Candela to Lumen Calculator

Convert between luminous intensity (candela) and luminous flux (lumens). Calculate lighting parameters for beam angles and solid angles.

Conversion Formula: Φ = I × Ω where Φ is luminous flux (lumens), I is luminous intensity (candela), and Ω is solid angle (steradians).

For beam angle: Ω = 2π(1 - cos(θ/2)) where θ is the beam angle in degrees.

Candela to Lumens
Lumens to Candela
Both Directions
Luminous intensity in candela (cd)
Full beam angle in degrees. For omnidirectional light, use 360°.
steradians (sr)
Solid angle in steradians. Leave blank to calculate from beam angle.
Candle (1 cd, 360°)
LED Spotlight (100 cd, 30°)
Household Bulb (800 lm, 120°)
Car Headlight (1500 cd, 15°)
Theater Spotlight (10,000 cd, 10°)
Omnidirectional (1200 lm, 360°)
Calculating...

Understanding Candela and Lumens

Candela (cd) and lumen (lm) are units used in photometry to measure light. Candela measures luminous intensity - how bright a light source appears in a particular direction. Lumens measure luminous flux - the total amount of visible light emitted by a source.

Key Relationship: Lumens = Candela × Solid Angle (in steradians)

The solid angle depends on the beam angle of the light source. A narrow beam concentrates the same luminous intensity into a smaller solid angle, resulting in higher candela values for the same lumen output.

Photometric Units Comparison

Unit Symbol Measures Definition Common Use
Lumen lm Luminous flux Total visible light emitted Light bulb brightness
Candela cd Luminous intensity Brightness in a specific direction Spotlights, LED specifications
Lux lx Illuminance Lumens per square meter Lighting level on surfaces
Nit nt Luminance Candela per square meter Display brightness
Foot-candle fc Illuminance Lumens per square foot Architectural lighting (US)

Solid Angle Calculation

1

Steradian Definition: A steradian (sr) is the SI unit of solid angle. One steradian is defined as the solid angle subtended at the center of a sphere by an area on its surface equal to the square of its radius.

2

Beam Angle to Solid Angle: For a conical beam with full angle θ (in degrees), the solid angle Ω (in steradians) is calculated as:

Ω = 2π(1 - cos(θ/2))

3

Special Cases:

  • Full sphere (θ = 360°): Ω = 4π sr ≈ 12.57 sr
  • Half sphere (θ = 180°): Ω = 2π sr ≈ 6.28 sr
  • Narrow beam (small θ): Ω ≈ π(θ/2)² (when θ is in radians)

Common Light Source Examples

Standard Candle
1 cd

Approximately the luminous intensity of a common candle. Emits about 12.6 lm in all directions (360° beam angle).

60W Incandescent Bulb
800 lm

Typical household bulb with omnidirectional emission. Approximately 64 cd when averaged over all directions.

LED Flashlight
200 lm, 15°

Concentrated beam produces high intensity: approximately 10,000 cd in the center of the beam.

Car Headlight
1,500 cd

Designed for forward illumination with a controlled beam pattern to avoid blinding other drivers.

Applications

  • Lighting Design: Selecting appropriate light sources for architectural and interior lighting
  • Automotive: Designing headlights and signal lights that meet regulatory requirements
  • Photography: Understanding flash units and studio lighting equipment
  • Display Technology: Specifying brightness and viewing angles for screens and monitors
  • Safety Standards: Ensuring emergency and warning lights meet visibility requirements

Calculator Features:

  • Convert between candela and lumens in both directions
  • Account for beam angle or direct solid angle input
  • Visualize beam angle and light distribution
  • Compare different light sources with common examples
  • Understand the relationship between intensity, flux, and beam angle

Frequently Asked Questions

Lumens measure the total amount of visible light emitted by a source (luminous flux). Candela measures how bright that light appears in a particular direction (luminous intensity). A light source with a narrow beam can have high candela but moderate lumens, while an omnidirectional source with the same lumens will have lower candela.

Beam angle determines the solid angle over which light is distributed. A smaller beam angle concentrates light into a narrower beam, resulting in higher candela for the same lumen output. The relationship is: Lumens = Candela × Solid Angle, where solid angle depends on beam angle.

A steradian (sr) is the SI unit of solid angle. One steradian is the solid angle subtended at the center of a sphere by an area on its surface equal to the square of the sphere's radius. A full sphere encompasses 4π steradians (approximately 12.57 sr).

Lumens indicate total light output (important for general illumination), while candela indicates peak intensity (important for spotlights, flashlights, and directional lighting). Both specifications together give a complete picture of a light's performance. For example, a flashlight might have 500 lumens but 20,000 candela in the hotspot.

This calculator provides theoretical values based on ideal Lambertian distribution (uniform brightness within the beam angle). Real-world lights may have non-uniform distributions, multiple intensity peaks, or different beam shapes. For precise applications, consult manufacturer photometric data, which often includes intensity distribution curves.