• Multiply the lumen output of the bulb by 45.84.
  
• Divide by the number of inches from the bulb squared.
  

This is the longer detailed formulas for calculating the number of Foot-Candles (Lumens/ft.²) coming from a bulb:

The divisor must be equal to the actual area that is being illuminated by the bulb, which is not based on your floor plans. The divisor in Formula A is calculating a spherical propagation of light, which is what the light is really illuminating.

Formula A:
Foot-Candles = Lumens ÷ (4 × Pi × d²)

Where:
d = The distance from the bulb in feet.
Pi = 3.14159

If you wanted to know how many Foot-Candles of light are striking your plant 10" away from a 400 watt HPS that puts out 50,000 lumens you would do this:

Foot-Candles = 50000 ÷ (4 × Pi × (10/12)²)
Foot-Candles = 50000 ÷ (12.57 × 0.6944)
Foot-Candles = 50000 ÷ ( 8.729)
Foot-Candles = 5,728

So, there are 5,728 Foot-Candles of light hitting your plant 10" from a 400 watt HPS with no reflector.

Now, because we are using reflectors it will actually be more. Let's calculate how many Foot-Candles hit your plant 10" away with a typical 120° reflector.

Formula B:
Foot-Candles = Lumens ÷ (2 × Pi × d² × (1 - cos(A/2)))

Where:
A = The degree of the reflector. (Most of us have 120° reflectors)
d = The distance from the bulb in feet.
Pi = 3.14159

To make this easier we already know the value of d² when the distance is 10" from the bulb. That value as calculated above is 0.6944.

Foot-Candles = 50000 ÷ ( 2 Pi × d² (1 - cos(120/2)))
Foot-Candles = 50000 ÷ ( 2 Pi × d² (1 - cos(60)))
Foot-Candles = 50000 ÷ ( 2 Pi × d² (1 - 0.5))
Foot-Candles = 50000 ÷ ( 6.283 × 0.6944 × 0.5)
Foot-Candles = 50000 ÷ (2.181)
Foot-Candles = 22,918

So, you would get 22,918 Foot-Candles (Lumens/ft.²) of light 10" away from a 400 watt HPS using a 120° reflector.

The picture below is a Blaze main cola that is 16" long. It is 10" from a 1,000 watt HPS. This HPS puts out 140,000 lumens. The illuminance in the units of Foot-Candles (Lumens/ft.²) are marked and labeled with the distance in inches from the bulb. You'll see the bottom of the cola is getting the illuminance of equatorial sun.



Disclaimer: This post was intended to simply show the wide range of illuminance that indoor plants endure when using lights. The typical rules of thumb are still the best way to calculate your lighting needs. Here are a few:

*Using 60 - 100 watts per square foot of HID lighting will provide enough light to bring out the best in the genetics that you're growing, provided that you don’t grow the plants over 3 feet tall. If you do it’s not a problem, you just won’t get bud at the bottom of the plants.

*Keep lights close to the plants to provide penetration to lower branches.

*Air cool reflectors to dissipate the heat so that the only concern you'll have on the distance of your light to the top of the plants will be the amount of light.

*Don't put 400 watt HPS lights any closer than 7 inches from the top of the plants regardless of temperature.

*Don't put 1,000 watt HPS lights any closer than 12 inches from the top of the plants regardless of temperature.

In other words, my plant above is too close to the light and you can see how it’s turning color at the very top.

Quote:

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*Don't put 400 watt HPS lights any closer than 7 inches from the top of the plants regardless of temperature.

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...Great post. I quess that's why some of my tops get a yellow/whiteish tip at times. Thanx...

Quote:

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Exactly, too much light usually causes a white-ish tone and the plant matter turns like rubber. I think the plant tries to gather moisture in the area.
Too much heat creates brown, dryness and burning of plant matter. They look quite different.

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thats some great advice!

Quote:

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cali grower, thanks for that chart, its in the cannagrower bible I was wondering who made that haha

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I made all the charts. They were made in Microsoft Excel. If you can put up an image of how they look in the CannaGrower Bible I’d appreciate it. Did they take my name off of them? I see my charts pop up on other websites, but my name is still on them.

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I made the first graph, which was the Foot-Candles for an HPS bulb, on August 5, 2004. I could never find accurate graphs for PAR lumens, so I just made them myself. The graphs are based on pure geometry and physics.

To make the graph, you first need to calculate the number of Foot-Candles that you’d get from any distance from the bulb. This is shown above.

After calculating the number of Foot-Candles, a conversion is used to find the number of micromoles per square meter per second (umol/m²/s) of irradiance within the frequencies 400nm – 700nm (PAR).

The conversions are as follows:
The conversion is a multiplier.

High Pressure Sodium - 0.131
Metal Halide - 0.152
Sun – 0.199

After finding the PAR irradiance I just compared it to the 1,990 umol/m²/s we get from the sun by dividing by that value and showing the values as a percentage.

I use Microsoft Excel to make the charts and graphs. I take the cells on the chart to produce the graph. Each cell on the chart becomes one point on the graph.

This is how it looks when it's being put together.