Lumens to Millicandela Calculator

How the Lumens to Millicandela Calculator Works

The lumens to millicandela calculator determines the luminous intensity (millicandela) of a light source based on its luminous flux (lumens) and beam angle. This calculation is essential for understanding how concentrated a light beam is in a specific direction, which is particularly useful in applications like LED design, flashlights, and spotlights.

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

Understanding Lumens and Millicandelas

Lumens (lm) measure the total amount of visible light emitted by a source, representing its luminous flux. Millicandelas (mcd), on the other hand, quantify luminous intensity, indicating how much light is emitted in a particular direction. While lumens assess overall brightness, millicandelas focus on the concentration of light in a specific direction.

For instance, a flashlight and a bulb may emit the same number of lumens, but the flashlight's design concentrates light into a narrow beam, resulting in a higher millicandela value compared to the bulb's dispersed light.

Conversion Formula

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

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

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 divides the total luminous flux by this angle to determine the luminous intensity.

Practical Examples

Example 1:

A light source emits 1000 lumens 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 millicandela:

millicandela = 1000 × 1000 / 0.84 ≈ 1,190,476 mcd

Example 2:

A spotlight emits 500 lumens 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 millicandela:

millicandela = 1000 × 500 / 0.0955 ≈ 5,235,602 mcd

These examples illustrate how a narrower beam angle results in a higher millicandela value for the same lumen 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, increasing luminous intensity (millicandela), while a wider beam spreads light over a larger area, reducing intensity. Therefore, knowing the beam angle is crucial when converting lumens to millicandelas, as it directly influences the calculation.

Can Lumens and Millicandelas Be Directly Compared?

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

Beam Angle vs. Millicandela for Common Lumens

Lumens (lm)	Beam Angle (°)	Solid Angle (sr)	Millicandela (mcd)
100	10	0.024	4,166,667
100	30	0.214	467,290
100	60	0.84	119,048
100	90	1.84	54,348
100	120	3.14	31,847
100	180	6.28	15,924

This table demonstrates how the same lumen output results in varying millicandela values 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 lumens and millicandelas and accurately applying the conversion formula, professionals can make informed decisions in lighting design and ensure optimal illumination for various applications.