Enter your lens or mirror's Radius of Curvature and Diameter, choose your Units, and the SAG Calculator works out the Surface Sag — how deep your curved surface dips from edge to center — along with the Sag to Diameter Ratio and F-Number Equivalent.
Surface Sag
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Sag to Diameter Ratio
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F-Number Equivalent
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Surface sag is the distance from the optical surface to a plane perpendicular to the optical axis at the edge of the clear aperture. It represents how much the curved surface deviates from a flat surface.
SAG is calculated using the formula: SAG = R - √(R² - (D/2)²), where R is the radius of curvature and D is the diameter. This formula comes from the geometry of a spherical surface.
SAG determines the thickness variation across an optical element and affects manufacturing requirements, mounting considerations, and optical performance. It's critical for lens design and fabrication planning.
Positive SAG occurs with convex surfaces (shorter radius), while negative SAG occurs with concave surfaces. The sign indicates the direction of curvature relative to the optical axis.
SAG increases with diameter for a given radius of curvature. Larger diameter optical elements require more material thickness and present greater manufacturing challenges.
SAG is typically measured in millimeters for most optical applications, though micrometers may be used for precision work and inches for larger optical systems.
Yes, SAG can be negative for concave surfaces where the center of the surface is recessed relative to the edges. The calculator handles both positive and negative curvatures.
SAG calculations should typically be accurate to at least 4 decimal places for precision optics. Manufacturing tolerances and measurement capabilities determine the required precision level.