Candela ↔ Lumens Calculator
Convert intensity to total output and back through the beam angle — the missing link between a spotlight's candela rating and its lumens.
Result
Candela and lumens only line up through the beam angle: the same lumens packed into a narrow cone reads as a much higher candela than when spread into a wide flood.
Intensity, flux, and the cone between them
Candela and lumens answer different questions. Candela ask how bright the source is if you stand in its beam; lumens ask how much light it produces in total. A laser-like torch and a soft lantern can share the same lumen count yet feel nothing alike, because one crams that flux into a pencil beam and the other spills it in every direction.
The geometry that connects them is solid angle. The beam covers a cone of Ω = 2π(1 − cos(θ/2)) steradians, and the total flux is simply the intensity times that solid angle. That is why a reflector or lens, which narrows the beam, can dramatically raise candela without adding a single lumen — it just gathers the light you already had into a tighter cone.
Frequently Asked Questions
What is the difference between candela and lumens?
Candela measure luminous intensity — how bright a source is in one particular direction. Lumens measure luminous flux — the total light poured into the whole beam. A tight torch can have a huge candela rating in its narrow beam while emitting modest total lumens, because all its light is concentrated forward.
How do you convert candela to lumens?
You need the beam angle. The beam fills a solid angle Ω = 2π(1 − cos(θ/2)) steradians, where θ is the full beam angle, and then lumens = candela × Ω. Turned around, candela = lumens ÷ Ω. Without the beam angle the two quantities cannot be converted.
What is a beam angle?
The beam angle is the full width of the cone of light, in degrees, usually measured to where intensity falls to half its centre value. Spotlights are narrow (roughly 15–30°), floods are wide (40–90°), and a bare bulb that radiates in every direction approaches 360°.
Why does a narrow beam have more candela?
Because the same lumens are squeezed into a smaller cone. Solid angle shrinks fast as the beam narrows, so packing a fixed flux into a tight beam raises the intensity — the candela — sharply. Widen the beam and that intensity drops even though the total light is unchanged.
What is a steradian?
A steradian is the SI unit of solid angle — the three-dimensional equivalent of an angle. A full sphere contains 4π (about 12.57) steradians. The beam's solid angle is the slice of that sphere the light actually covers.
Educational estimate assuming a uniform cone. Real beams have a soft edge and an intensity that varies across the beam, so a datasheet figure will differ slightly.