Candela to Lumen Calculator
Convert candela (cd) to lumens (lm) based on beam angle. This calculator determines the total luminous flux from a light source's intensity and beam spread. See also our Lumen to Candela Calculator and Lux to Lumen Calculator.
How to Convert Candela to Lumens
Converting candela to lumens requires knowing the beam angle of the light source. Candela measures the luminous intensity in a specific direction, while lumens measure the total luminous flux emitted within the beam cone. A wider beam angle means the same candela value produces more total lumens because the light covers a larger solid angle. Follow these steps to perform the conversion:
- Identify the candela value: Find the luminous intensity rating of your light source in candela (cd). This is often listed as peak beam candlepower (PBCP) or center beam candlepower (CBCP) on product datasheets.
- Determine the beam angle: Locate the beam angle in degrees. This is the full cone angle where intensity drops to 50% of the peak value. Common values are 15° for narrow spots, 30° for spots, 60° for floods, and 120° for wide floods.
- Convert the beam angle to radians: Multiply the beam angle in degrees by π/180. For example, 30° × π/180 = 0.5236 radians.
- Calculate the solid angle in steradians: Use the formula Ω = 2π × (1 − cos(θ/2)), where θ is the beam angle in radians. This gives you the solid angle of the beam cone.
- Multiply candela by the solid angle: The total lumens within the beam equals the candela value multiplied by the solid angle in steradians: Lumens = Candela × Ω.
This method assumes uniform light distribution within the beam cone. Real-world light sources typically have a Gaussian or cosine distribution, meaning the center is brighter than the edges. The calculated lumen value represents the equivalent total flux if the beam were perfectly uniform at the stated candela intensity across the entire cone.
Candela to Lumen Formula
Lumens = Candela × 2π × (1 - cos(θ/2))
Where:
Lumens (lm) = Total luminous flux within the beam
Candela (cd) = Luminous intensity (light per unit solid angle)
θ = Beam angle in degrees (full cone angle)
2π × (1 - cos(θ/2)) = Solid angle Ω in steradians (sr)
The solid angle represents the "size" of the cone in 3D space:
- A full sphere = 4π ≈ 12.566 steradians
- A hemisphere = 2π ≈ 6.283 steradians
- A 60° cone ≈ 0.842 steradians
- A 30° cone ≈ 0.214 steradians
- A 10° cone ≈ 0.024 steradians
Note: Convert degrees to radians before applying cosine:
θ_rad = θ_degrees × π / 180The solid angle is a measure of how large a cone appears from its apex. A full sphere subtends 4π steradians (approximately 12.566 sr). The formula 2π × (1 − cos(θ/2)) calculates the solid angle of a cone with half-angle θ/2. As the beam angle increases from 0° to 360°, the solid angle increases from 0 to 4π steradians. This geometric relationship is fundamental to photometry and connects the directional measurement (candela) to the total output measurement (lumens).
Example Calculation
Problem: Convert 1000 candela with a 30° beam angle to lumens.
Step 1: Convert beam angle to radians
θ = 30° × π/180 = 0.5236 radians
Step 2: Calculate the half-angle
θ/2 = 15° = 0.2618 radians
Step 3: Calculate the solid angle
Ω = 2π × (1 − cos(15°))
Ω = 2π × (1 − 0.96593)
Ω = 2π × 0.03407
Ω = 6.2832 × 0.03407
Ω = 0.2141 steradians
Step 4: Calculate lumens
Lumens = 1000 cd × 0.2141 sr
Lumens = 214.1 lm
Answer: A 1000-candela light source with a 30° beam angle produces approximately 214.1 lumens of total luminous flux within the beam cone. This is equivalent to a focused spotlight that concentrates its output into a narrow beam, making it appear very bright in one direction despite having a relatively modest total lumen output.
Candela to Lumens Conversion Table
This reference table shows lumen values for 100 cd, 500 cd, and 1000 cd at beam angles from 10° to 180°. Use it to quickly estimate total light output from candela specifications.
| Beam Angle | Solid Angle (sr) | 100 cd → lm | 500 cd → lm | 1000 cd → lm |
|---|---|---|---|---|
| 10° | 0.0239 | 2.4 lm | 12.0 lm | 23.9 lm |
| 15° | 0.0538 | 5.4 lm | 26.9 lm | 53.8 lm |
| 20° | 0.0955 | 9.6 lm | 47.7 lm | 95.5 lm |
| 30° | 0.2141 | 21.4 lm | 107.1 lm | 214.1 lm |
| 45° | 0.4783 | 47.8 lm | 239.2 lm | 478.3 lm |
| 60° | 0.8418 | 84.2 lm | 420.9 lm | 841.8 lm |
| 90° | 1.8406 | 184.1 lm | 920.3 lm | 1,840.6 lm |
| 120° | 3.1416 | 314.2 lm | 1,570.8 lm | 3,141.6 lm |
| 150° | 4.4429 | 444.3 lm | 2,221.5 lm | 4,442.9 lm |
| 180° | 6.2832 | 628.3 lm | 3,141.6 lm | 6,283.2 lm |
Notice how the lumen output increases dramatically with beam angle. A 1000 cd source with a 10° beam produces only 23.9 lumens, while the same intensity at 120° produces 3,141.6 lumens. This demonstrates why narrow-beam spotlights can have very high candela ratings despite modest total lumen output, and why wide-angle floodlights need high lumen ratings to achieve useful candela values.
Understanding Candela, Lumens, and Lux
Candela, lumens, and lux are the three fundamental photometric units used to describe visible light. Each measures a different aspect of light output and perception. Understanding how they relate to each other is essential for anyone working with lighting design, product specifications, or illumination engineering.
Candela (cd) is the SI base unit of luminous intensity. It measures how bright a light source appears when viewed from a specific direction. One candela is roughly equivalent to the light intensity of a single common candle. Candela is direction-dependent — a flashlight might produce 10,000 cd in its beam direction but nearly 0 cd to the side. Candela is the preferred unit for specifying directional light sources like spotlights, flashlights, laser pointers, and signal lights.
Lumens (lm) measure the total luminous flux — the total amount of visible light emitted by a source in all directions. Unlike candela, lumens are not direction-dependent. A 100-watt incandescent bulb produces about 1,600 lumens regardless of which direction you measure from. Lumens are the best unit for comparing the total brightness of light bulbs, room lighting, and any application where you care about overall light output rather than directional intensity.
Lux (lx) measures illuminance — the amount of light falling on a surface per unit area. One lux equals one lumen per square meter. Lux depends on both the light source output and the distance from the source. A 1000-lumen spotlight creates high lux values on a nearby surface but low lux values on a distant wall. Lux is used to specify lighting requirements for workspaces (500 lux for offices), roads (15-30 lux), and photography.
| Unit | Measures | SI Quantity | Depends On | Best For |
|---|---|---|---|---|
| Candela (cd) | Intensity in one direction | Luminous intensity | Direction only | Spotlights, flashlights |
| Lumen (lm) | Total light output | Luminous flux | Source only | Bulbs, room lighting |
| Lux (lx) | Light on a surface | Illuminance | Source + distance + area | Workspace standards |
The relationships between these units are: Lumens = Candela × Solid Angle (steradians), and Lux = Lumens / Area (m²) = Candela / Distance² (for a point source). These formulas allow you to convert between any of the three units when you know the beam geometry and measurement distance.
Practical Applications
The candela to lumen conversion is essential across multiple industries where understanding total light output from directional intensity specifications is critical for proper lighting design and product selection.
- LED Lighting Design: LED manufacturers often specify their products in candela because LEDs are inherently directional. When designing a lighting installation, engineers need to convert these candela ratings to lumens to calculate total room illumination, determine how many fixtures are needed, and ensure compliance with building codes that specify minimum lumen levels per square meter. For example, a recessed downlight rated at 2000 cd with a 40° beam produces about 586 lumens — knowing this helps determine spacing between fixtures.
- Flashlight Specifications: The flashlight industry uses both candela and lumens in product specifications. Peak beam intensity in candela determines throw distance (how far the beam reaches), while total lumens indicates overall brightness. A tactical flashlight rated at 50,000 cd with a 10° hotspot produces about 1,196 lumens total. Understanding this conversion helps consumers compare flashlights that emphasize different metrics and choose the right tool for their needs — whether they need long throw or broad illumination.
- Stage Lighting: Theater and concert lighting designers work with photometric data that specifies intensity in candela at various angles. Converting to lumens helps them calculate total light output for energy budgeting, heat management, and dimming calculations. A moving head fixture might produce 150,000 cd at its narrowest 8° beam setting (about 1,463 lumens in the beam) versus 5,000 cd at a wide 45° flood setting (about 2,392 lumens). The wider setting actually produces more total lumens despite lower intensity.
- Automotive Headlights: Vehicle headlight regulations specify minimum and maximum candela values in specific directions (e.g., ECE R112 requires minimum 6,400 cd for low beam at the hot zone). Converting these directional requirements to total lumens helps headlight designers select appropriate LED modules and reflector geometries. A modern LED headlight module might need to produce 20,000 cd in the primary beam direction with a 30° × 10° beam pattern, requiring careful optical design to achieve the target lumen output efficiently.
- Aviation and Marine Signals: Navigation lights and signal beacons must meet strict candela requirements for visibility at specified distances. Airport approach lights require minimum 5,000 cd for daytime visibility. Converting to lumens helps engineers select LED arrays and power supplies. A runway edge light producing 10,000 cd in a 10° vertical × 360° horizontal pattern needs approximately 5,483 lumens total output from its LED source.
- Security and Surveillance Lighting: IR illuminators for security cameras are rated in candela to indicate how far they can illuminate a scene. Converting to lumens helps determine power requirements and heat dissipation needs. A long-range IR illuminator rated at 100,000 cd with a 5° beam produces only about 598 lumens total, making it energy-efficient despite its extreme intensity in one direction.
Frequently Asked Questions
What is the difference between candela and lumens?
Candela measures luminous intensity — how bright a light appears in a specific direction. Lumens measure luminous flux — the total amount of light emitted in all directions within the beam. Think of candela as the brightness you perceive looking directly at a light, while lumens represent the total light energy being produced. A narrow-beam flashlight has high candela but may have fewer lumens than a wide-angle bulb that appears dimmer from any single direction but produces more total light. The conversion between them depends entirely on the beam angle (solid angle) of the light source.
How many lumens is 1000 candela?
The lumen output of 1000 candela depends on the beam angle. At 15° beam angle: 53.8 lumens. At 30° beam angle: 214.1 lumens. At 45° beam angle: 478.3 lumens. At 60° beam angle: 841.8 lumens. At 90° beam angle: 1,840.6 lumens. At 120° beam angle: 3,141.6 lumens. For a full sphere (360°): 12,566.4 lumens. The wider the beam, the more total lumens are produced from the same candela intensity because the light covers a larger solid angle.
What is beam angle in lighting?
Beam angle is the angular width of a light cone measured between the two directions where the intensity drops to 50% of the peak (center) value. It defines how spread out or focused a light beam is. A 15° beam angle creates a tight spotlight effect, while a 120° beam angle creates broad floodlighting. The beam angle is different from the field angle (where intensity drops to 10% of peak). Most LED product specifications list the beam angle, which is the more commonly used measurement for comparing directional light sources.
How do I convert candela to lux?
To convert candela to lux, use the formula: Lux = Candela / Distance². This applies to a point source illuminating a surface perpendicular to the beam direction. For example, a 1000 cd light source produces 1000 lux at 1 meter, 250 lux at 2 meters, and 111 lux at 3 meters. The lux value decreases with the square of the distance (inverse square law). For our dedicated tool, try the Candela to Lux Calculator.
What candela rating do I need for a flashlight?
The candela rating you need depends on your intended use. For everyday carry (EDC) and close-range tasks: 2,000–10,000 cd provides 90–200 meter throw. For security and law enforcement: 20,000–60,000 cd provides 280–490 meter throw. For search and rescue: 100,000–500,000 cd provides 630–1,414 meter throw. The ANSI FL1 beam distance formula is: Distance (meters) = √(Candela × 4) = 2 × √Candela. Choose based on how far you need to see clearly, keeping in mind that higher candela usually means a narrower hotspot.
Why do LED specs use candela instead of lumens?
LED manufacturers often specify candela because LEDs are inherently directional light sources. Unlike incandescent bulbs that emit light in all directions, an LED chip emits light primarily forward in a defined cone. Candela more accurately represents the useful light output in the intended direction without needing to account for light lost to the sides or back. Additionally, candela is independent of beam angle — a 100 cd LED produces 100 cd regardless of its optic. This makes it easier to compare bare LED chips before secondary optics are applied. Lumens, while useful for total output, can be misleading for directional applications where only the forward intensity matters.