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Convert candela (cd) to lumens (lm) and lumens to candela using Φ = I × Ω. Set solid angle in steradians—default 4π matches a uniform point source radiating into a full sphere.
Last updated: April 8, 2026
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4π ≈ 12.56637 sr (full sphere). Narrow beams use smaller Ω.
Candela
1 cd
Lumens
12.5663706144 lm
Solid angle
12.5663706144 sr
Quick facts
Formula
lm = cd × Ω (sr)
Formula
cd = lm ÷ Ω
Solid angle
Ω = 4π sr
100 cd at 4π sr (isotropic):
Input
100 cd
Result
1,256.6371 lm
Luminous intensity (candela) describes how bright a source is in a given direction. Luminous flux (lumens) describes total luminous power emitted into a region of space. The bridge is the solid angle Ω in steradians: multiply candela by steradians to get lumens. For a source that is uniform in all directions, integrate over a full sphere: Ω = 4π sr.
lumens (lm) = candela (cd) × Ω (sr)candela (cd) = lumens (lm) ÷ Ω (sr)Isotropic point source: Ω = 4π srNarrow beams use smaller Ω; for cone half-angle θ (radians), Ω = 2π(1 − cos θ) for a right circular cone with apex at the source.
| cd | lm (approx.) |
|---|---|
| 1 | 12.566371 |
| 10 | 125.6637 |
| 100 | 1256.637 |
| 500 | 6283.19 |
| 1,000 | 12566.37 |
Need electrical power too? Lumens to watts converter.
Get Custom Calculator for Your PlatformResult: ≈ 628.3185 lm
Result: 800 lm at 2π sr ≈ 127.3240 cd
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