Luminous Intensity Formula

Luminous intensity (candela) is the light emitted into a particular direction, measured per unit solid angle. Divide the lumens by the solid angle in steradians.

I = Φ ÷ Ω

What the terms mean

Symbol Meaning
I Luminous intensity, in candela
Φ Luminous flux, in lumens
Ω Solid angle, in steradians (sr)

Worked example

1,000 lumens concentrated into a 2 sr cone gives 500 candela.

Solid angle from beam. For a beam of full angle θ, the solid angle is Ω = 2π(1 − cos(θ÷2)). Narrow beams pack the same lumens into fewer steradians, raising candela.

See the Inverse Square Law and Candela Distribution Calculator.

Luminous intensity (candela)

Luminous intensity, measured in candela (cd), is the light emitted in a particular direction per unit solid angle (the steradian). In plain terms it captures how concentrated a beam is, independent of distance — which is why it’s the basis for comparing spotlights. For a source radiating evenly into a cone, intensity ≈ lumens ÷ solid angle, and a narrower cone packs the same lumens into fewer steradians, raising the candela.

Candela links directly to illuminance through the inverse-square law: lux = candela ÷ distance². That’s what makes intensity so useful — once you know a fixture’s candela toward a target, you can predict the lux landing on it at any distance. High candela means punch and reach; total lumens still tells you overall output.

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