Millicandela to Lumens Calculator
Convert luminous intensity in millicandela (mcd) to luminous flux in lumens (lm) for a beam with a cone apex angle. Enter the millicandela value and the apex angle in degrees, and press Calculate — the lumens result comes from Φv(lm) = Iv(mcd) × 2π(1 − cos(θ/2)) / 1000. Everything runs locally in your browser.
Enter luminous intensity
Type the luminous intensity Iv in millicandela (mcd) — how bright the source looks straight down its beam, in thousandths of a candela (1 cd = 1000 mcd). Zero or higher is accepted; zero millicandela 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. Angles greater than 0° and up to 360° (a source radiating in every direction) are accepted.
Press Calculate, read lumens
The luminous flux Φv appears in lumens (lm) with up to six decimals, together with the solid angle Ω in steradians. Copy the result to your clipboard, or press Reset to clear everything and start over.
Millicandela to lumens calculation
- Millicandela 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 millicandela (mcd), times the solid angle Ω in steradians (sr), divided by 1000: Φv(lm) = Iv(mcd) × 2π(1 − cos(θ/2)) / 1000, where θ is the cone apex angle in degrees. For example, 1000 mcd within a 30° cone gives 1000 × 0.214094 / 1000 ≈ 0.214094 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 ≈ 12.566371 sr.
- What is 1000 millicandela in lumens?
- It depends on the beam angle. 1000 mcd equals 1 candela, and a uniform, isotropic 1 cd source radiating in every direction (θ = 360°) gives Φv = 1 × 4π ≈ 12.57 lm. Confined to a 30° cone the same 1000 mcd yields only ≈ 0.214 lm — candela measures beam intensity, lumens measure total light output.
- Millicandela vs candela
- One candela (cd) is exactly 1000 millicandela (mcd). LED datasheets commonly quote intensity in mcd — a typical indicator LED is 100–5000 mcd. To run this conversion in candela instead, divide your mcd value by 1000 and multiply the lumens result by 1000; equivalently, use the / 1000 built into the formula above.
- 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 millicandela spreads over fewer steradians and the total flux drops — a laser pointer has huge millicandela but tiny lumens.
- Limits of this conversion
- The formula assumes the source is uniform inside the cone and isotropic within it. Real LEDs have hot spots and spill, so the result is an idealized estimate. Apex angles of 0° or below and above 360° are rejected because a cone cannot open wider than a full sphere (and a 0° cone carries no light).
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.