Candela to Lumens Calculator

About the Candela to Lumens Calculator

A candela to lumens calculator converts luminous intensity (candela) to total luminous flux (lumens) by multiplying by the solid angle in steradians that the light source illuminates. This conversion is essential for working with directional light sources — spotlights, LED emitters, flashlights, automotive headlamps, and theatrical fixtures — where candela specifies how intensely the light shines in a given direction, while lumens tell you the total light output across the entire beam. A narrow spotlight with 10,000 candela in a 5° beam produces very few total lumens; a wide floodlight with the same total lumens has much lower peak candela. Understanding this relationship is fundamental to photometrics and LED specification. Candela is the SI base unit of luminous intensity; lumen is the SI unit of luminous flux — and the conversion factor between them is the solid angle. Our calculator handles all standard beam configurations from a pinpoint 1-steradian reference to full sphere (4π sr ≈ 12.566 sr) and hemisphere (2π sr ≈ 6.283 sr), with buttons for common presets and a manual entry for precise beam angles. Used by LED engineers, lighting designers, photographers, and stage lighting professionals worldwide.

How It Works

lm = cd × Ω (steradians). The solid angle Ω for a cone with half-angle θ: Ω = 2π(1 - cos θ). Common solid angles: Full sphere = 4π ≈ 12.566 sr; Hemisphere = 2π ≈ 6.283 sr; 90° half-angle cone = 6.283 sr; 60° half-angle cone = 3.14 sr; 30° half-angle cone = 0.842 sr; 15° half-angle cone = 0.214 sr; 5° spotlight cone = 0.024 sr. Example 1 (LED emitter): 5,000 mcd (5 cd) emitter with 30° half-angle. Ω = 2π(1-cos30°) = 2π × 0.134 = 0.842 sr. lm = 5 × 0.842 = 4.21 lm — a bright but narrow emitter. Example 2 (omnidirectional bulb): 1,000 lm bulb emitting in all directions. Average cd = 1,000 / 12.566 = 79.6 cd in any direction. Example 3 (automotive headlamp): ECE R112 LED low beam headlamp: peak candela ≈ 45,000 cd in the central beam, but total lumens ≈ 1,500-2,000 lm because the beam is narrow and carefully controlled.

Tips & Best Practices

• ✓Reading LED datasheets: component LED datasheets specify intensity in mcd (millicandela) at a viewing angle — typically the half-power point (the angle where intensity drops to 50% of peak). This is not the same as the beam's total solid angle. Use the half-power angle as the cone half-angle to estimate solid angle.
• ✓Stage lighting CBCP (Center Beam Candlepower): theatrical spotlights specify CBCP as the peak intensity in the center of the beam. To find total lumens, you need the full photometric data (goniophotometric curve) — not just CBCP. The calculator approximates using the beam angle half-width.
• ✓Automotive lighting regulations: UN ECE R112 (EU) and FMVSS 108 (US) specify minimum and maximum candela values at specific test angles for vehicle headlamps. These are regulatory minimums, not lumen requirements. The candela-to-lumens conversion shows total beam flux from specified intensity values.

Who Uses This Calculator

LED engineers converting component datasheet mcd values to lumen output for system design. Stage and theatrical lighting designers calculating fixture output from CBCP specifications. Automotive engineers translating headlamp candela compliance test results to total flux. Photographers sizing studio flash equipment from candela specifications to effective exposure output.