Enter a light source's luminous intensity and beam angle to calculate its total luminous flux in lumens.
How to Use the Candela to Lumens Calculator
Enter the light source's rated intensity into Luminous Intensity, then set Beam Angle to match its actual beam spread — Solid Angle and Luminous Flux recalculate the instant either field changes.
Candela and lumens sound interchangeable on a spec sheet, but they measure different things. Candela is intensity in one direction. Lumens is the total light spread across the whole beam. A narrow spotlight and a wide floodlight can carry an identical candela rating and still put out wildly different total lumens, because the floodlight spreads its light across a much larger solid angle. Converting one unit to the other is impossible without knowing how wide that beam actually is.
Solid Angle Is the Missing Variable
The bridge between candela and lumens is the solid angle — the three-dimensional angle a beam actually occupies, measured in steradians. A full sphere covers 4π steradians, about 12.566; a tightly focused spotlight might occupy only a sliver of that.
solid angle (sr) = 2π × (1 − cos(θ ÷ 2))
lumens = candela × solid angleθ is the beam's full apex angle in degrees — the number printed on most bulb and fixture datasheets as "beam angle." Halve it, convert to radians, and the rest follows directly.
Run the calculator's own defaults — 500 cd at a 120° beam angle — and the solid angle works out to roughly 3.14 sr, about a quarter of a full sphere, for a total of 1,571 lm. Widen that same 500 cd source out to a full 360° sphere and it would need to be radiating about 6,283 lm to justify the same intensity rating in every direction at once. Narrow the beam instead and lumens drops just as fast — no separate "brightness" concept hiding underneath any of this, just geometry.