Candela to Lumen Converter

Enter the luminous intensity and beam apex angle to get the luminous flux.

Result

841.8 lm
0.8418 sr
60.00° apex, 1,000.00 cd

How it is calculated

The tool first finds the solid angle of a cone-shaped beam from its full apex angle θ in degrees: Ω = 2π × (1 − cos(θ ÷ 2)), in steradians (sr). Then lumens = candela × Ω. It assumes the intensity is the same everywhere inside the cone and zero outside, so it gives the flux of an idealised even beam. The apex angle is the full width of the beam, not the half-angle. It must be above 0 and at most 360; at 360° the solid angle is 4π (12.5664 sr), the whole sphere. Candela must be above zero; otherwise (or with an angle above 360) no result is shown. A real fixture's intensity usually falls off toward the edge of the beam, so treat the answer as an estimate.

Worked example

A spotlight is rated 1000 cd with a 60° beam. Half the apex angle is 30°, and cos 30° = 0.8660. Solid angle: 2π × (1 − 0.8660) = 2π × 0.1340 = 0.8418 sr. Luminous flux: 1000 × 0.8418 = 841.8 lm. The tool shows 841.8 lm, a solid angle of 0.8418 sr and the inputs you used. A narrower 30° beam at the same 1000 cd would give only about 214 lm.

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Common mistakes

  • Entering the half-angle from a datasheet. The tool wants the full cone angle, so a beam described as 30° either side must be entered as 60°.
  • Entering the angle in radians. The field takes degrees, so 1.05 for a 60° beam is read as about one degree and gives a tiny result.
  • Assuming lumens equal candela. They only match at one steradian, which is about 65.5° of apex angle; every other beam angle changes the result.
  • Taking the candela of a peak-intensity spot with a fall-off at the edges as a constant value over the beam, which overestimates the true flux.
  • Using an angle above 180° for a lamp that only lights one side. The tool allows up to 360°, which means a full sphere, but most directional fixtures stay at or below 180°.

About this calculator

Candela (cd) measures luminous intensity — how much light a source throws in one specific direction — while lumens (lm) measure luminous flux, the total light output spread across the beam. The two are related through the solid angle the beam covers: Φv = Iv · Ω, where for a cone-shaped beam with apex (full) angle θ the solid angle in steradians is Ω = 2π(1 − cos(θ/2)).

Manufacturers often publish a spotlight or LED fixture’s candela rating and beam angle on the datasheet rather than its total lumen output, since candela describes brightness along the beam axis (what matters for throw distance) while lumens describe overall output (what matters for illuminating an area). Lighting designers use this conversion to compare fixtures on a common basis or to estimate the total flux of a narrow spotlight versus a wide floodlight.

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