How to Calculate Illuminance

••• Creatas/Creatas/Getty Images

Illuminance is the quantity of light incident on a surface per unit of area. In the U.S., lumens per square foot is used, which is the same as foot-candles. The metric unit is lumens per square meter, or lux.

For a point source of light without reflections, only a fraction of the emitted light reaches a surface. Illuminance depends on the light’s intensity and its distance away and it is calculated using the Point Source method. In an indoor setting, all light emitted from a fixture is available except what is absorbed by the ceiling and walls. For this case the Lumen method is used.

Point Source Method

    Determine the area of a sphere with a radius equal to the specified distance from the source. Use the distance in feet or meters, depending on whether U.S. or metric units are preferred. Square the distance and multiply it by Pi and then by four. This is the area of a sphere at the specified distance.

    Divide the light intensity in lumens by the spherical area. The result is the illuminance in foot-candles or lux, depending on whether feet or meters were used.

    If the light hits the surface at an angle less than 90 degrees, apply a correction factor by multiplying the calculated illuminance value by the cosine of the off-axis angle.

Lumen Method

    Determine the the intensity in lumens from the light sources in the room.

    Calculate the the area of the room in square feet or square meters.

    Divide the total light intensity by the area.

    Multiply the result by the appropriate coefficient of utilization.

Converting between US and Metric units

    Multiply lux by .0929 to get foot-candles.

    Multiply foot-candles by 10.76 to get lux.

    As an alternative, you may choose to use the standard factor of 10 for the conversion. If so, divide lux by 10 to get foot-candles, and multiply foot-candles by 10 to get lux.

    Tips

    • Figures for the coefficient of utilization are provided by light fixture manufacturers for various room configurations. The coefficient of utilization is the light delivered to a surface divided by the total light emitted by the source. Depending on the design of the light fixture and the geometry and materials in the room, this coefficient will usually be in the range of 0.5 to 0.9.

References

About the Author

Don Patton began writing after retiring from an engineering career in 2006. He holds a Bachelor of Science in electrical engineering from the University of California at Berkeley and continued with graduate study in software engineering.

Photo Credits

  • Creatas/Creatas/Getty Images

Dont Go!

We Have More Great Sciencing Articles!