Lumen to Millicandela Calculator

What is Lumen and Millicandela?

Lumen (lm) is the SI derived unit of luminous flux, which measures the total amount of light emitted by a source in all directions. Millicandela (mcd) is one-thousandth of a candela, which is the SI base unit of luminous intensity. It measures the amount of light emitted by a source in a particular direction.

The Lumen to Millicandela Formula

The formula for converting lumens to millicandela is:

\[I = \frac{\Phi}{2\pi (1 - \cos(\frac{\theta}{2}))} \times 1000\]

Where:

• \(I\) = Luminous intensity (millicandela)
• \(\Phi\) = Luminous flux (lumens)
• \(\theta\) = Apex angle (radians)

Step-by-Step Lumen to Millicandela Calculation

1. Identify the luminous flux in lumens (\(\Phi\)) and the apex angle in degrees (\(\theta\)).
2. Convert the apex angle from degrees to radians by multiplying by \(\frac{\pi}{180°}\).
3. Apply the formula: \(I = \frac{\Phi}{2\pi (1 - \cos(\frac{\theta}{2}))} \times 1000\).
4. The result is the luminous intensity in millicandela (\(I\)).

Example Calculation

Let's calculate the luminous intensity for a light source with 1000 lumens and an apex angle of 60°:

1. \(\Phi = 1000 \text{ lm}\), \(\theta = 60°\)
2. \(\theta \text{ in radians} = 60° \times \frac{\pi}{180°} = \frac{\pi}{3} \text{ radians}\)
3. \[\begin{align} I &= \frac{1000}{2\pi (1 - \cos(\frac{\pi}{6}))} \times 1000 \\ &\approx \frac{1000}{2\pi \times 0.1340} \times 1000 \\ &\approx 1188.4 \text{ millicandela} \end{align}\]

Visual Representation

This diagram illustrates how a 1000 lumen light source with an apex angle of 60° produces a luminous intensity of approximately 1188.4 millicandela. The red point represents the light source, and the yellow cone shows the spread of light based on the apex angle.