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Complementary Board Cut Geometry

Relate board thickness, complementary angles and the short/long edge lengths of a planar joint.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 3 cm board thickness at a 30° cut gives a 6 cm plank projection and a complementary 60° angle. A 4 cm short edge then corresponds to a 10 cm long edge.

Alpha+beta = 90°; thickness = plank projection×sin(angle); long-minus-short edge equals its plank projection.

Worked example

Enter these known values and leave the other values blank.

Plank thickness (t): 3 cm
Angle α: 30 deg
Inner part distance (a): 4 cm

Outer part distance (A): 10 cm
Knee side (aₚ): 6 cm
Outer distance (B): 5.774 cm
Inner distance (b): 2.3094 cm
Knee side (bₚ): 3.464 cm
Angle ß: 60 deg
Outer length of plank (C): 11.547 cm
Inner length of the plank (c): 4.619 cm
Length Cᴀ: 5.196 cm
Length Cʙ: 1.732 cm

Assumptions and limitations

Angles are positive and strictly below 90°. This is two-dimensional cut geometry, without saw kerf, blade bevel, tool calibration or structural approval.
Use compatible measurement units. Clear an unknown before solving for it, and lock independent known values when comparing changes. Currency choices label amounts without exchange-rate conversion.

Common questions

Can I solve backward from the result?

Clear the unknown and enter independent known values. A rounded whole count cannot uniquely recover a continuous dimension; keep the original measured dimensions for procurement planning.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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