SAG Calculator

In optics, sag (sagitta) is the depth of a curved lens or mirror surface — the distance from the edge of a circular aperture to the surface's highest point. Enter the radius of curvature and diameter of your optical surface into the SAG Calculator, then select your preferred units, to get the surface sag in millimeters. Secondary outputs include the sag-to-diameter ratio and the F-number equivalent of the surface.

mm

Distance from the surface to the center of curvature

mm

Clear aperture diameter of the optical surface

Results

Surface Sag

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Sag to Diameter Ratio

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F-Number Equivalent

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Frequently Asked Questions

What is surface sag in optics?

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.

How is SAG calculated?

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.

Why is SAG important in optical design?

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.

What's the difference between positive and negative SAG?

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.

How does diameter affect surface sag?

SAG increases with diameter for a given radius of curvature. Larger diameter optical elements require more material thickness and present greater manufacturing challenges.

What units are commonly used for SAG measurements?

SAG is typically measured in millimeters for most optical applications, though micrometers may be used for precision work and inches for larger optical systems.

Can SAG be negative?

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.

How accurate should SAG calculations be?

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.