Lumen to Millicandela Calculator
Convert lumens (lm) to millicandela (mcd): mcd = 1000 × lm ÷ 2π(1 − cos(θ/2)). Reverse mcd to lumens. Runs locally in your browser. Fast and free.
Trust summary Engine tested · Specification checked · v1.1.0
- Input interpretation
- Enter values to calculate.
- Result
- —
- Model
- Millicandela from lumens and full beam angle, or lumens from millicandela and angle.
- Scope
- Uniform intensity over a circular cone
- Verification
- Engine tested · Specification checked · v1.1.0
- Named expert review
- Optional · Not performed
- Specification basis
- I(cd)=Φ/Ω; mcd=1000·cd; Ω=2π(1−cos(θ/2))
Formulas
Core equations used by this calculator.
How to use
Choose direction
lm → mcd for intensity from flux, or mcd → lm for the reverse.
Enter lumens (or mcd) and full beam angle
Use the manufacturer’s full beam / viewing angle in degrees.
Read mcd or lumens
Result assumes uniform intensity over the cone. Divide mcd by 1000 to get candela.
Example calculations
Common configurations with formula and result.
1000 lm · 60°
Default
Same as candela
÷ 1000
1 lm · 10°
Narrow LED-like beam
Full sphere
12.566 lm · 360°
mcd → lm
500,000 mcd · 60°
mcd per lumen vs full beam angle θ
Common values at a glance.
| θ (full) | Ω (sr) | mcd per lm |
|---|---|---|
| 10° | 0.0239 | ≈ 41,825 |
| 30° | 0.214 | ≈ 4,672 |
| 60° | 0.842 | ≈ 1,188 |
| 90° | 1.840 | ≈ 543 |
| 120° | 3.142 | ≈ 318 |
| 180° | 6.283 | ≈ 159 |
| 360° | 12.566 | ≈ 80 |
Lumen to Millicandela calculator specification
Version 1.1.0 · Engine tested
- Engine tested 3 published cases
- Named expert review Not performed
- Calculation version 1.1.0
- Definition
- Millicandela (mcd) is one-thousandth of a candela: 1 cd = 1000 mcd. Indicator LEDs are often rated in mcd. For a uniform cone with full apex angle θ, cd = lm ÷ Ω with Ω = 2π(1 − cos(θ/2)), so mcd = 1000 × lm ÷ Ω. Reverse: lm = (mcd ÷ 1000) × Ω.
- What it calculates
- Millicandela from lumens and full beam angle, or lumens from millicandela and angle.
- Inputs
- Lumens (lm) or millicandela (mcd)
- Full beam angle θ in degrees
- Outputs
- mcd (lm → mcd) or lm (mcd → lm)
- Formula
Ω=2π(1−cos(θ/2)); mcd=1000·Φ/Ω- Assumptions
- Uniform intensity over a circular cone
- θ is full apex angle
- 1 cd = 1000 mcd
- Units
- lm, ° → mcd
- Boundary conditions
- θ = 0 → Ω = 0 → undefined (UI returns 0)
- θ = 360° → Ω = 4π
- Example
- 1000 lm, 60° → ≈ 1,187,949 mcd
- Validation cases
3 published on this page
- 1000 lm, 60° → ≈ 1,187,948.67 mcd
- 500000 mcd, 60° → lm → ≈ 420.89 lm
- 12.566 lm, 360° → ≈ 1000 mcd
- Specification basis
- I(cd)=Φ/Ω; mcd=1000·cd; Ω=2π(1−cos(θ/2))
- Calculation version
- 1.1.0
Background
Interpretation and common distinctions.
Convert lumens (lm) to millicandela (mcd) using the full beam (apex) angle.
I((mcd)) = 1000 × (Phi((lm)))/(2π(1 − cosfracθ2))
Default: 1000 lm · 60° → ≈ 1,187,949 mcd (≈ 1187.95 cd).
mcd vs candela vs lumens
| Unit | Measures |
|---|---|
| Lumen (lm) | Total luminous flux |
| Candela (cd) | Luminous intensity in a direction |
| Millicandela (mcd) | Same intensity, scaled: 1 cd = 1000 mcd |
Indicator and discrete LEDs are commonly specified in mcd. You still need a beam / viewing angle to relate flux and intensity.
Solid angle
Ω((sr)) = 2π(1 − cos(θ)/2)
Then mcd = 1000 × Phi / Ω, and lm = (mcd/1000) × Ω.
Related tools
Other calculators in this family: Lumen to Candela, Candela to Lumen, Lumen to Lux, Candela to Lux .
Frequently asked questions
Key distinctions behind the calculation.
How do I convert lumens to millicandela?
mcd = 1000 × lm ÷ 2π(1 − cos(θ/2)), where θ is the full beam angle in degrees. You need a beam angle (or solid angle).
What is a millicandela?
One millicandela is 0.001 candela. LED datasheets often use mcd for small indicator and discrete LEDs.
How do mcd and candela relate?
1 cd = 1000 mcd. Convert mcd → cd by dividing by 1000, or use the lumen to candela calculator for the same beam angle.
Why can’t I convert lm to mcd without an angle?
Lumens are total flux; mcd is directional intensity. The link is the solid angle of the beam.
Is θ half-angle or full angle?
This calculator uses the full apex / viewing angle. If a sheet lists ±30°, enter 60°.
Why are LED mcd ratings so high?
Narrow viewing angles concentrate flux into a small solid angle, so intensity (mcd) looks large even when total lumens are modest.
Can I convert mcd back to lumens?
Yes — use mcd → lm: lm = (mcd ÷ 1000) × Ω with the same beam angle.
Does uniformity matter?
Yes. The formula assumes constant intensity inside the cone. Real LEDs peak on-axis — treat results as estimates.