Understanding the conversion between lux and candela is crucial for lighting design and photometric calculations. Lux measures illuminance, while candela quantifies luminous intensity, two fundamental photometric units.
This article explores the detailed methodology for converting lux to candela, including formulas, tables, and real-world applications. It aims to provide a comprehensive technical guide for engineers, designers, and lighting professionals.
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- Convert 500 lux at 2 meters to candela
- Calculate candela from 1000 lux at 1.5 meters
- Find candela for 250 lux measured at 3 meters
- Determine candela from 750 lux at 0.8 meters
Comprehensive Tables for Lux to Candela Conversion
Below are extensive tables showing common lux values measured at various distances and their corresponding candela values. These tables are designed for practical use in lighting engineering and photometric analysis.
| Illuminance (Lux) | Distance (m) | Luminous Intensity (Candela) |
|---|---|---|
| 100 | 1 | 100 |
| 200 | 1.5 | 450 |
| 300 | 2 | 1200 |
| 400 | 2.5 | 2500 |
| 500 | 3 | 4500 |
| 600 | 3.5 | 7350 |
| 700 | 4 | 11200 |
| 800 | 4.5 | 16200 |
| 900 | 5 | 22500 |
| 1000 | 5.5 | 30250 |
These values assume a point light source emitting uniformly in all directions, which is a common simplification in photometric calculations.
Fundamental Formulas for Lux to Candela Conversion
Converting lux (illuminance) to candela (luminous intensity) requires understanding the relationship between these photometric quantities and the geometry of light propagation.
- Illuminance (E) is the luminous flux incident per unit area, measured in lux (lx), where 1 lx = 1 lumen/m².
- Luminous Intensity (I) is the luminous flux emitted per unit solid angle, measured in candela (cd), where 1 cd = 1 lumen/steradian.
- Distance (d) is the separation between the light source and the illuminated surface, measured in meters (m).
- Solid Angle (Ω) is the three-dimensional angle over which the light is emitted, measured in steradians (sr).
The primary formula linking lux and candela for a point source is derived from the inverse square law:
- I = luminous intensity in candela (cd)
- E = illuminance in lux (lx)
- d = distance from the source in meters (m)
This formula assumes a point source emitting light uniformly in all directions (isotropic source) and that the surface is perpendicular to the light rays.
For non-point sources or directional light, the solid angle Ω must be considered:
- Φ = luminous flux in lumens (lm)
- Ω = solid angle in steradians (sr)
Since illuminance E is related to luminous flux Φ by:
- A = illuminated area in square meters (m²)
And the solid angle Ω subtended by area A at distance d is:
Combining these, luminous intensity can be expressed as:
This confirms the initial formula and highlights the geometric dependency of the conversion.
Detailed Explanation of Variables and Units
- Lux (lx): Measures illuminance, the amount of luminous flux per unit area. It quantifies how much light hits a surface.
- Candela (cd): Measures luminous intensity, the amount of luminous flux emitted in a particular direction per unit solid angle.
- Distance (d): The straight-line distance from the light source to the point where illuminance is measured.
- Luminous Flux (Φ): Total light output from a source, measured in lumens (lm).
- Solid Angle (Ω): The three-dimensional angle over which light is emitted or received, measured in steradians (sr). For a full sphere, Ω = 4π sr.
- Area (A): The surface area illuminated by the light source, measured in square meters (m²).
Understanding these variables is essential for accurate photometric conversions and lighting design.
Real-World Application Examples of Lux to Candela Conversion
Example 1: Calculating Candela from Measured Lux at a Known Distance
A lighting engineer measures an illuminance of 500 lux on a surface located 2 meters from a point light source. The goal is to find the luminous intensity in candela of the source.
- Given: E = 500 lx, d = 2 m
- Formula: I = E × d2
Step 1: Square the distance:
Step 2: Multiply illuminance by squared distance:
Therefore, the luminous intensity of the source is 2000 candela.
Example 2: Determining Candela for a Directional Light Source
A spotlight emits a luminous flux of 1500 lumens over a solid angle of 0.5 steradians. Calculate the luminous intensity in candela.
- Given: Φ = 1500 lm, Ω = 0.5 sr
- Formula: I = Φ / Ω
Step 1: Divide luminous flux by solid angle:
The spotlight has a luminous intensity of 3000 candela in the direction of emission.
Additional Technical Considerations in Lux to Candela Conversion
While the basic formula I = E × d2 is widely used, several factors can affect the accuracy of lux to candela conversion in practical scenarios:
- Angular Distribution: Real light sources often emit light non-uniformly. The luminous intensity varies with angle, requiring angular photometric data for precise calculations.
- Surface Orientation: Illuminance depends on the angle of incidence. If the surface is not perpendicular to the light rays, the effective illuminance decreases by the cosine of the angle.
- Reflectance and Absorption: Surfaces may reflect or absorb light, altering measured lux values and complicating back-calculation to candela.
- Distance Measurement Accuracy: Precise distance measurement is critical since luminous intensity scales with the square of distance.
- Extended Sources: For sources larger than a point, the geometry of the source and measurement point must be considered, often requiring integration over the source area.
Advanced photometric software and goniophotometers are often used to capture detailed luminous intensity distributions for complex sources.
Standards and Guidelines for Photometric Measurements
International standards provide frameworks for measuring and converting photometric quantities:
- ISO/CIE 19476:2014 – Characterization of the performance of illuminance meters and luminance meters.
- IEC 60598-1 – Luminaires – General requirements and tests.
- CIE 127:2007 – Measurement of luminous intensity distributions.
Adhering to these standards ensures consistency and reliability in photometric conversions and lighting design.
Summary of Key Points for Lux to Candela Conversion
- Lux measures illuminance (lm/m²), candela measures luminous intensity (lm/sr).
- The fundamental conversion formula is I = E × d2, assuming a point source and perpendicular surface.
- For directional sources, luminous intensity is calculated as I = Φ / Ω.
- Accurate distance and angular measurements are critical for precise conversion.
- Real-world applications include lighting design, photometric testing, and compliance with lighting standards.
By mastering these concepts and formulas, lighting professionals can accurately convert between lux and candela, optimizing illumination for diverse environments.