Enter the radius of curvature and the diameter into the calculator to determine the SAG (Sagitta).

SAG Formula

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

SAG = R – SQRT ( R^2 – (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?


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?


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 = .7843