Lumens to Candela Calculator

How the Lumens to Candela Calculator Works

The lumens to candela calculator determines the luminous intensity (candela) of a light source based on its luminous flux (lumens) and beam angle. This calculation is essential for lighting design, allowing professionals to understand how concentrated a light beam is in a specific direction.

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

Understanding Lumens and Candelas

Lumens (lm) measure the total amount of visible light emitted by a source, representing its luminous flux. Candelas (cd), on the other hand, quantify luminous intensity, indicating how much light is emitted in a particular direction. While lumens assess overall brightness, candelas 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 candela value compared to the bulb's dispersed light.

Conversion Formula

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

candela = 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 candela:

candela = 1000 / 0.84 ≈ 1190.48 cd

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 candela:

candela = 500 / 0.0955 ≈ 5235.6 cd

This example illustrates how a narrower beam angle results in a higher candela 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 (candela), while a wider beam spreads light over a larger area, reducing intensity. Therefore, knowing the beam angle is crucial when converting lumens to candelas, as it directly influences the calculation.

Can Lumens and Candelas 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 candelas 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. Candela for Common Lumens

Lumens (lm)	Beam Angle (°)	Solid Angle (sr)	Candela (cd)
100	10	0.024	4166.67
100	30	0.214	467.29
100	60	0.84	119.05
100	90	1.84	54.35
100	120	3.14	31.85
100	180	6.28	15.92

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