This is an approximation of total light output in lumens when the half angle is defined by the angular value off axis where the output falls below 50% of max output. No attempt is made to account for the shape of the distribution pattern between 100% and 50% output.
Below is a chart that compares the Lumen output of a given LED die having various half angles. You can use this chart to compare a 1000 mcd LED having a 60° half angle with other LEDs having different beam intensities and different half angles. Notice that a 10° 35,000 mcd LED has nearly the same total Lumen output as the 1000 mcd 60° LED. Remember that half angle is one-half of the Viewing Angle.
Note that the Lumens put out by LEDs falls far short of regular incandescent bulbs. LEDs are 'point sources" while bulbs radiate light in almost all directions. A 4-Watt night light bulb delivers about 20 Lumens - in all directions. If it radiated light in one direction (assuming one steradian) it would deliver approximately 1.6 Lumens. See the Lumens chart below for some standard size incandescent light bulbs. Note that incandescant bulbs become more efficient as the size increases.
Calculate Watts for LEDs
Did you ever wonder how many watts an LED is consuming? It is very easy to calculate. Simply take the forward voltage drop and multiply it by the current (remember Oms Law - P=I*E). So assume you have a bright white LED that is rated at 3.2 Volts forward voltage. You'll find this in the spec sheet. If you're running at 20 mA, total power is calculated by multiplying:
Power in Watts = Amps * Volts or 3.2 * 0.020 = 0.064 Watts!
Now you can see why these light sources are so energy efficient! If you had a 15,000 mcd LED with a 30° Viewing angle, you'd be delivering 3.2 lumens using 0.064 watts. That is 50 lumens per watt! Compare that to the 5 to 15 lumens per watt from regular incandescent lamps above.
Note: To set the current at 20 mA: Assume you will power it with 5 volts at 20 mA using a resistor in series with the LED. To set the current at 20 mA subtract the forward voltage from the power source (5.0 - 3.2 = 1.8 volts). We will want a resistor to drop 1.8 volts at 20 mA, so: 1.8 volts divided by .02 Amps = 90 ohms.
Simple huh?
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