Candela to Lumen Converter
Calculate luminous flux from luminous intensity with precision
Luminous Flux
326.60 lm
Quick Conversions
Popular Conversions
| Candela (cd) | Apex Angle (°) | Lumens (lm) | Application |
|---|---|---|---|
| 50 | 10° | 1.20 | Laser pointer, narrow beam |
| 100 | 25° | 29.45 | Spotlight, focused beam |
| 200 | 40° | 239.00 | Track lighting |
| 500 | 60° | 1632.99 | Accent lighting |
| 1000 | 90° | 6144.29 | Flood light |
| 1500 | 120° | 14137.17 | Wide area lighting |
| 2000 | 180° | 12566.37 | Hemispheric light source |
| 5000 | 120° | 47123.89 | Stadium lighting |
Conversion Formula & Calculation Steps
Primary Formula:
Where:
• Φv = Luminous flux in lumens (lm)
• Iv = Luminous intensity in candela (cd)
• Ω = Solid angle in steradians (sr)
Solid Angle Calculation:
Where θ is the apex angle in degrees
Complete Formula:
Calculation Steps
- Identify the luminous intensity in candela (cd)
- Determine the apex angle (θ) in degrees
- Convert the apex angle from degrees to radians: θrad = θ × π/180
- Calculate the solid angle: Ω = 2π × [1 – cos(θ/2)]
- Multiply luminous intensity by solid angle: lm = cd × Ω
Example Calculation
Given: Iv = 500 cd, θ = 90°
Step 1: Convert angle: 90° ÷ 2 = 45°
Step 2: Calculate cosine: cos(45°) ≈ 0.7071
Step 3: Calculate solid angle: Ω = 2π × (1 – 0.7071) = 2π × 0.2929 ≈ 1.8402 sr
Step 4: Calculate lumens: Φv = 500 × 1.8402 ≈ 920.1 lm
Result: 500 candela at 90° apex angle = 920.1 lumens
Visual Comparison
The following bars represent luminous flux output for 1000 cd at different apex angles:
10° Narrow Beam
40° Spot Light
90° Flood Light
120° Wide Flood
180° Hemisphere
Real-World Applications
Flashlight Beam
Narrow 15° beam
≈ 171 lumens
Car Headlight
Medium 50° beam
≈ 8836 lumens
Stage Spotlight
Narrow 20° beam
≈ 9549 lumens
LED Bulb
Wide 120° beam
≈ 2827 lumens
Lighting Scenarios
| Scenario | Typical Angle | Intensity Range | Flux Range |
|---|---|---|---|
| Architectural accent | 25-40° | 200-800 cd | 58-956 lm |
| Retail display | 40-60° | 500-2000 cd | 597-6532 lm |
| Office lighting | 90-120° | 300-1000 cd | 1843-9425 lm |
| Street lighting | 60-90° | 2000-10000 cd | 6532-61443 lm |
| Photography flash | 50-70° | 5000-20000 cd | 2945-16330 lm |
| Searchlight | 5-15° | 500000-2000000 cd | 11937-286479 lm |
Key Concepts Explained
What is Candela?
Candela (cd) is the SI unit of luminous intensity. It measures the strength of light emission in a specific direction per unit solid angle. One candela represents the luminous power emitted by a light source in a particular direction, making it direction-dependent. The candela quantifies how bright a light source appears when looking directly at it from a specific angle.
What is Lumen?
Lumen (lm) is the SI unit of luminous flux. It measures the total amount of visible light emitted by a source in all directions. Unlike candela, lumens account for the entire light output regardless of direction. A higher lumen value indicates more total light energy being emitted, which directly correlates to perceived brightness in a space.
The Apex Angle
The apex angle (θ) defines the cone of light emission from a source. It represents the angle between the central axis of maximum intensity and the point where intensity drops to 50% of the maximum. Narrow apex angles (10-30°) create focused beams suitable for spotlights, while wide angles (90-180°) produce broad, diffuse illumination for general lighting.
Solid Angle (Steradian)
A steradian (sr) is the three-dimensional equivalent of a radian. It measures solid angles in 3D space, similar to how radians measure plane angles in 2D. One steradian subtends an area on a sphere equal to the square of the sphere’s radius. The solid angle determines how much of the surrounding space receives light from the source.
Relationship Between Units
The candela-to-lumen conversion depends entirely on the apex angle. A light source with high candela but a narrow beam produces fewer total lumens than one with lower candela but a wide beam. For example, 1000 cd at 10° yields only 23.87 lumens, while the same 1000 cd at 180° produces 12,566 lumens.
Angle Comparison Chart
Luminous flux output for 1000 candela at various apex angles:
| Apex Angle | Solid Angle (sr) | Lumens (lm) | Percentage of Hemisphere |
|---|---|---|---|
| 5° | 0.0060 | 6.03 | 0.1% |
| 10° | 0.0239 | 23.87 | 0.4% |
| 20° | 0.0955 | 95.49 | 1.5% |
| 30° | 0.2141 | 214.13 | 3.4% |
| 45° | 0.4799 | 479.87 | 7.6% |
| 60° | 0.8427 | 842.65 | 13.4% |
| 90° | 1.8402 | 1840.15 | 29.3% |
| 120° | 3.1416 | 3141.59 | 50.0% |
| 150° | 4.4429 | 4442.88 | 70.7% |
| 180° | 6.2832 | 6283.19 | 100.0% |
Frequently Asked Questions
Why do I need the apex angle to convert candela to lumens?
Candela measures intensity in one direction, while lumens measure total light output. The apex angle defines how much space the light covers. Without knowing how the light spreads, we cannot determine the total flux. A narrow beam concentrates light in a small area (fewer lumens), while a wide beam distributes it broadly (more lumens).
Can I convert lumens back to candela?
Yes, but you must know the apex angle. The reverse formula is: cd = lm ÷ [2π × (1 – cos(θ/2))]. Since lumens represent total output and candela represents directional intensity, the beam angle remains essential for accurate conversion in either direction.
What is a typical apex angle for household LED bulbs?
Most household LED bulbs have apex angles between 100-120° to provide wide, general illumination. Spotlights and track lighting typically use 25-60°, while floodlights employ 90-120°. Decorative or accent lights may use narrower angles of 15-40°.
Does the distance from the light source affect the conversion?
No. The candela-to-lumen conversion is independent of distance. However, illuminance (measured in lux) does depend on distance. While the relationship between candela and lumens remains constant for a given apex angle, the light received by a surface decreases with the square of the distance.
How does this relate to lux measurements?
Lux measures illuminance (light received per square meter), while lumens measure total flux (light emitted). To find lux from lumens, divide lumens by the illuminated area. To convert candela to lux, divide candela by the square of the distance to the surface: lux = cd ÷ distance².
What happens at 180° apex angle?
At 180°, the light source emits in a complete hemisphere. The solid angle equals 2π steradians, which is half of a complete sphere (4π steradians). This represents the maximum practical apex angle for directional sources. The formula becomes: lumens = candela × 2π.
Are candela and lux the same?
No. Candela measures the intensity of light emitted from a source, while lux measures the intensity of light received by a surface. One lux equals one lumen per square meter. Candela is source-dependent, while lux is surface-dependent and decreases with distance from the source.
Why do some lights list both candela and lumens?
Candela indicates peak beam intensity (useful for throw distance and spotting capability), while lumens indicate total light output (useful for overall brightness). Flashlights often list both: high candela means the beam reaches far, while high lumens mean bright overall illumination. Both metrics together provide a complete picture of light performance.