Lumen to Millicandela Calculator
Convert lumens (lm) to millicandela (mcd) based on beam angle. This calculator is essential for LED specifications, indicator lights, and optical engineering where intensity is expressed in millicandela. See also our Millicandela to Lumen Calculator and Lumen to Candela Calculator.
How to Convert Lumens to Millicandela
Converting lumens to millicandela requires knowing the beam angle of the light source. Lumens measure total light output in all directions within the beam, while millicandela measures the peak intensity in one direction. Narrower beams concentrate the same lumens into a smaller solid angle, resulting in higher millicandela values. Here is the step-by-step process:
- Determine the lumen output: Find the total luminous flux of the LED or light source in lumens. For indicator LEDs, this is typically 0.1–20 lumens.
- Identify the beam angle: Check the LED datasheet for the viewing angle (typically specified as the full angle at half-maximum intensity). Common values for indicator LEDs are 5°–60°.
- Calculate the solid angle: Convert the beam angle to steradians using Ω = 2π × (1 − cos(θ/2)), where θ is the beam angle in radians.
- Calculate candela: Divide lumens by the solid angle: Candela = Lumens / Ω.
- Convert to millicandela: Multiply candela by 1,000: mcd = Candela × 1,000.
Millicandela is the standard unit for specifying LED indicator brightness in electronics. A typical red indicator LED might be rated at 50–200 mcd, while a high-brightness LED for outdoor signage might reach 10,000–50,000 mcd. The millicandela rating tells you how bright the LED appears when viewed directly along its optical axis.
Lumen to Millicandela Formula
mcd = (Lumens / (2π × (1 − cos(θ/2)))) × 1000
Where:
mcd = Millicandela (luminous intensity × 1000)
Lumens (lm) = Total luminous flux
θ = Beam angle in degrees (full cone angle)
2π × (1 − cos(θ/2)) = Solid angle Ω in steradians
Step-by-step:
1. Convert angle to radians: θ_rad = θ° × π / 180
2. Calculate solid angle: Ω = 2π × (1 − cos(θ_rad / 2))
3. Calculate candela: cd = Lumens / Ω
4. Convert to millicandela: mcd = cd × 1000
Relationship:
1 candela (cd) = 1,000 millicandela (mcd)
1 millicandela (mcd) = 0.001 candela (cd)The formula divides the total luminous flux by the solid angle of the beam cone to find the average intensity within that cone. For LEDs with Lambertian (cosine) emission patterns, the peak intensity is typically 1.5–2× the average intensity calculated by this formula. Datasheet mcd values usually represent the peak on-axis intensity, which may be higher than this geometric average for non-uniform beam profiles.
Example Calculation
Problem: An LED produces 5 lumens with a 20° beam angle. What is its intensity in millicandela?
Step 1: Convert beam angle to radians
θ = 20° × π/180 = 0.3491 radians
Step 2: Calculate the solid angle
Ω = 2π × (1 − cos(10°))
Ω = 2π × (1 − cos(0.1745))
Ω = 2π × (1 − 0.98481)
Ω = 6.2832 × 0.01519
Ω = 0.09547 sr
Step 3: Calculate candela
cd = 5 / 0.09547 = 52.37 cd
Step 4: Convert to millicandela
mcd = 52.37 × 1000 = 52,372 mcd
Answer: A 5-lumen LED with a 20° beam angle has an intensity of approximately 52,372 mcd (52.4 cd). This is a high-brightness LED suitable for outdoor indicators, automotive signals, or focused task lighting applications.
Lumens to Millicandela Reference Table
Millicandela values for common lumen outputs at various beam angles. Useful for LED selection and optical design.
| Lumens | 5° (mcd) | 10° (mcd) | 20° (mcd) | 30° (mcd) | 60° (mcd) | 120° (mcd) |
|---|---|---|---|---|---|---|
| 0.1 lm | 16,580 | 4,170 | 1,047 | 467 | 119 | 32 |
| 0.5 lm | 82,900 | 20,850 | 5,237 | 2,337 | 594 | 159 |
| 1 lm | 165,800 | 41,700 | 10,474 | 4,674 | 1,188 | 318 |
| 2 lm | 331,600 | 83,400 | 20,949 | 9,348 | 2,376 | 637 |
| 5 lm | 829,000 | 208,500 | 52,372 | 23,370 | 5,941 | 1,592 |
| 10 lm | 1,658,000 | 417,000 | 104,744 | 46,740 | 11,882 | 3,183 |
| 20 lm | 3,316,000 | 834,000 | 209,489 | 93,480 | 23,764 | 6,366 |
Notice the dramatic effect of beam angle: 1 lumen at 5° produces 165,800 mcd, while the same 1 lumen at 120° produces only 318 mcd — a 521× difference. This is why narrow-beam LEDs appear much brighter when viewed on-axis despite having the same total light output as wide-angle LEDs.
LED Indicator Brightness Classifications
LED indicators are classified by their millicandela rating, which determines visibility under different ambient lighting conditions. Understanding these classifications helps engineers select the right LED for their application — from dim panel indicators to high-visibility outdoor signals.
| Classification | mcd Range | Typical Use | Visibility |
|---|---|---|---|
| Low brightness | 1–100 | Panel indicators, status LEDs | Indoor, dim ambient |
| Standard | 100–500 | Equipment indicators, displays | Indoor, normal ambient |
| High brightness | 500–5,000 | Bright indicators, small signs | Indoor, bright ambient |
| Ultra-high brightness | 5,000–20,000 | Outdoor signs, traffic signals | Outdoor, daylight |
| Power LED | 20,000–100,000+ | Automotive, signage, lighting | Direct sunlight |
For outdoor visibility in direct sunlight, LEDs need at least 5,000 mcd. Traffic signals typically use LEDs rated at 10,000–50,000 mcd to ensure visibility from 200+ meters in bright daylight. Indoor panel indicators only need 20–100 mcd since they operate in controlled ambient lighting conditions.
Frequently Asked Questions
What is the difference between lumens and millicandela?
Lumens measure total light output in all directions (luminous flux), while millicandela measures light intensity in one specific direction (luminous intensity). An LED with high millicandela but low lumens has a narrow, focused beam — bright when viewed head-on but little total light. An LED with high lumens but low millicandela has a wide beam — lots of total light spread over a large area. The beam angle connects the two: narrower beams produce higher mcd from the same lumens.
How many millicandela is 1 lumen?
It depends entirely on the beam angle. At 5° beam: 1 lumen = 165,800 mcd. At 10°: 41,700 mcd. At 20°: 10,474 mcd. At 30°: 4,674 mcd. At 60°: 1,188 mcd. At 120°: 318 mcd. At 180° (hemisphere): 159 mcd. Without knowing the beam angle, you cannot convert between lumens and millicandela. This is a fundamental principle of photometry — total flux and directional intensity are different physical quantities connected only through geometry.
What mcd rating do I need for an outdoor LED indicator?
For outdoor visibility: Shaded outdoor areas need 1,000–3,000 mcd. Partial sunlight requires 3,000–8,000 mcd. Direct sunlight visibility requires 8,000–20,000 mcd. Traffic signal visibility at 200m in sunlight requires 10,000–50,000 mcd. Aviation warning lights need 20,000+ mcd. Always test in actual conditions, as ambient light, viewing angle, and LED color affect perceived brightness. Red and amber LEDs appear brighter to the human eye than blue or green at the same mcd rating.
Why do LED datasheets use millicandela instead of lumens?
Indicator LEDs use millicandela because their primary purpose is to be seen from a specific direction — you look directly at the LED to read its status. Millicandela tells you exactly how bright it appears from that viewing direction. Lumens would be less useful because indicator LEDs don't need to illuminate a room — they need to be visible to an observer. For general illumination LEDs (bulbs, panels), lumens are used because total light output matters more than directional intensity.
How does beam angle affect millicandela?
Beam angle has an inverse-square relationship with millicandela for the same lumen output. Halving the beam angle approximately quadruples the millicandela. A 1-lumen LED at 10° produces 41,700 mcd, while the same 1 lumen at 20° produces only 10,474 mcd — about 4× less. This is because narrower beams concentrate the same total light into a smaller solid angle, increasing the intensity per unit solid angle (which is what candela/millicandela measures).
Can I compare LEDs with different beam angles using mcd?
Comparing mcd directly between LEDs with different beam angles is misleading. A 10,000 mcd LED with a 5° beam produces far less total light than a 10,000 mcd LED with a 60° beam. For fair comparison, convert both to lumens first: Lumens = mcd/1000 × 2π × (1 − cos(θ/2)). The 5° LED produces 0.06 lumens while the 60° LED produces 8.4 lumens — 140× more total light despite identical mcd ratings. Always compare lumens for total brightness or mcd for directional visibility, but not mcd across different beam angles.