SAG Calculator
Determine the sagitta (sag) depth of any curved surface. Input the radius of curvature and chord length in inches, feet, millimeters, or meters to calculate how much the surface deviates from a straight line.
The radius of the circular arc or curve
The straight-line distance across the surface at its widest point
What is sagitta (sag) in geometry?
Sagitta (Latin for arrow) is the distance from the midpoint of a circular arc to the midpoint of its chord. In practical terms, it measures how much a curved surface deviates from a straight line across its width. The sagitta is used in optics for lens curvature, in construction for arched openings, in engineering for cable sag calculations, and in woodworking for bending forms.
How is sag calculated?
Sagitta is calculated using the formula: s = R - √(R² - (L/2)²), where s is the sagitta, R is the radius of curvature, and L is the chord length (total width). For example, a surface with a 120in radius and 48in chord: s = 120 - √(14400 - 576) = 120 - √13824 = 120 - 117.58 = 2.42 inches. This works for any consistent unit system.
What is the difference between sag and camber?
Sag and camber describe opposite curvatures. Sag (or sagitta) measures the inward curvature or dip of a surface relative to its chord, like a cable hanging between two poles or a concave lens surface. Camber measures the outward bow or crown of a surface, like a road arch for drainage or a convex lens. Both use the same mathematical formula but in opposite directions.
What are practical applications of sagitta calculations?
Sagitta calculations are used in: Optics — determining lens curvature and focal length. Construction — designing arched windows, doorways, and arched bridges. Electrical — calculating cable sag between utility poles. Woodworking — creating bending forms for curved furniture. Metalworking — measuring deflection in beams and panels. Astronomy — calculating mirror curvature for telescopes. Awning and sign manufacturing — estimating fabric stretch over frames.