Angle Cut Calculator

How to use this angle cut calculator

What this calculator does. This tool turns the outside vertical and horizontal dimensions of a right-angle opening into a complete layout for a diagonal knee brace. It calculates the outside brace length, the two complementary end-cut angles, the corresponding inside-edge dimensions, and two small layout offsets that help transfer the cuts to a plank of known thickness. It is a geometric estimator, not a structural-design approval: it does not size the brace for load, select fasteners, account for defects in lumber, or certify a connection.

When to use it. Use it when laying out a timber knee brace between a post and beam, checking a diagonal support for formwork, preparing a roof or shed brace, or comparing whether an available plank is long enough for a planned opening. The underlying right-triangle relationships follow the NIST explanation of SI length units and standard trigonometry.

How to calculate. The calculator opens with a complete demonstration: a 10 cm plank, a 40 cm vertical leg, and a 44.72135955 cm horizontal leg. The Excel button is ready immediately. To use your own measurements:

1. Select the Measurement unit. If you change units after entering values, the current lengths are converted automatically.
2. Replace Plank thickness (t), Outer part distance (A), and Outer distance (B) with positive decimal measurements. Use a period as the decimal separator; scientific notation and ambiguous decimal commas are rejected.
3. Read Outer length of plank (C) first, then use Angle α and Angle β to set out the two complementary cuts. Review the inner dimensions and Cᴀ/Cʙ offsets in the result cards and schedule.
4. Select Download Excel to export the current typed inputs and calculated values as a real XLSX workbook. Reset clears the demonstration and results; export remains unavailable until all three required dimensions are valid again.

Input guide. Plank thickness (t) is a required positive length in the selected unit; 10 cm is the example. Increasing thickness leaves the outside triangle unchanged but reduces the usable inside edge and increases both layout offsets. Do not enter nominal lumber size when the actual dressed width is different. Outer part distance (A) is the required vertical leg; 40 cm is the example. A larger A makes the brace longer and generally shifts α downward because α is measured relative to the vertical leg. Outer distance (B) is the required horizontal leg; 44.72135955 cm is the example. A larger B increases brace length and α. All three lengths must be finite and greater than zero, and the plank must be narrow enough to leave a positive inner brace length. Measurement unit accepts centimeters, millimeters, or inches and changes display and workbook units without altering the physical geometry.

Output guide. Outer length of plank (C) is the hypotenuse and is an exact geometric identity before display rounding. Angle α is the cut angle associated with the vertical leg, while Angle β is its complement; together they equal 90°. Inner part distance (a) and Inner distance (b) locate the parallel inside edge of the plank. Inner length of plank (c) is the straight inside-edge distance between its two intersections and must stay positive. Length Cᴀ and Length Cʙ are end-layout offsets calculated from plank thickness and the tangent of each angle. A zero or negative inner dimension indicates the plank is too thick for the selected opening.

Worked example. With A = 40 cm and B = 44.72135955 cm, the Pythagorean theorem gives C = √(40² + 44.72135955²) = 60.00 cm. The first angle is α = arccos(40/60) = 48.19°, and β = 90° – 48.19° = 41.81°. For a 10 cm plank, Cᴀ = 10/tan(48.19°) = 8.94 cm and Cʙ = 10/tan(41.81°) = 11.18 cm. The parallel inside edge is 39.88 cm long. These values match the first-open results and exported workbook.