Lumen Calculator (Lumen to Lux to Candela)

Photometry relies on three core units: lumens (total visible light output), lux (light falling on a surface), and candela (luminous intensity in a specific direction). Our calculator uses three primary equations to bridge these values. First, luminous flux relates to candela and beam angle theta through the formula lumens = candela * 2 * π * (1 - cos(θ / 2)). Second, illuminance in lux relates to candela and distance via inverse-square law: lux = candela / distance^2. Finally, surface illumination is directly derived from total lumens spread over a specific area: lux = lumens / area.

Imagine you are installing a specialized spotlight in an art gallery. The lamp emits a luminous intensity of 500 candela focused within a total beam angle (θ) of 60 degrees. To find out the total luminous flux (lumens), we substitute our numbers into the formula: lumens = 500 * 2 * π * (1 - cos(60° / 2)). Since cos(30°) ≈ 0.866, we get lumens = 500 * 6.2832 * (1 - 0.866) = 3141.6 * 0.134 = 420.97 lumens. If this light shines directly onto a sculpture 3 meters away, the illuminance at that surface is lux = 500 / 3^2 = 500 / 9 = 55.56 lux.

Always measure distance in meters when working with standard SI photometric equations to ensure your lux values are correct. Keep beam angle limitations in mind; symmetric conical spreads are assumed unless specified otherwise. When translating lumens to lux over large areas, remember that light spreads quadratically, meaning doubling your distance from the light source reduces the illumination level to one-fourth of its original intensity.