Converting luminous intensity from candela to lumens is essential for accurate photometry and lighting system design. This conversion helps professionals determine total light output, considering beam angle, formulas, examples, and applications.
Candela to Lumens Calculator
How is the conversion calculated?
Fundamentals of Luminous Intensity and Luminous Flux
Candela (cd): The candela is the SI unit of luminous intensity. It measures the perceived power emitted by a light source in a specific direction. One candela represents the light intensity of a source that emits monochromatic radiation of frequency 540 × 10¹² Hz and has a radiant intensity of 1/683 watt per steradian in that direction.
Lumen (lm): The lumen measures luminous flux, representing the total visible light emitted by a source across all directions. Unlike candela, which focuses on intensity in a particular direction, lumens quantify the total light output, which is important for determining room brightness or illumination coverage.
Solid Angle (Ω): The solid angle, measured in steradians (sr), represents a three-dimensional angle through which light is emitted. It is analogous to how a planar angle (in degrees or radians) measures spread in two dimensions but in three-dimensional space.
Beam or Apex Angle (θ): Many lighting sources emit light in a conical distribution. The apex angle is the full angle of this cone, which determines the spread of light and directly affects the conversion from candela to lumens. Narrow beam angles concentrate light into a smaller area, increasing intensity, whereas wide angles distribute light more broadly, reducing intensity per unit area.
Core Formulas for Candela to Lumens Conversion
The basic relationship between luminous flux (Φv) in lumens and luminous intensity (Iv) in candelas is:
For a light source with a conical beam, the solid angle can be calculated as:
Combining the two, luminous flux for a conical light source becomes:
Explanation of Variables
- Luminous Intensity (Iv)
- Unit: candela (cd)
- Represents the perceived brightness in a particular direction.
- Common values:
- LED indicator lights: 1–10 cd
- Flashlights: 100–1,000 cd
- Streetlights: 500–10,000 cd
- Beam Angle (θ)
- Unit: degrees (°)
- Determines the spread of light from a source.
- Narrow angles (10°–20°) are typical for spotlights and task lighting.
- Medium angles (30°–60°) are common for general indoor lighting.
- Wide angles (90°–120°) are used in floodlights and streetlights.
- Solid Angle (Ω)
- Unit: steradian (sr)
- Represents the three-dimensional “slice” of space that light occupies.
- A full sphere subtends 4π steradians.
Candela to Lumen Conversion Table
Below is an extensive table with common values for various luminous intensities and beam angles:
| Candela (cd) | 10° Beam Angle (lm) | 30° Beam Angle (lm) | 60° Beam Angle (lm) | 90° Beam Angle (lm) | 120° Beam Angle (lm) |
|---|---|---|---|---|---|
| 1 | 0.024 | 0.214 | 0.842 | 1.840 | 3.142 |
| 5 | 0.119 | 1.072 | 4.208 | 9.201 | 15.708 |
| 10 | 0.239 | 2.141 | 8.418 | 18.403 | 31.416 |
| 50 | 1.195 | 10.704 | 42.088 | 92.015 | 157.080 |
| 100 | 2.390 | 21.409 | 84.179 | 184.030 | 314.159 |
| 500 | 11.954 | 107.045 | 420.894 | 920.151 | 1,570.796 |
| 1,000 | 23.909 | 214.094 | 841.788 | 1,840.302 | 3,141.593 |
| 5,000 | 119.544 | 1,070.471 | 4,208.940 | 9,201.510 | 15,707.963 |
| 10,000 | 239.088 | 2,140.942 | 8,417.879 | 18,403.019 | 31,415.927 |
This table allows engineers to quickly approximate the total luminous flux for common lighting designs based on intensity and beam angle.
Real-World Applications
Example 1: LED Spotlight Design
Scenario: A designer wants a spotlight with 500 cd luminous intensity and a 20° beam angle.
Calculation:
Interpretation: A 500 cd LED spotlight with a narrow 20° beam produces 47.5 lumens, sufficient for highlighting small objects or accent lighting.
Example 2: Street Lighting
Scenario: A streetlight has a luminous intensity of 1,000 cd and a wide 90° beam angle.
Calculation:
Interpretation: The streetlight emits 3,140 lumens, sufficient for illuminating a standard roadway safely and efficiently.
Advanced Considerations
- Non-Uniform Light Distribution: Many LEDs and luminaires do not have perfect uniformity; intensity varies across the beam. This can affect actual lumen output. Advanced photometric measurements often use intensity distribution curves to account for this.
- Temperature Effects: Luminous efficacy can change with operating temperature. LEDs typically lose efficiency at higher temperatures.
- Reflectors and Lenses: Optical components can increase or decrease effective luminous flux by directing light or causing losses.
- Standards Compliance: Professional lighting designs must consider local and international standards, including the Illuminating Engineering Society (IES) recommendations for illuminance levels and beam uniformity.
Summary of Key Points
- Conversion Formula: Φv=Iv⋅Ω=Iv⋅2π(1−cos(θ/2))
- Luminous Intensity (cd) determines directional brightness.
- Luminous Flux (lm) quantifies total emitted light.
- Beam Angle controls the light spread and affects conversion significantly.
- Real-World Use Cases: Spotlights, streetlights, indoor and architectural lighting.
Accurate candela to lumen conversion is fundamental for energy-efficient lighting, proper illumination design, and compliance with photometric standards. Professionals must consider beam angles, intensity distribution, optical losses, and environmental factors when performing these calculations.