge and w the face width of the piece, both in millimetres. θ is the saw angle from square. Δ is how much longer the long edge is at each end. L is the long-edge length.
Across the face width the mitre line rises by w tan θ. That is the extra length on the long edge at one end. With both ends mitred outward, the long edge gains twice that.
At 45°, tan θ = 1, so each end adds the full face width. A 500 mm short edge on 70 mm stock becomes 640 mm long point. At 22.5° each end adds only about 29 mm.
Watch out: θ is the saw angle from square, not the included corner angle. Both ends must slope out towards the same edge.
Convert between edge lengths for matching mitres at both ends.
Enter your values to see the result.
Good to know
Both ends slope outward to the same long edge. Saw angle is from square, not the included corner angle.
Sources
- Geometry / arithmetic
This is a calculation aid, not a structural design or compliance certificate. Every default is an example, not a specification for your project.