Mitre & Corner Angle Calculator – Saw Settings & Polygons

Calculate mitre settings from a measured corner angle

This mitre and corner angle calculator converts a clearly defined corner measurement into the setting for a mirrored pair of flat, equal-width pieces. It displays the smaller included angle, the cut-line angle to the long edge and the saw setting from a square crosscut. These values are labelled separately because confusing their conventions is a common source of an incorrect joint.

Use measured-corner mode for a particular joint or regular-polygon mode for an equal-sided frame. Optional stock width gives the one-end long-point to short-point offset and diagonal cut-line length. Optional saw-range and measurement-sensitivity sections add useful checks without making the basic calculation more complicated.

Start with the angle convention

The included angle is the smaller angle between the two board directions extending away from the joint. It must be greater than zero and no more than 180 degrees. A square corner has a 90-degree included angle. A straight continuation is 180 degrees and needs a square cut in this equal-split model.

A reflex angle measures the larger route around the same two directions. It is greater than 180 and less than 360 degrees. Select reflex mode only when that is what your measuring tool or drawing reports. The calculator subtracts the reflex value from 360 to obtain the smaller included angle. A 270-degree reflex corner therefore corresponds to a 90-degree included corner.

“Inside” and “outside” alone are not enough to establish what a gauge displays. Some tools report an angle between arms, some report a supplement, and some calculate a saw setting themselves. Identify the reading convention in the instrument instructions. Do not take a value already labelled as a mitre setting and enter it again as a corner angle.

Why half the angle may not be the saw setting

Dividing the included angle by two gives the angle between the cut line and the long edge of each equal piece. Many mitre-saw scales instead read zero at a square crosscut. On that convention, the setting is 90 degrees minus the half-angle. The calculator uses that zero-at-square convention explicitly.

For a 120-degree included corner, each cut line is 60 degrees to its long edge. The saw setting is 30 degrees from square, not 60 degrees. For a 90-degree included corner, both numbers happen to be 45 degrees, which can hide the distinction until a different corner is measured.

The corresponding two cuts are mirrored. The displayed magnitude does not prescribe a universal left or right swing, because the correct orientation depends on which piece is on which side, its reference face and the keeper side. Mark the pieces and confirm a scrap pair before committing the measured material.

Flat joints and equal widths

This model assumes matching widths meeting in one plane with an equal split. It reports zero bevel tilt for that flat arrangement. It does not calculate compound crown moulding, unequal-width mitres, bevelled boxes or a tilted workpiece. Those cases require additional geometry and an appropriate setup method.

The corner diagram uses two direction lines and a dashed bisector. It explains the included angle rather than showing a physical fence, blade or workpiece clamp. The dashed line represents the equal joint split. It should not be used as a cutting-position illustration for a specific saw.

Regular polygon frames

For a regular polygon with a whole number of sides, the included corner angle is 180 degrees minus 360 divided by the number of sides. The saw setting is therefore 180 divided by the number of sides. A six-sided regular frame has a 120-degree included corner and a 30-degree saw setting.

This angle calculation does not determine frame side lengths, rebates, inner dimensions or stock consumption. All sides and corners must follow the intended regular geometry. An irregular frame needs its individual corner measurements; selecting the same number of sides does not make an irregular shape regular.

Long point and short point offsets

Enable stock-width geometry when the pieces are flat and you need to understand the two ends of a single mitred cut. Enter the actual face width perpendicular to the long edges. The offset equals that width multiplied by the tangent of the saw setting. It is the distance along a long edge between the long and short points of one end.

For 100 mm wide flat stock and a 30-degree saw setting, the one-end offset is approximately 57.735 mm. The diagonal cut line across the face is approximately 115.470 mm. These values describe the same triangle from two directions and exclude the material removed by the blade.

Do not automatically add or subtract twice the offset from an overall piece measurement. The required adjustment depends on whether the two ends slope the same way or opposite ways and whether the specified length is measured long-to-long, short-to-short or along another reference. This calculator deliberately labels its offset as one-end geometry rather than guessing the intended finished length.

Compare the entered saw range

The optional range field accepts the mitre capacity you have checked for your saw and intended direction. The result compares the required magnitude with that number. It does not infer a machine's range from its brand or appearance and does not account for every width, height or bevel capacity restriction.

A setting beyond the entered range is reported as such. The calculator does not prescribe removing guards, overriding stops or using an improvised support arrangement. Consult the instructions for the actual machine and choose a suitable established method for the work.

Measurement uncertainty

If the measured corner could differ by a known number of degrees, enable the uncertainty field. Half of that corner-angle uncertainty transfers to the equal saw setting in this model. A 120-degree included angle with an uncertainty of plus or minus one degree gives a saw-setting range of 29.5 to 30.5 degrees.

This range does not describe saw repeatability, blade deflection or the fit error in millimetres. It only shows how the arithmetic responds to the measured angle. The tool rejects a range that crosses the selected convention boundary, so the result does not silently switch from an included to a reflex interpretation.

Check the calculation against the actual equipment

Manufacturer instructions distinguish simple mitres from compound cuts and explain their angle conventions. See the Bosch angle-measurement manual for an example of tool-specific conventions, and use the manual supplied with your own measuring tool and saw. The calculator supplies geometry, not machine-specific operating instructions.

Keep the reference face and keeper side clear, check the measured corner, and verify a sample pair. A mathematically correct setting can still produce a poor joint if the material is bowed, the surfaces are not coplanar or the saw is out of adjustment. Print the result with a project name to preserve the convention used.

Mitre angle FAQs

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