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Convert luminous intensity to total light output with beam angle
Lumens = Candela × Solid Angle (Ω)
Ω = 2π × (1 - cos(θ/2))
Where θ is the beam angle in radians. For a 60° beam, Ω = 0.8418 steradians
| Beam Angle | 100 cd | 500 cd | 1,000 cd | 5,000 cd |
|---|---|---|---|---|
| 10° (Narrow spot) | 2.4 lm | 12.0 lm | 24.0 lm | 120.1 lm |
| 20° (Spot) | 9.5 lm | 47.4 lm | 94.8 lm | 474.0 lm |
| 30° (Narrow flood) | 21.4 lm | 106.8 lm | 213.6 lm | 1,068.0 lm |
| 40° (Flood) | 37.7 lm | 188.7 lm | 377.4 lm | 1,887.0 lm |
| 60° (Wide flood) | 84.3 lm | 421.5 lm | 843.0 lm | 4,215.0 lm |
| 90° (Very wide) | 157.1 lm | 785.4 lm | 1,570.8 lm | 7,854.0 lm |
| 120° (Omnidirectional) | 282.7 lm | 1,413.7 lm | 2,827.4 lm | 14,137.2 lm |
| 180° (Full sphere) | 628.3 lm | 3,141.6 lm | 6,283.2 lm | 31,416.0 lm |
Candela (cd) measures luminous intensity - the brightness in a specific direction - while lumens (lm) measure total light output in all directions. Think of candela as a focused beam's strength and lumens as the total light energy produced. A laser pointer might have high candela in one direction but few total lumens, while a standard light bulb has moderate candela but high lumens spread over wide angles. Converting between them requires knowing the beam angle or solid angle (measured in steradians). For a uniform light source within a cone, lumens equal candela multiplied by the solid angle. This relationship is crucial for spotlight specifications, architectural lighting design, and understanding how directional fixtures compare to omnidirectional bulbs. A 1,000 cd spotlight with a 60° beam produces 843 lumens, but the same candela with a 10° beam only produces 24 lumens.
No, the beam angle is essential because candela measures intensity in one direction while lumens measure total output. The same candela rating produces vastly different lumens depending on beam spread. A 1,000 cd spotlight with 10° beam produces only 24 lumens, while the same candela with 60° produces 843 lumens. Without beam angle, conversion is impossible. Some manufacturers specify both values.
Traditional incandescent and omnidirectional LED bulbs emit light in nearly all directions (approximately 300-360° total coverage, or 180° hemisphere for bulbs with bases). Standard LED spotlights range from 25-40°, floods are 40-60°, and wide floods exceed 60°. Track lighting typically uses 25-40° beams, while accent lights may be as narrow as 10-15°. Always check specifications as "flood" and "spot" aren't standardized terms.
High-performance flashlights emphasize candela because users care about beam intensity at distance (throw) more than total light output. A 50,000 candela tactical flashlight can illuminate objects hundreds of meters away, while a 1,000 lumen lantern with wide beam might only reach 50 meters despite higher total output. Candela indicates the concentrated brightness, while lumens represent overall efficiency. Professional specifications include both values.
Narrower beams appear brighter at the center because the same lumens are concentrated into smaller areas, increasing illuminance (lux). A 1,000 lumen spotlight with 10° beam creates intense brightness in a small spot, while the same lumens in a 60° flood provides moderate illumination over a larger area. This is why spotlights are used for accent lighting and floods for general illumination, despite similar lumen outputs.
A steradian (sr) is the SI unit of solid angle, analogous to how radians measure plane angles. One steradian represents the solid angle that subtends an area equal to r² on a sphere of radius r. A complete sphere contains 4π ≈ 12.566 steradians. Candela is defined as lumens per steradian, making steradians essential for converting between directional intensity and total output. This geometric relationship holds regardless of distance.
Yes, if they have identical candela ratings and beam angles, they produce the same lumens by definition. However, real fixtures rarely have perfectly uniform intensity within their beam angles. LED spotlights often have sharper beam cut-offs while halogen creates more gradual transitions. Additionally, color temperature affects perception - a 5000K LED may appear brighter than a 3000K halogen despite equal lumens. Always verify both candela and total lumen specifications.