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Curved Rail and Template Calculator

Calculate circular-arc geometry and five equally spaced template coordinates from a chord and rise.

Prefilled values are examples. Replace them with measurements and current costs for your project.

Inputs

Chord and rise

Range: at least 0.01 in

Range: at least 0.0001 in

Measure the perpendicular distance from the chord midpoint to the circular arc. The chord is the x-axis from the left endpoint (x=0); positive rise is positive y. Use a positive rise; the calculator reports whether the arc is minor, semicircular, or major.

Result

Circular arc length
110.3468 in
Signed circle-center offset from chord midpoint
52.5000 in
Central angle
87.2056°
Circular arc radius
72.5000 in
Arc station 0%: x from left chord end
0.0000 in
Arc station 0%: y from chord
0.0000 in
Arc station 100%: x from left chord end
100.0000 in
Arc station 100%: y from chord
0.0000 in
Arc station 25%: x from left chord end
23.0742 in
Arc station 25%: y from chord
14.8146 in
Arc station 50%: x from left chord end
50.0000 in
Arc station 50%: y from chord
20.0000 in
Arc station 75%: x from left chord end
76.9258 in
Arc station 75%: y from chord
14.8146 in
Minor arc (less than 180 degrees).
Five x/y coordinates are sampled at equal fractions of the arc sweep (0, 25, 50, 75, 100%). x=0 is the left chord endpoint and y=0 is the chord; major-arc points may lie outside the chord span.

Formula

Circular arc radius
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Central angle
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Circular arc length
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Results are planning aids based on the inputs and assumptions shown. Verify dimensions, stock sizes, hardware clearances, kerf, and current prices against your project before cutting or quoting.