Millicandela to Lumen Calculator
Convert millicandela (mcd) to lumens (lm) based on beam angle. Determine the total luminous flux from an LED's intensity rating. Essential for comparing LED indicators and calculating total light output from datasheet specifications. See also our Lumen to Millicandela Calculator and Candela to Lumen Calculator.
How to Convert Millicandela to Lumens
Converting millicandela to lumens determines the total light output from an LED's directional intensity specification. This is the reverse of the more common lumen-to-mcd conversion and is essential when you have an LED datasheet specifying intensity in mcd and need to know total luminous flux for lighting calculations. Follow these steps:
- Find the millicandela rating: Check the LED datasheet for the typical or maximum luminous intensity in mcd. This is usually measured at 20mA forward current for standard indicator LEDs.
- Convert to candela: Divide millicandela by 1,000: Candela = mcd / 1,000. For example, 5,000 mcd = 5 cd.
- Determine the beam angle: Find the viewing angle (2θ½) on the datasheet. This is the full angle where intensity drops to 50% of the peak value.
- Calculate the solid angle: Use Ω = 2π × (1 − cos(θ/2)) where θ is the beam angle in radians.
- Calculate lumens: Multiply candela by the solid angle: Lumens = Candela × Ω = (mcd/1000) × 2π × (1 − cos(θ/2)).
This conversion is particularly important when designing LED arrays for illumination. If you know each LED's mcd rating and beam angle, you can calculate the total lumens from the array and determine whether it meets your illumination requirements. It also helps compare LEDs from different manufacturers that may specify brightness in different units.
Millicandela to Lumen Formula
Lumens = (mcd / 1000) × 2π × (1 − cos(θ/2))
Where:
Lumens (lm) = Total luminous flux within the beam
mcd = Millicandela (luminous intensity × 1000)
θ = Beam angle in degrees (full viewing angle)
2π × (1 − cos(θ/2)) = Solid angle Ω in steradians
Step-by-step:
1. Convert mcd to candela: cd = mcd / 1000
2. Convert angle to radians: θ_rad = θ° × π / 180
3. Calculate solid angle: Ω = 2π × (1 − cos(θ_rad / 2))
4. Calculate lumens: lm = cd × Ω
Key relationships:
1,000 mcd = 1 cd
1 cd at 1 sr = 1 lumen
Full sphere = 4π sr ≈ 12.566 srThe formula multiplies the intensity (in candela, converted from mcd) by the solid angle of the beam cone. Since millicandela is simply candela × 1000, the conversion first divides by 1000 to get candela, then applies the standard candela-to-lumens formula. The solid angle determines what fraction of a full sphere the beam covers — a 120° beam covers π steradians (25% of a sphere), while a 10° beam covers only 0.024 steradians (0.19% of a sphere).
Example Calculation
Problem: An LED indicator is rated at 5,000 mcd with a 20° viewing angle. What is its total luminous flux in lumens?
Step 1: Convert to candela
cd = 5,000 / 1,000 = 5 cd
Step 2: Convert beam angle to radians
θ = 20° × π/180 = 0.3491 radians
Step 3: Calculate the solid angle
Ω = 2π × (1 − cos(10°))
Ω = 2π × (1 − 0.98481)
Ω = 6.2832 × 0.01519
Ω = 0.09547 sr
Step 4: Calculate lumens
Lumens = 5 × 0.09547
Lumens = 0.4774 lm
Answer: A 5,000 mcd LED with a 20° beam angle produces approximately 0.48 lumens of total luminous flux. This is typical for a high-brightness indicator LED — very visible when viewed directly (5 cd intensity) but producing less than half a lumen of total light output due to the narrow beam.
Millicandela to Lumens Reference Table
Total lumen output for common mcd ratings at various beam angles. Helps determine actual light output from LED datasheet specifications.
| mcd | 10° (lm) | 20° (lm) | 30° (lm) | 60° (lm) | 120° (lm) |
|---|---|---|---|---|---|
| 100 | 0.0024 | 0.0095 | 0.0214 | 0.0842 | 0.3142 |
| 500 | 0.012 | 0.048 | 0.107 | 0.421 | 1.571 |
| 1,000 | 0.024 | 0.095 | 0.214 | 0.842 | 3.142 |
| 5,000 | 0.120 | 0.477 | 1.071 | 4.209 | 15.708 |
| 10,000 | 0.239 | 0.955 | 2.141 | 8.418 | 31.416 |
| 20,000 | 0.479 | 1.910 | 4.283 | 16.836 | 62.832 |
| 50,000 | 1.197 | 4.774 | 10.706 | 42.090 | 157.080 |
| 100,000 | 2.394 | 9.547 | 21.413 | 84.180 | 314.159 |
A standard 5,000 mcd indicator LED with a 20° beam produces only 0.48 lumens — far less than a general illumination LED. Even a 100,000 mcd LED at 10° produces only 2.4 lumens. This illustrates why indicator LEDs are designed for visibility (high mcd in one direction) rather than illumination (high total lumens). For lighting applications, you need LEDs rated in lumens, not millicandela.
Understanding LED Datasheet Specifications
LED datasheets contain several optical parameters that are often confused. Understanding the relationship between millicandela, lumens, beam angle, and viewing angle is essential for proper LED selection and circuit design.
- Luminous Intensity (mcd): The peak on-axis brightness measured at a specified forward current (typically 20mA for indicators). This is the value used in our conversion formula. It represents the maximum brightness when viewed directly from the front.
- Viewing Angle (2θ½): The full angle between the two directions where intensity drops to 50% of the peak value. Also called the half-power beam width. A 20° viewing angle means the LED appears half as bright at 10° off-axis compared to directly on-axis.
- Luminous Flux (lm): Total light output in all directions. Some datasheets provide this directly, eliminating the need for conversion. When not provided, use our formula with the mcd and viewing angle values.
- Radiant Intensity (mW/sr): Similar to millicandela but measures total radiant power (including invisible wavelengths) rather than human-perceived brightness. Used primarily for IR LEDs where luminous units don't apply.
- Forward Current (If): The mcd rating is specified at a particular current. Increasing current increases brightness approximately linearly up to the maximum rated current. Operating at half the rated current produces roughly half the mcd output.
When comparing LEDs from different manufacturers, ensure you are comparing mcd values at the same forward current and junction temperature. A 5,000 mcd LED at 20mA is not directly comparable to a 5,000 mcd LED at 50mA — the first is more efficient per milliamp of drive current.
Frequently Asked Questions
How many lumens is 5000 mcd?
The lumen output of 5,000 mcd depends on the beam angle: At 10° beam: 0.12 lumens. At 20° beam: 0.48 lumens. At 30° beam: 1.07 lumens. At 60° beam: 4.21 lumens. At 120° beam: 15.71 lumens. A typical 5,000 mcd indicator LED with a 20° viewing angle produces about 0.48 lumens — enough to be clearly visible as a status indicator but far too little for illumination purposes.
What is the relationship between millicandela and candela?
Millicandela is simply one-thousandth of a candela: 1 cd = 1,000 mcd, and 1 mcd = 0.001 cd. The "milli" prefix means 10⁻³. Millicandela is used for low-intensity sources like indicator LEDs (typically 10–50,000 mcd), while candela is used for higher-intensity sources like flashlights (100–100,000 cd) and spotlights (1,000–1,000,000 cd). The choice of unit is purely for convenience — avoiding very small or very large numbers.
Why is the lumen value so small for high-mcd LEDs?
High-mcd LEDs with narrow beam angles produce very few total lumens because the light is concentrated into a tiny solid angle. A 50,000 mcd LED at 10° produces only 1.2 lumens total. The high mcd makes it appear extremely bright when viewed on-axis, but the total light energy is minimal. This is by design — indicator LEDs need to be visible (high mcd) without wasting energy on total light output (lumens). It's like a laser pointer: very bright in one direction but negligible total light.
How do I calculate lumens for an LED array?
For an array of identical LEDs: Total Lumens = Single LED Lumens × Number of LEDs. First convert each LED's mcd to lumens using the beam angle, then multiply by the count. For example, 10 LEDs at 5,000 mcd with 20° beam: Each produces 0.48 lm, so the array produces 4.8 lumens total. For arrays with overlapping beams, the total lumens add linearly, but the peak mcd at any point depends on the geometric arrangement and spacing of the LEDs.
What beam angle should I use if the datasheet says "viewing angle"?
The "viewing angle" on LED datasheets is the same as the beam angle used in our formula — it's the full cone angle (2θ½) where intensity drops to 50% of peak. Use this value directly in the calculator. Some datasheets specify the half-angle (θ½) instead — in that case, double it before entering. If the datasheet shows a radiation pattern diagram, the viewing angle is the full width between the -3dB (50%) points on the polar plot.
Is the mcd-to-lumen conversion exact?
The conversion provides a geometric approximation assuming uniform intensity within the beam cone. Real LEDs have non-uniform beam profiles (typically Gaussian or Lambertian), meaning some light exists outside the rated beam angle. The actual total lumens may be 10–30% higher than the calculated value because the formula only accounts for light within the rated viewing angle. For precise measurements, use an integrating sphere to measure total lumens directly. The formula is accurate enough for engineering estimates and LED comparison purposes.