Lumen to Candela Calculator
Convert lumens (lm) to candela (cd) instantly using beam angle. This calculator determines the luminous intensity of a light source from its total luminous flux and beam spread angle. Whether you are designing LED spotlights, comparing flashlight specifications, or engineering automotive headlights, this tool provides accurate lumen to candela conversions for any beam angle from narrow spot to wide flood. Candela measures how bright a light appears in a specific direction, making it essential for directional lighting applications. See also our Candela to Lumen Calculator and Lumen to Lux Calculator.
How to Convert Lumens to Candela
Converting lumens to candela requires knowledge of the beam angle because lumens measure total luminous flux emitted by a source while candela measures luminous intensity in a specific direction. The relationship between these two photometric quantities depends on the solid angle (measured in steradians) subtended by the beam cone. A narrow beam concentrates the same total light output into a smaller solid angle, producing higher candela values. Follow these steps to perform the conversion:
- Determine the total luminous flux of your light source in lumens (lm). This is typically printed on the product packaging or listed in the manufacturer datasheet.
- Identify the beam angle of the light source in degrees. Common beam angles range from 10° for narrow spots to 120° for wide floods. The beam angle is defined as the full cone angle where intensity drops to 50% of peak.
- Convert the beam angle from degrees to radians by multiplying by π/180. For example, 60° becomes 1.0472 radians.
- Calculate the solid angle in steradians using the formula: Ω = 2π × (1 − cos(θ/2)), where θ is the beam angle in radians.
- Divide the lumen value by the solid angle to get candela: I = Φ / Ω, where Φ is luminous flux in lumens and Ω is solid angle in steradians.
- The result is the average luminous intensity in candela within the specified beam angle cone.
This method assumes uniform light distribution within the beam cone. In practice, most light sources have a Gaussian or cosine-shaped intensity profile with peak intensity at the center. The calculated candela represents the average intensity; the actual peak center-beam candlepower (CBCP) may be 1.5 to 3 times higher depending on the beam profile shape. For precise peak intensity calculations, consult the manufacturer photometric data or IES file.
Lumen to Candela Formula
The conversion from lumens to candela is based on the geometric relationship between luminous flux and luminous intensity through the solid angle of the beam cone. The candela is one of the seven SI base units, defined as the luminous intensity of a source that emits monochromatic radiation at 540 THz with a radiant intensity of 1/683 watt per steradian. One lumen equals one candela multiplied by one steradian, so dividing lumens by the solid angle in steradians yields candela.
Candela = Lumens / (2π × (1 − cos(angle/2)))
Where:
Candela (cd) = Luminous intensity (SI base unit)
Lumens (lm) = Total luminous flux
angle = Beam angle (full cone angle)
2π × (1 − cos(angle/2)) = Solid angle Ω in steradians (sr)
To convert beam angle from degrees to radians:
angle_rad = angle_degrees × π / 180
Solid angle calculation:
Ω = 2π × (1 − cos(angle_rad / 2)) steradians
Relationship:
1 lumen = 1 candela × 1 steradian
Full sphere = 4π ≈ 12.566 steradians
Hemisphere = 2π ≈ 6.283 steradiansThe formula assumes uniform intensity distribution within the beam cone. For a perfectly isotropic source emitting equally in all directions, the solid angle is 4π steradians (full sphere), and the candela equals lumens divided by 4π. As the beam narrows, the solid angle decreases and the candela value increases proportionally, concentrating the same total light into a smaller angular region. This inverse relationship between beam angle and candela is why narrow-beam flashlights achieve extremely high candela ratings despite modest lumen outputs.
Example Calculation
Let us convert 800 lumens with a 60° beam angle to candela step by step. This represents a typical LED downlight or recessed ceiling fixture used in residential and commercial lighting.
Given: Φ = 800 lumens, beam angle = 60°
Step 1: Convert beam angle to radians
θ = 60° × π / 180 = 1.0472 radians
Step 2: Calculate the half-angle
θ/2 = 1.0472 / 2 = 0.5236 radians (30°)
Step 3: Calculate cosine of half-angle
cos(0.5236) = cos(30°) = 0.8660
Step 4: Calculate solid angle in steradians
Ω = 2π × (1 − 0.8660)
Ω = 2π × 0.1340
Ω = 6.2832 × 0.1340
Ω = 0.8418 steradians
Step 5: Calculate candela
Candela = 800 / 0.8418
Candela = 950.3 cd
Answer: An 800-lumen light source with a 60° beam angle produces approximately 950.3 candela of average luminous intensity within its beam cone. This means the light delivers 950.3 lumens per steradian in the direction of the beam. The solid angle of 0.8418 steradians represents about 6.7% of the full sphere (4π ≈ 12.566 sr), indicating the light is moderately focused.
For comparison, the same 800 lumens concentrated into a 15° beam would produce approximately 14,896 candela — nearly 16 times higher intensity. This demonstrates why beam angle is critical when comparing light sources: a narrow-beam spotlight appears much brighter in its beam direction than a wide-beam flood light, even when both produce the same total lumen output.
Lumens to Candela Conversion Table
The following reference table shows candela values for common lumen outputs across various beam angles. Use this table for quick lookups when designing lighting systems, comparing LED specifications, or selecting fixtures for specific applications. Values assume uniform intensity distribution within the beam cone.
| Lumens | 15° Beam | 30° Beam | 45° Beam | 60° Beam | 90° Beam | 120° Beam |
|---|---|---|---|---|---|---|
| 100 lm | 1860.3 cd | 467.1 cd | 209.1 cd | 118.8 cd | 54.3 cd | 31.8 cd |
| 200 lm | 3720.7 cd | 934.2 cd | 418.2 cd | 237.6 cd | 108.7 cd | 63.7 cd |
| 400 lm | 7441.4 cd | 1868.3 cd | 836.3 cd | 475.2 cd | 217.4 cd | 127.3 cd |
| 600 lm | 11162.1 cd | 2802.5 cd | 1254.5 cd | 712.8 cd | 326.0 cd | 191.0 cd |
| 800 lm | 14882.7 cd | 3736.7 cd | 1672.7 cd | 950.4 cd | 434.7 cd | 254.6 cd |
| 1000 lm | 18603.4 cd | 4670.8 cd | 2090.8 cd | 1187.9 cd | 543.4 cd | 318.3 cd |
| 1500 lm | 27905.1 cd | 7006.3 cd | 3136.2 cd | 1781.9 cd | 815.1 cd | 477.5 cd |
| 2000 lm | 37206.9 cd | 9341.7 cd | 4181.7 cd | 2375.9 cd | 1086.8 cd | 636.6 cd |
| 3000 lm | 55810.3 cd | 14012.5 cd | 6272.5 cd | 3563.8 cd | 1630.2 cd | 954.9 cd |
| 5000 lm | 93017.2 cd | 23354.2 cd | 10454.1 cd | 5939.7 cd | 2716.9 cd | 1591.5 cd |
Note: Values assume uniform intensity distribution within the beam cone. Actual peak candela (center beam candlepower) may be 1.5–3× higher depending on the beam profile. At 15° beam angle, the solid angle is only 0.054 sr, concentrating light into just 0.43% of the full sphere. At 120°, the solid angle is 3.14 sr (π steradians), covering 25% of the full sphere.
When to Use Candela vs Lumens
Choosing between candela and lumens depends on whether you need to evaluate directional brightness or total light output. Both metrics are essential in lighting design, but they serve different purposes and are appropriate for different applications.
| Scenario | Use Candela When... | Use Lumens When... |
|---|---|---|
| Flashlights | Comparing throw distance and beam reach | Comparing total light for close-range flood |
| Room Lighting | Evaluating spotlight glare or accent intensity | Calculating total light needed for a room |
| Automotive | Meeting headlight intensity regulations | Comparing total headlight output |
| Stage Lighting | Calculating illumination at throw distance | Estimating total fixture output for budgeting |
| LED Selection | Comparing narrow-beam spotlight LEDs | Comparing general-purpose bulb replacements |
| Signal Lights | Ensuring visibility at required distances | Estimating power consumption |
Use candela when directional intensity matters — spotlights, flashlights, signal lights, automotive headlights, and any application where you need to know how bright the light appears from a specific viewing angle or at a specific distance. Candela combined with the inverse square law (lux = candela / distance²) lets you calculate illumination at any distance from the source.
Use lumens when total light output matters — general room illumination, comparing bulb replacements, calculating how many fixtures are needed for a space, and energy efficiency comparisons. Lumens tell you the total amount of visible light regardless of how it is distributed. The lumen method of lighting design uses total lumens to determine the number of fixtures needed to achieve a target average lux level in a room.
In many real-world scenarios, you need both metrics. For example, when selecting recessed downlights for an office, you use lumens to ensure adequate total light for the room size, and candela to verify the beam intensity does not cause uncomfortable glare at workstation positions. Understanding the lumen-to-candela relationship through beam angle helps you balance these competing requirements.
Frequently Asked Questions
How many candela is 800 lumens?
The candela value of 800 lumens depends entirely on the beam angle. At a 15° beam angle, 800 lumens equals approximately 14,896 candela. At 30°, it equals about 3,737 candela. At 60°, it equals about 950 candela. At 90°, it equals about 435 candela. At 120°, it equals about 255 candela. The narrower the beam angle, the higher the candela because the same total light is concentrated into a smaller solid angle, increasing directional intensity.
What is the difference between lumens and candela?
Lumens (lm) measure total luminous flux — the complete amount of visible light emitted by a source in all directions within its beam. Candela (cd) measures luminous intensity — how bright the light appears in a specific direction. One candela equals one lumen per steradian. A 1000-lumen bulb with a wide 120° beam has about 318 candela, but the same 1000 lumens focused into a 10° beam produces over 41,700 candela. Lumens describe total output; candela describes directional concentration.
Why do I need the beam angle to convert lumens to candela?
The beam angle determines the solid angle (in steradians) over which the light is distributed. Without knowing the beam angle, you cannot determine how concentrated the light is in any direction. A wider beam spreads the same lumens over a larger solid angle, reducing the candela value. The beam angle is essential because candela is an intensity measurement that depends on directional concentration. Two lights with identical lumen output but different beam angles will have vastly different candela values.
How do I find the beam angle of my light source?
The beam angle is usually listed on the product packaging, datasheet, or manufacturer website. For LED bulbs, common beam angles are 15-25° for accent spotlights, 36-40° for general spotlights, 60° for narrow floods, and 100-120° for wide floods. Standard A19 household bulbs typically have 200-300° distribution. If not specified, you can measure it by finding the angle where light intensity drops to 50% of the peak value (half-peak angle). MR16 spots are typically 24-36°, PAR30 are 25-40°, and PAR38 are 25-60°.
What is a steradian and how does it relate to beam angle?
A steradian (sr) is the SI unit of solid angle — the three-dimensional equivalent of a radian. One steradian is the solid angle subtended at the center of a sphere by a surface area equal to the square of the radius. A complete sphere subtends 4π (≈12.566) steradians. The beam angle converts to steradians using Ω = 2π × (1 − cos(θ/2)). A 65.5° beam angle equals exactly 1 steradian. At 1 steradian, 1 lumen equals exactly 1 candela, making it the natural crossover point between the two units.
Can I convert candela back to lumens?
Yes, the reverse formula is: Lumens = Candela × 2π × (1 − cos(θ/2)), where θ is the beam angle in radians. Simply multiply the candela value by the solid angle in steradians to get lumens. You can use our Candela to Lumen Calculator for this reverse conversion. Note that this gives the total lumens within the specified beam cone, assuming uniform intensity distribution across the beam.