Candela to Lumens Calculator
Convert luminous intensity in candela (cd) to luminous flux in lumens (lm) for a beam with a cone apex angle. Enter the candela value and the apex angle in degrees, and press Calculate — the lumens result comes from Φv(lm) = Iv(cd) × 2π(1 − cos(θ/2)). Everything runs locally in your browser.
Enter luminous intensity
Type the luminous intensity Iv in candela (cd) — how bright the source looks straight down its beam. A value of zero or higher is accepted; zero candela gives zero lumens.
Enter the apex angle
Type the full cone apex angle θ in degrees — the total opening angle of the beam, measured edge to edge through the axis. 0° (no beam) up to 360° (a source radiating in every direction) is accepted.
Press Calculate, read lumens
The luminous flux Φv appears in lumens (lm), rounded to two decimals, together with the solid angle Ω in steradians. Copy the result to your clipboard, or press Reset to clear everything and start over.
Candela to lumens calculation
- Candela to lumens formula
- For a uniform, isotropic light source inside a cone, the luminous flux Φv in lumens (lm) is equal to the luminous intensity Iv in candela (cd), times the solid angle Ω in steradians (sr): Φv(lm) = Iv(cd) × 2π(1 − cos(θ/2)), where θ is the cone apex angle in degrees. For example, 1000 cd within a 120° cone gives 1000 × π ≈ 3141.59 lm.
- How the solid angle Ω is computed
- The solid angle Ω in steradians (sr) is equal to 2 times pi times 1 minus cosine of half the cone apex angle θ in degrees (°): Ω(sr) = 2π(1 − cos(θ/2)). A 120° cone has Ω = π sr; a full sphere (θ = 360°) has Ω = 4π ≈ 12.566 sr.
- What is 1 candela in lumens?
- It depends on the beam angle. A uniform, isotropic point source of 1 candela radiates in every direction (θ = 360°), so Φv = 1 × 4π ≈ 12.57 lm. Confine the same 1 cd to a 30° cone and the flux drops to 1 × 0.2141 ≈ 0.21 lm — candela measures beam intensity, lumens measure total light output.
- Why does a narrow beam give so few lumens?
- Candela already "includes" concentration: it is lumens per steradian. Shrinking the apex angle shrinks the solid angle Ω = 2π(1 − cos(θ/2)), so the same candela spreads over fewer steradians and the total flux drops — a laser pointer has huge candela but tiny lumens.
- What apex angle should I use for a flashlight or LED?
- Use the full beam angle printed on the datasheet (the angle between the two directions where intensity falls to half — the "apex" of the cone measured edge to edge, not half from the axis). A common "flashlight" beam of 15° total spread is θ = 15 here, Ω ≈ 0.0538 sr.
- Limits of this conversion
- The formula assumes the source is uniform inside the cone and isotropic within it. Real lamps have hot spots and spill, so the result is an idealized estimate. Apex angles above 360° are rejected because a cone cannot open wider than a full sphere.
Privacy: every calculation runs in your browser tab — no value you type is sent anywhere. Copy result uses your clipboard only. Results assume a uniform cone beam; verify real luminaires with a goniophotometer or integrating sphere.