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Convert luminous intensity in candela (cd) to total luminous flux in lumens (lm) using beam angle. Free calculator with conversion tables, formulas, and worked examples.
Solid angle: 0.8418 sr
Lumens = Candela x 2pi x (1 - cos(theta/2))
Use this reference table to quickly look up lumen output for common candela values and beam angles found in residential, commercial, and stage lighting.
| Candela (cd) | Beam Angle | Lumens (lm) |
|---|---|---|
| 50 | 15° | 2.7 |
| 100 | 10° | 2.4 |
| 100 | 30° | 21.4 |
| 100 | 60° | 84.2 |
| 250 | 25° | 37.2 |
| 500 | 20° | 47.7 |
| 500 | 40° | 189.5 |
| 500 | 60° | 420.9 |
| 1,000 | 10° | 23.9 |
| 1,000 | 30° | 214.1 |
| 1,000 | 60° | 841.8 |
| 1,000 | 120° | 3,141.6 |
| 2,000 | 15° | 107.5 |
| 5,000 | 10° | 119.5 |
| 5,000 | 40° | 1,894.6 |
| 10,000 | 8° | 153.1 |
| 10,000 | 30° | 2,140.9 |
| 50,000 | 5° | 299.0 |
Candela (cd) is one of the seven SI base units. It measures luminous intensity, which describes how bright a light source appears in a single, specific direction. Imagine shining a flashlight straight ahead: the candela rating tells you how intense the beam is along that center axis. A higher candela value means a more concentrated, far-reaching beam.
Lumens (lm) measure luminous flux, the total quantity of visible light emitted by a source in all directions combined. When you buy a household LED bulb rated at 800 lumens, that number describes the total light radiating outward. The lumen is an SI derived unit defined as one candela multiplied by one steradian (the unit of solid angle).
The crucial distinction is directionality. A laser pointer might register thousands of candela along its beam yet emit fewer than one lumen total. Conversely, a bare incandescent bulb may have modest candela in any single direction but produce 800 lumens spread across nearly a full sphere. To convert between the two you must know the beam angle, or more precisely the solid angle in steradians, that the light covers. This makes the candela-to-lumens conversion dependent on three variables: intensity, angle, and the geometric relationship between them.
The concept traces back to the original definition of candela based on the light output of a single candle, which was later standardized in 1979 using the luminous efficacy of monochromatic radiation at 540 THz. Today, both candela and lumens are essential for specifying everything from LED downlights to automotive headlamps and theatrical spotlights.
Lumens = Candela × Solid Angle (Ω)
Ω = 2π × (1 − cos(θ / 2))
Where θ is the full beam angle in radians. Convert degrees to radians by multiplying by π/180.
Given: 1,000 cd, beam angle = 60°
Given: 5,000 cd, beam angle = 10°
Given: 75 cd, beam angle = 360° (full sphere)
Note: 75 cd uniform across a full sphere is roughly equivalent to a standard 60W incandescent bulb.
For beam angles near 60°, the solid angle is approximately 0.84 sr, so lumens are roughly 84% of the candela value. For a 30° beam it is about 0.21 sr (21% of cd), and for 120° it is about 3.14 sr (pi times cd). Memorizing these three anchor points lets you quickly estimate lumen output without a calculator.
| Beam Angle | Solid Angle (sr) | Lumens |
|---|---|---|
| 10° | 0.0239 | 23.9 |
| 20° | 0.0955 | 95.5 |
| 30° | 0.2141 | 214.1 |
| 40° | 0.3789 | 378.9 |
| 60° | 0.8418 | 841.8 |
| 90° | 1.8403 | 1840.3 |
| 120° | 3.1416 | 3141.6 |
| 180° | 6.2832 | 6283.2 |
| 360° | 12.5664 | 12566.4 |
| Candela | Lumens at 60° | Typical Application |
|---|---|---|
| 50 | 42.1 | Under-cabinet LED |
| 100 | 84.2 | Desk lamp |
| 250 | 210.4 | Recessed downlight |
| 500 | 420.9 | Pendant fixture |
| 1,000 | 841.8 | Stage flood |
| 2,500 | 2,104.5 | Commercial bay |
| 5,000 | 4,208.9 | Warehouse fixture |
| 10,000 | 8,417.9 | Stadium flood |
| Beam Angle | 100 cd | 500 cd | 1,000 cd | 5,000 cd |
|---|---|---|---|---|
| 10° | 2.4 lm | 12.0 lm | 23.9 lm | 119.5 lm |
| 20° | 9.5 lm | 47.7 lm | 95.5 lm | 477.3 lm |
| 30° | 21.4 lm | 107.0 lm | 214.1 lm | 1,070.5 lm |
| 40° | 37.9 lm | 189.5 lm | 378.9 lm | 1,894.6 lm |
| 60° | 84.2 lm | 420.9 lm | 841.8 lm | 4,208.9 lm |
| 90° | 184.0 lm | 920.2 lm | 1,840.3 lm | 9,201.5 lm |
| 120° | 314.2 lm | 1,570.8 lm | 3,141.6 lm | 15,708 lm |
| 180° | 628.3 lm | 3,141.6 lm | 6,283.2 lm | 31,415.9 lm |
Architects and designers need lumens to calculate total room illumination, while fixture spec sheets often list candela. Converting between the two ensures spaces meet illuminance standards.
Spot lights are rated in candela and bulbs in lumens. Converting to a common unit lets you compare an LED spot to an omnidirectional bulb on equal footing.
Knowing total lumens helps calculate lumens-per-watt efficiency. A high-candela narrow beam may use less energy than a flood producing the same lumens over a wider area.
Building codes and roadway standards specify minimum lux levels. Converting candela to lumens is the first step in determining whether a fixture meets those requirements.
The formula requires the beam angle in radians for the cosine function. Forgetting to convert from degrees is the most common error and will produce wildly incorrect results.
Manufacturer spec sheets sometimes list the half-angle (the angle from center to edge). The formula uses the full beam angle. If you have a half-angle, double it before plugging it in.
The formula assumes constant candela across the entire beam cone. Real fixtures have a hotspot in the center that fades toward the edges, so calculated lumens may differ slightly from measured values.
Lumens measure total light output; lux measures light per square meter at a surface. You cannot substitute one for the other. To go from lumens to lux you also need distance and area.
Some datasheets report peak candela (center of beam) while others report average over the beam cone. Peak candela will overestimate total lumens if used directly in the formula.
For an omnidirectional source emitting equally in all directions, the solid angle is 4-pi (about 12.566 sr), not 2-pi. Using 2-pi gives only the hemisphere value.
No. Candela measures luminous intensity in one direction while lumens measure total light output across the entire beam. The same candela rating produces vastly different lumen totals depending on beam spread. A 1,000 cd spotlight with a 10-degree beam produces only about 24 lumens, while the same 1,000 cd at 60 degrees produces roughly 843 lumens. Without beam angle, the conversion is impossible.
Traditional incandescent and omnidirectional LED bulbs emit light across nearly 300-360 degrees of total coverage, or roughly 180 degrees per hemisphere for bulbs mounted in a base. Standard LED spotlights range from 25 to 40 degrees, floods cover 40 to 60 degrees, and wide floods exceed 60 degrees. Track lighting typically uses 25-40 degree beams, while accent lights can be as narrow as 10-15 degrees.
High-performance flashlights emphasize candela because users care about beam intensity at distance, known as 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 a wide beam might only reach 50 meters despite higher total output. Candela indicates concentrated brightness, while lumens represent overall efficiency.
Narrower beams appear brighter at the center because the same lumens are concentrated into a smaller area, increasing illuminance measured in lux. A 1,000 lumen spotlight with a 10-degree beam creates intense brightness in a small spot, while the same lumens in a 60-degree flood produces moderate illumination over a much larger area. This is why spotlights are used for accent lighting and floods for general illumination.
A steradian is the SI unit of solid angle, analogous to how radians measure flat angles. One steradian subtends an area equal to the square of the radius on the surface of a sphere. A complete sphere contains 4-pi, approximately 12.566, steradians. Because candela is defined as lumens per steradian, the steradian is essential for converting between directional intensity and total light output.
Yes, if they have identical candela ratings and beam angles the formula yields the same lumen value. However, real fixtures rarely have perfectly uniform intensity within their beam. LED spotlights often have sharper beam cut-offs, while halogen lights create more gradual transitions. Color temperature also affects perception: a 5000K LED may appear brighter than a 3000K halogen despite identical lumens.
Candela measures luminous intensity, the brightness of a light source in a specific direction. Lumens measure total luminous flux, the overall amount of visible light emitted in all directions. Lux measures illuminance, the amount of light falling on a surface per square meter. In simple terms: candela describes how bright the source looks, lumens describe how much light it produces overall, and lux describes how well a surface is lit.
Reverse the formula: Candela equals Lumens divided by the solid angle in steradians. First calculate the solid angle using the beam angle: solid angle equals 2-pi times (1 minus cosine of half the beam angle). Then divide the lumen value by that solid angle. For example, 843 lumens at a 60-degree beam gives 843 divided by 0.8418, which equals approximately 1,001 candela.
This calculator is provided for informational and educational purposes only. Always verify critical lighting calculations with manufacturer data and professional measurement equipment. UnitTables is not liable for errors or decisions based on these results.