---
title: "Solid Angle ↔ Cone calculator — AperiOptic"
description: "Convert solid angle (sr) to half-cone angle and vice versa. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/solid-angle-cone"
---

# Solid Angle ↔ Cone calculator

Convert solid angle (sr) to half-cone angle and vice versa.

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

Formula: `Ω = 2π(1 − cosθ)`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Half-cone angle | `th` | deg | 10 |

## Result with the default inputs

- Solid angle: 0.0955 sr
- msr: 95.4557 msr
- Full cone: 20 °

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/solid-angle-cone?th=10`](https://aperioptic.com/calculators/solid-angle-cone?th=10). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Solid angle](https://en.wikipedia.org/wiki/Solid_angle)

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

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