Calculate spherical or pure-conic optical sag, circular-arc geometry, parabolic cable sag, or suspension target sag. Cable supports must be at equal height; suspension uses fork travel or rear-shock stroke with a manufacturer-specific target.

Geometry and ideal-model estimates only. Cable mode uses equal-height supports and a parabolic load model; it cannot establish safe cable capacity.

SAG Formula

The following formula is used to calculate the SAG of an optic.

SAG = R - SQRT (R² - (D / 2) ^ 2)
  • Where SAG is the arc height of the optics
  • R is the radius of curvature
  • D is the diameter of the curve

What is SAG?

Definition:

SAG is a term used in optics to describe the distance or length between the vertex point along the curve and the center point of a line drawn perpendicular to the curve from one edge to the other.

This is used mostly in optics when dealing with convex or concave curvatures of lenses.

How to calculate SAG?

Example:

The following example problem outlines how to calculate the SAG of an optical lens.

First, determine the radius of curvature. In this example, the radius of curvature is measured to be 100 mm.

Next, determine the diameter of the vertex. In this example, the diameter is measured to be 25 mm.

Finally, calculate the SAG using the formula above:

SAG = R - SQRT ( R^2 - (D/2) ^ 2 )

SAG = 100 - SQRT ( 100^2 - (25/2) ^ 2 )

SAG ≈0.784326 mm (exact spherical minor-cap result). The paraxial estimate D²/(8R) is 0.78125 mm. Circular-arc modes distinguish minor and major segments. Pure-conic mode uses K with no higher-order aspheric terms. Cable mode uses S =wL²/(8H) and support tension √(H²+(wL/2)²), with uniform load per horizontal length; this is not an exact self-weight catenary. Suspension target sag equals travel/stroke × target%/100; do not use rear-wheel travel to interpret shock-shaft measurements.