🔭 Sagitta Calculator

Mirror curve depth for amateur telescope makers — enter any value, the rest solve live.

Mirror

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Sagitta (editable)

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Type into any field above (or focal length / ratio) to drive the solve. The active driver is highlighted like this.

Results

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Mirror weight by glass type

Uses the edge thickness above. Blank = solid cylinder minus the ground-out bowl.

Cross-section

Concave mirror profile. Depth is exaggerated for visibility — not to scale.
Formulas & notes

With diameter D, radius r = D/2, focal length f, focal ratio F = f/D, radius of curvature RoC = 2f:

Parabolic sagitta = r² / (4f)  ·  Spherical sagitta = RoC − √(RoC² − r²)

Sphere−parabola difference = r⁴ / (8·RoC³) — the extra depth at center needed to turn a sphere into a paraboloid (usually negligible, split between center and edge when figuring).

Correction in waves uses green light (≈ 0.000022 in / 560 nm): difference / 0.000022.

Sagittal volume (spherical cap) = π·s²·(3·RoC − s) / 3. Weight = (cylinder − bowl volume) × glass density.

Center of mass (from the flat back) treats the blank as a uniform solid — the cylinder's centroid at t/2 balanced against the removed bowl, whose spherical-cap centroid sits s(4·RoC − s) / (4(3·RoC − s)) below the front rim.