Millicandela to Lumen Calculator

What is Millicandela and Lumen?

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

The Millicandela to Lumen Formula

The formula for converting millicandela to lumen is:

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

Where:

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

Step-by-Step Millicandela to Lumen Calculation

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

Example Calculation

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

1. \(I = 1000 \text{ mcd} = 1 \text{ cd}\), \(\theta = 60°\)
2. \(\theta \text{ in radians} = 60° \times \frac{\pi}{180°} = \frac{\pi}{3} \text{ radians}\)
3. \[\begin{align} \Phi &= 2\pi \times 1 \times (1 - \cos(\frac{\pi}{6})) \\ &\approx 2\pi \times 1 \times 0.1340 \\ &\approx 0.8414 \text{ lumens} \end{align}\]

Visual Representation

This diagram illustrates how a 1000 millicandela light source with an apex angle of 60° produces a luminous flux of approximately 0.8414 lumens. The red point represents the light source, and the yellow cone shows the spread of light based on the apex angle.