Lumen to Candela Calculator

What is Lumen and 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. Candela (cd) is the SI base unit of luminous intensity, which measures the amount of light emitted by a source in a particular direction.

The Lumen to Candela Formula

The formula for converting lumen to candela is:

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

Where:

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

Step-by-Step Lumen to Candela 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: \(I = \frac{\Phi}{2\pi (1 - \cos(\frac{\theta}{2}))}\).
4. The result is the luminous intensity in candela (\(I\)).

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. \[\begin{align} I &= \frac{1000}{2\pi (1 - \cos(\frac{\pi}{6}))} \\ &\approx \frac{1000}{2\pi \times 0.1340} \\ &\approx 1189.2 \text{ candela} \end{align}\]

Visual Representation

This diagram illustrates how a 1000 lumen light source with an apex angle of 60° produces a luminous intensity of approximately 1189.2 candela. The red point represents the light source, and the yellow cone shows the spread of light based on the apex angle.