By Zencalcy Editorial TeamLast reviewed About us
Sag is the depth of an arc measured from its chord — the sagitta. Optical shops, fabricators and glaziers all need it: it tells you how much material a curved panel takes and whether a mirror blank is deep enough to grind.
Sagitta of a curved surface from radius and chord.
Sag = R − √(R² − (c/2)²)
R is the radius of curvature and c is the chord width. The chord must be no larger than the diameter (2R). For shallow curves the approximation sag ≈ c² ÷ (8R) is within 1%.
| Symbol | Meaning |
|---|---|
| R | Radius of curvature. |
| c | Chord width across the arc. |
| s | Sag depth (sagitta). |
Sag = 20 − √(400 − 25) = 0.639 ft, or 7.67 inches. The arc length is about 10.34 ft.
Continue with the Gravel Calculator, Sand Calculator, Rock Calculator, or the River Rock Calculator — or browse more materials & quantities and all construction calculators.
It is the standard measure of a curved surface's depth: mirror blanks, lens surfaces, curved glass, arched openings and fabricated panels.
Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026