How to Convert Luminous Intensity to Lumens

Light bulbs are usually in lumens while LEDs tend to be in candelas.

Luminous intensity is a measure of the intensity of light at its source. Its units are usually in candelas, where one candela is approximately the brightness of an ordinary wax candle. A lumen is the unit for luminous flux, which is a measure of the intensity of light where it falls on a surface. The two are not measuring the same thing and cannot be converted directly. However, a rough conversion is possible when taking into account the distance between the light source and the surface where the light falls.

Instructions

1. Measure the distance between your light source and where you need to know the light intensity in lumens. A common distance might be between the ceiling and a table or the floor. We'll call this distance "r."

2. Measure the size of the area that the light typically covers at that distance. If you are looking at a light bulb or LED (light emitting diode) which mentions a "beam angle," you can use that to calculate how wide a circular patch of light would be, given the measured distance.

3. Divide the area by the distance squared: area / r^2. This is also called a solid angle, which is in units of steradians (sr).

4. Multiply by the luminous intensity (in candelas) that you're starting with: lumens = (area / r^2) * candelas.

Tips & Warnings

• If you know both the beam angle and the cd/lm factor for your LED or bulb, there is a table from the LED Center (linked in Resources) which you might find helpful.

• For help calculating area from beam angle, refer to the Math Is Fun webpage about circle sectors.

References

• Lighting Design Knowledgebase: Luminous Intensity
• Lighting Design Knowledgebase: Luminous Flux
• Lighting Design Knowledgebase: Solid Angle

Resources

• Read this Article in Spanish
• LED Center: Candela (millicandela) to Lumen Conversion Wizard
• LED Center: How do I Convert Between Candelas and Lumens?
• Math Is Fun: Circle Sector and Segment