---
title: "Sag of a Spherical Surface calculator — AperiOptic"
description: "Sagitta of a spherical (or conic) surface from radius and aperture. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/sag-of-a-spherical-surface"
---

# Sag of a Spherical Surface calculator

Sagitta of a spherical (or conic) surface from radius and aperture.

Category: [Aberrations](https://aperioptic.com/calculators)

Formula: `z = c·r²/(1 + √(1 − c²·r²)), c = 1/R`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Radius R | `R` | mm | 100 |
| Half-aperture r | `r` | mm | 12.5 |

## Result with the default inputs

- Sag: 0.7843 mm

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/sag-of-a-spherical-surface?R=100`](https://aperioptic.com/calculators/sag-of-a-spherical-surface?R=100). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Sagitta (optics)](https://en.wikipedia.org/wiki/Sagitta_(optics))

[All optics calculators](https://aperioptic.com/calculators)

---

The interactive page: https://aperioptic.com/calculators/sag-of-a-spherical-surface (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt