Right-triangle solutions for shop layout. Enter two sides to get the hypotenuse, the remaining angles and the lengths you need to mark out.
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Request a Proposal →The Pythagorean theorem (a² + b² = c²) is the most-used formula in shop math. From checking squareness to calculating bolt circle coordinates, it underpins countless machining and inspection calculations.
The 3-4-5 rule: measure 3 units along one edge, 4 along the perpendicular, and check that the diagonal is 5 units. For machine inspection: measure the diagonals of a rectangular part -- if they are equal, the corners are 90 deg . This works for any rectangle.
For a bolt circle of diameter D with N equally spaced holes: X = (D/2)×cos(angle), Y = (D/2)×sin(angle). Use the Pythagorean theorem to verify that (X² + Y²) = (D/2)² for any hole. The bolt circle calculator handles the full calculation.
The Pythagorean theorem applies only to right triangles (one 90 deg angle). For any triangle, use the law of cosines: c² = a² + b² - 2ab×cos(C). The Pythagorean theorem is the special case where cos(90 deg ) = 0.
Enter any two sides of a right triangle. The calculator gives the hypotenuse and both acute angles. Use this for checking squareness, calculating diagonal distances, finding chamfer lengths, and locating hole positions.
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Use the calculator freely. If the result points to a tooling or process problem, we can source the exact carbide tooling you need from vetted factories in China. Compare factory-direct pricing.
Before you commit to a spec, it helps to know what the market pays for it. These are real, publicly listed factory prices — not a quotation, and not a guess.
We source the tool families below direct from vetted Chinese factories, matched to the material and tolerance you just worked out. Every batch ships with its material certificate and dimensional record.
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WORKING OUT A DIAGONAL? Layout maths feeds straight into a tool drawing, so it is worth being right before you send it. See what a tool shop needs from your drawing.
We source carbide cutting tools from China for job shops. We do not own a factory, which is why we can quote your drawing against two or three plants that actually run your material.
Cutting formulas with the units worked through · Speed and feed starting points for all six ISO material groups · How to read a carbide grade past its ISO code. 12 pages.
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