Lumens to Millicandela Calculator
Convert luminous flux in lumens (lm) to luminous intensity in millicandela (mcd) for a beam with a cone apex angle. Enter the lumens value and the apex angle in degrees, and press Calculate — the millicandela result comes from Iv(mcd) = 1000 × Φv(lm) / (2π(1 − cos(θ/2))). Everything runs locally in your browser.
How to convert lumens to millicandela
For a uniform light source radiating inside a cone with apex angle θ, the solid angle is Ω = 2π(1 − cos(θ/2)) in steradians. The luminous intensity in millicandela is Iv(mcd) = 1000 × Φv(lm) / Ω(sr). Enter the luminous flux in lumens and the apex angle in degrees (more than 0° and at most 360°; 360° means the source radiates uniformly in all directions) and press Calculate.
Enter luminous flux
Type the luminous flux Φv in lumens (lm) — the total light the source puts out. Zero up to 1,000,000,000,000 lm is accepted; zero lumens gives zero millicandela.
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 millicandela
The luminous intensity Iv appears in millicandela (mcd) together with the solid angle Ω in steradians. Press Reset to clear the fields, the result and any message and start over.
Lumens to millicandela calculation
- Lumens to millicandela formula
- For a uniform, isotropic light source inside a cone, the luminous intensity Iv in millicandela (mcd) is equal to 1000 times the luminous flux Φv in lumens (lm), divided by the solid angle Ω in steradians (sr): Iv(mcd) = 1000 × Φv(lm) / (2π(1 − cos(θ/2))), where θ is the cone apex angle in degrees. For example, 50 lm inside a 120° cone gives 1000 × 50 / π ≈ 15915.494 mcd.
- 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 hemisphere (θ = 180°) has Ω = 2π ≈ 6.283 sr; a full sphere (θ = 360°) has Ω = 4π ≈ 12.566 sr.
- What is 1 lumen in millicandela?
- It depends on the beam angle. A uniform 1 lm source radiating in every direction (θ = 360°) gives 1000 / 4π ≈ 79.577 mcd. Confined to a 180° hemisphere it gives 1000 / 2π ≈ 159.155 mcd, and squeezed into a 60° cone the same 1 lm reaches about 1,187,949 mcd — lumens count total light, millicandela count how strongly it leaves the source in one direction.
- Millicandela versus candela
- One candela (cd) is exactly 1000 millicandela (mcd), just like one ampere is 1000 milliampere. Indicator LEDs are usually specified in mcd: a bright status LED might be 1000 to 5000 mcd on axis — the same 1 to 5 cd. Use the candela direction of this conversion when your datasheet works in cd instead.
- Why does a narrower beam give more millicandela?
- Millicandela is milli-lumens per steradian. The same total flux squeezed into a smaller solid angle Ω = 2π(1 − cos(θ/2)) concentrates into fewer steradians, so the intensity per direction rises — a projector lens turns modest lumens into very large candela.
- 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. An apex angle of 0° is rejected because the solid angle would be zero (division by zero), and 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. Results assume a uniform cone beam; verify real luminaires with a goniophotometer or integrating sphere.