Solid angle converter
Convert solid angle between steradians and square degrees, the units of how much sky, or how much of a beam, something covers.
That's 5× as wide as a torch beam, while a floodlight is 1.4× wider. That covers about 7.958% of everything around you.
What it means
How wide is that?
A solid angle describes a cone of directions, not an area. The same solid angle covers more surface the further out you go.
Every unit
Your solid angle in every unit
Learn
Three things worth knowing
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1 sr = 3,282.8 square degrees
That is (180/π)². The whole sky is 4π sr, which is 41,253 square degrees, and the full Moon covers only 0.2 of one.
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The steradian is a ratio
It is the area on a sphere divided by the radius squared, so it has no dimensions at all. That is why it disappears from equations as easily as the radian does.
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Square degrees are not degrees squared
A square patch 2° by 2° is 4 square degrees, but a round patch 2° across covers only 3.14. Square degrees measure area on the sky, so shape matters as much as width.
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Popular solid angle conversions
Background
About solid angle
An ordinary angle divides a circle; a solid angle divides a sphere. The whole sphere is 4π steradians, or 41,253 square degrees, so a single steradian is about 8% of everything around you.
It is the unit behind candelas, lumens and every radiation pattern.