Calculator
What the Solid Angle Converter does
Solid Angle Converter: 1 sr = 3282.80635 deg², so multiply a steradian value by 3282.80635 to get square degree, or divide to go back. Example: 1 sr = 3282.80635 deg².
From Value, From and To, this tool derives Result, How it was calculated and Reverse conversion. Edit a field and the answer updates in place.
Typical users are people following a recipe or spec written elsewhere. Two industries often use the same word for slightly different quantities.
There is no back end here. The calculation runs where you are sitting, not on a server somewhere.
The method, a field-by-field reference and a worked example built from the defaults are all on this page.
What do the Solid Angle Converter fields mean?
The Solid Angle Converter uses 3 inputs. Each input has a default that makes sense on its own, so a partial edit still gives a valid result.
| Field | What to enter | Default |
|---|---|---|
| Value | required | 1 |
| From | choose from Steradian (sr), Millisteradian (msr), Square degree (deg²) or Sphere (full solid angle) (sphere) | Steradian (sr) |
| To | choose from Steradian (sr), Millisteradian (msr), Square degree (deg²) or Sphere (full solid angle) (sphere) | Square degree (deg²) |
How does the Solid Angle Converter work?
Both units are converted through solid angle's base unit (sr), so any of the 4 units in the dropdowns can be paired in either direction without loss of accuracy.
Factors follow the internationally agreed definitions. The inch has been exactly 25.4 mm since 1959, and an exact definition is used wherever one exists. Where a unit is fixed by measurement rather than by agreement, the accepted CODATA or IAU value is used.
Worked example
These are the values the Solid Angle Converter loads by default, and the result it produces from them. Here is the calculation as it stands the moment the page loads.
| Value | 1 |
|---|---|
| From | Steradian (sr) |
| To | Square degree (deg²) |
| Result | 3282.80635 deg² |
|---|---|
| How it was calculated | 1 sr = 3282.80635 deg², so 1 × 3282.80635 = 3282.80635 deg² |
| Reverse conversion | 0.00030461742 sr (if you meant 1 deg²) |
The steradian: angle in three dimensions
The steradian (sr) is the three-dimensional analogue of the radian, instead of measuring an angle along a flat circle, it measures how much of the sky (or of a sphere’s surface, as seen from its centre) a given cone of directions covers. A full sphere covers exactly 4π steradians (about 12.566 sr).
Worth knowing
- A hemisphere, everything visible looking outward from a point on a flat horizon, covers exactly 2π steradians, half the full sphere, following the same logic as the radian dividing a flat circle in half at π radians.
- Solid angle is the natural unit for describing how a light source, antenna or radiation source spreads its output in three dimensions. A spotlight with a narrow beam covers a small solid angle, while a bare bulb radiating in all directions covers the full 4π sr.
- Luminous intensity (candela) and illuminance (lux) are both defined in terms of solid angle, which is why the steradian, despite being an unusual unit in everyday conversation, sits quietly behind several more familiar lighting-related units elsewhere in this converter category.
Definitions: BIPM SI Brochure · NIST reference on units
How to use it
- Fill in Value.
- Pick a value for From: the options are Steradian (sr), Millisteradian (msr), Square degree (deg²) or Sphere (full solid angle) (sphere).
- Pick a value for To: the options are Steradian (sr), Millisteradian (msr), Square degree (deg²) or Sphere (full solid angle) (sphere).
- Live output means you can search for a target value by nudging an input up and down.
- The panel reports Result, How it was calculated and Reverse conversion.
- Copy Link is the quickest way to send the exact scenario to someone else.
What this tool does not do
- Repeated conversions compound rounding, so convert once from the original value where you can.
- Conversion factors use SI definitions; some industries use their own rounded factors.
- The result reflects the moment you ran it; anything that changes over time is not tracked.
- Confirm the units before you act on the output. The arithmetic is only as sound as what went in.
Frequently asked questions
3 things: Value, From and To. Nothing starts empty, which makes it easy to isolate the effect of a single variable.
With the values loaded when the page opens, result comes out as 3282.80635 deg². Any edit re-runs the calculation, so there is no stale number on screen.
No. There is no upload step, no database, and nothing to delete afterwards.
Nothing at all. There is no registration, no paywall and no per-use quota.
It implements the published definition directly, without shortcuts or approximations.