Right triangle calculator
Enter any two values and the rest are calculated. The legs are labeled along the machine axes — along the axis (Z) and along the radius (X) — so the result maps straight onto coordinates.
Quick answer
Leg along the axis a (Z), radial leg b (X), angle to the axis α: b = a × tan α, c = a / cos α. Example: a = 10 mm, α = 30° → b ≈ 5.774 mm on the radius (11.547 on the diameter), hypotenuse c ≈ 11.547 mm.
- Angle to the face β, °
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- Diameter change 2b, mm
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Who needs it and why
Almost any missing dimension on a drawing is a right triangle: you have an angle and one size and need another.
- A missing drawing dimension — a slope, a transition, an angled undercut.
- Point coordinates — where an angled section ends in Z and X.
- Setting the compound — on a manual lathe: the angle and the travel along the hypotenuse.
- Checking — verify dimensions worked out elsewhere.
Common cases have their own calculators with ready G-code:chamfer and radius,taper.
The formulas
c = √(a² + b²)b = a · tan α, a = c · cos α, b = c · sin αβ = 90° − α— the angle to the face