Millicandela to Lumens Calculator

How the Millicandela to Lumens Calculator Works

The millicandela to lumens calculator converts luminous intensity (millicandela) to luminous flux (lumens) by considering the beam angle of the light source. This conversion is crucial for understanding the total light output of directional light sources like LEDs.

By inputting the luminous intensity in millicandelas and the beam's apex angle in degrees, the calculator computes the luminous flux in lumens. This aids in selecting appropriate lighting fixtures for tasks requiring specific illumination levels.

Understanding Millicandela and Lumens

Millicandela (mcd) measures luminous intensity, indicating how much light is emitted in a particular direction. One millicandela equals one-thousandth of a candela. Lumens (lm), on the other hand, quantify luminous flux, representing the total amount of visible light emitted by a source in all directions.

For instance, an LED with a high millicandela rating and a narrow beam angle may produce fewer lumens than an LED with a lower millicandela rating but a wider beam angle. Understanding both units is essential for accurate lighting design.

Conversion Formula

To convert millicandela to lumens, the following formula is used:

lumens = (millicandela × 2π × (1 - cos(θ/2))) / 1000

Where:

• θ is the beam's apex angle in degrees.

This formula calculates the solid angle (in steradians) over which the light is distributed and multiplies it by the luminous intensity to determine the luminous flux.

Practical Examples

Example 1:

A light source emits 1000 millicandela with a beam angle of 60°.

First, calculate the solid angle:

Ω = 2π × (1 - cos(60°/2)) = 2π × (1 - cos(30°)) ≈ 2π × (1 - 0.866) ≈ 2π × 0.134 ≈ 0.84 steradians

Then, compute the lumens:

lumens = (1000 × 0.84) / 1000 = 0.84 lm

Example 2:

A spotlight emits 5000 millicandela with a narrow beam angle of 20°.

Calculate the solid angle:

Ω = 2π × (1 - cos(20°/2)) = 2π × (1 - cos(10°)) ≈ 2π × (1 - 0.9848) ≈ 2π × 0.0152 ≈ 0.0955 steradians

Then, compute the lumens:

lumens = (5000 × 0.0955) / 1000 ≈ 0.4775 lm

These examples illustrate how a narrower beam angle results in a lower lumen value for the same millicandela output.

Why Is Beam Angle Important in This Conversion?

The beam angle determines how light is distributed from the source. A narrower beam concentrates light into a smaller area, resulting in higher luminous intensity (millicandela) but lower luminous flux (lumens). Conversely, a wider beam spreads light over a larger area, increasing the total luminous flux. Therefore, knowing the beam angle is crucial when converting millicandela to lumens, as it directly influences the calculation.

Can Millicandela and Lumens Be Directly Compared?

While both units measure aspects of light, they represent different properties and are not directly interchangeable without considering the beam angle. Millicandela quantifies the intensity in a specific direction, whereas lumens measure the total light output. To accurately compare or convert between them, additional information about the light distribution, such as the beam angle, is necessary.

Beam Angle vs. Lumens for Common Millicandela Values

Millicandela (mcd)	Beam Angle (°)	Solid Angle (sr)	Lumens (lm)
1000	10	0.024	0.024
1000	30	0.214	0.214
1000	60	0.84	0.84
1000	90	1.84	1.84
1000	120	3.14	3.14
1000	180	6.28	6.28

This table demonstrates how the same millicandela value results in varying lumen outputs depending on the beam angle.

Tips for Accurate Conversion

• Measure Beam Angle Precisely: Ensure accurate measurement of the beam's apex angle for precise calculations.

• Use Consistent Units: Maintain consistency in units (degrees for angles) throughout the calculation.

• Consider Light Distribution: Understand the light source's distribution pattern, as assumptions of uniform distribution may not hold for all fixtures.

• Utilize Reliable Calculators: Employ trustworthy online calculators or tools that account for beam angle in their computations.

By comprehending the relationship between millicandela and lumens and accurately applying the conversion formula, professionals can make informed decisions in lighting design and ensure optimal illumination for various applications.