Convert candela and steradians into lumens, with reference rows for narrow beams, hemispheres, and full-sphere output. Use it to test different inputs quickly, compare outcomes, and understand the main factors behind the result before moving on to related tools or deeper guidance.
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Luminous flux from intensity and solid angle Candela measures intensity in a direction. Lumens measure total luminous flux across a
chosen solid angle. This worksheet keeps the formula visible so you can see how beam spread
changes the total light output.
Candela to lumens calculator: convert luminous intensity and solid angle into luminous
A candela to lumens calculator is only useful if it keeps the beam geometry visible. Candela measures luminous intensity in a direction, while lumens measure total luminous flux across a chosen solid angle. This page converts candela and steradians into lumens, shows the underlying formula, and adds reference cases such as a 1 steradian beam, a hemisphere, and a full-sphere distribution so the result is easier to interpret.
What candela and lumens measure
Candela and lumen are related SI photometric units, but they describe different things. Candela measures luminous intensity in a given direction. Lumen measures luminous flux, which is the total light output flowing through a specified solid angle. That is why you cannot convert candela to lumens without also knowing the solid angle in steradians.
This distinction matters in real lighting work because two sources can share the same candela value while producing different total lumens if the light is spread across different beam widths. A narrow beam concentrates intensity; a wider beam spreads the same intensity across more solid angle and therefore corresponds to more total flux.
How the candela-to-lumens formula works
The conversion itself is straightforward once the solid angle is known. Luminous flux in lumens equals luminous intensity in candela multiplied by the solid angle in steradians. If the angle doubles while candela stays the same, the lumen value also doubles.
This is why a proper candela to lumens calculator should not hide the steradian input. The real interpretation comes from seeing both the intensity and the angular spread together rather than treating lumens as if they came from candela alone.
Converts directional light intensity into total luminous flux across the chosen solid angle.
Full sphere = 4π sr, hemisphere = 2π sr
Useful reference solid angles when comparing directional beams with broad or omnidirectional emission.
Worked examples and reference cases
If a source has an intensity of 100 candela across 1 steradian, it corresponds to 100 lumens. If the same 100 candela is spread across a hemisphere, or about 6.283 steradians, it corresponds to about 628.3 lumens. Across a full sphere, or about 12.566 steradians, it corresponds to about 1,256.6 lumens.
Those examples show why beam spread changes interpretation so much. The same candela value can represent a very different total light output depending on how narrowly or broadly the source distributes light. The reference sheet on this page is meant to make that relationship obvious at a glance.
This page converts between candela, steradians, and lumens only. It does not determine beam angle from fixture geometry, it does not calculate lux at a distance, and it does not model luminous efficacy or electrical power. Those are separate lighting questions that need different inputs and formulas.
It also assumes the entered solid angle is already correct. If the steradian estimate is wrong, the lumen output will be wrong as well. Use it as a transparent unit-and-relationship worksheet, not as a full optical design tool.
Further reading
BIPM — SI base units — Official SI reference page covering the candela as an SI base unit.
NIST — SI Units — Official NIST overview of SI units and the structure of base and derived units.
Frequently asked questions
Can I convert candela to lumens without steradians?
No. Candela alone is not enough because lumens depend on both intensity and solid angle. You need the steradian value, or enough beam information to derive it, before the conversion can be completed.
Why does the same candela value produce different lumens?
Because candela measures intensity in a direction, while lumens measure total flux across a solid angle. If the same intensity is spread across a larger angular region, the total lumen value increases proportionally.
What are 2π and 4π steradians used for?
They are common reference solid angles. A hemisphere is 2π steradians and a full sphere is 4π steradians. Those reference cases are useful when comparing directional beams with broad or nearly omnidirectional light output.
Is this the same as converting candela to lux?
No. Lux depends on illuminance at a surface and usually requires distance or area information. Candela to lumens uses solid angle instead, so it answers a different lighting question.
