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 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)

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

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

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

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.

We can create a free, personalized calculator just for you!

Contact us and let's bring your idea to life.

Category
Loan
Tax
Interest
Investment
Profit & Loss
Credit and Debt Planning
Algebra
Statistics
Matrix
Number
Plane Geometry
Solid Geometry
Trigonometry
Construction
Analytic Geometry
Math graphing
Color Converter
Numeral system
Unit
Energy
Temperature
Power
Frequency
Charge
Voltage
Lighting
Classic Physic
Electronic
Engineering
Chemistry
Electrical
Date
Time
Commemorative days
Observance days
Health and medicine
Family and Fun
Weather
Webmaster tools