Candela to Lumen Calculator

What is Candela and Lumen?

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

The formula for converting candela 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 Candela to Lumen Calculation

1. Identify the luminous intensity in candela (I) 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: \(\Phi = 2\pi I (1 - \cos(\frac{\theta}{2}))\).
4. The result is the luminous flux in lumens (\(\Phi\)).

Example Calculation

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

1. \(I = 1000 \text{ cd}\), \(\theta = 60°\)
2. \(\theta \text{ in radians} = 60° \times \frac{\pi}{180°} = \frac{\pi}{3} \text{ radians}\)
3. \[\begin{align} \Phi &= 2\pi \times 1000 \times (1 - \cos(\frac{\pi}{6})) \\ &\approx 2\pi \times 1000 \times 0.1340 \\ &\approx 841.4 \text{ lumens} \end{align}\]

Visual Representation

This diagram illustrates how a 1000 candela light source with an apex angle of 60° produces a luminous flux of approximately 841.4 lumens. The red point represents the light source, and the yellow cone shows the spread of light based on the apex angle.