Candela to Lumen Converter

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.

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°.