Candela to Lumen Converter & Apex Beam Angle Calculator

Candela, Lumens, Solid Angles & Inverse-Square Photometry

Photometry measures electromagnetic radiation weighted by the human eye's spectral sensitivity V(λ):

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• Candela to Lumen Conversion Formula (Conical Beam)**:

Φ_v = I_v × Ω (Luminous Flux in Lumens, lm)

Ω = 2π (1 - ((θ) / (2)))

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• Standard Geometric Beam Configurations**:

• Isotropic Spherical Emitter (360^): Ω = 4π ≈ 12.5664 sr Φ_v = 4π × I_v

• Hemispherical Emitter (180^): Ω = 2π ≈ 6.2832 sr Φ_v = 2π × I_v

• Lambertian Diffuse Emitter: Φ_v = π × I_v ≈ 3.1416 × I_v

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• Inverse-Square Law for Illuminance (E)**:

E = (I_v) / (d^2)

E_fc = E_lux10.7639

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• Standard Photometric Benchmarks**:

• Wax Candle: 1.0 cd @ 360^ Φ = 12.57 lm E(1m) = 1.0 lux

• SMD Indicator LED: 500.0 mcd @ 120^ Φ = 1.57 lm E(0.5m) = 2.0 lux

• PAR38 Spotlight: 1,000.0 cd @ 60^ Φ = 841.79 lm E(2m) = 250.0 lux

• Tactical Flashlight: 25,000.0 cd @ 20^ Φ = 2,386.9 lm E(5m) = 1,000.0 lux

• Automotive High Beam: 50,000.0 cd @ 15^ Φ = 2,674.3 lm E(10m) = 500.0 lux

How to Use This Calculator

Enter your Luminous Intensity (Candela / cd) (e.g. 1000 in cd), From Luminous Intensity Unit — choose from Candela (cd = lm/sr - SI Base Unit), Millicandela (mcd = 10⁻³ cd - Indicator LEDs), Kilocandela (kcd = 1,000 cd - High Beams / Searchlights), Full Beam Apex Angle (2θ in degrees) (e.g. 60 for floodlight, 360 for isotropic in deg (°)), Illuminance Target Distance (d in meters) (e.g. 2.0 in m), and Lighting & Optical Source Benchmark — choose from Custom Beam Angle & Intensity, Standard Wax Candle (1.0 cd @ 360° Isotropic) → 12.57 Lumens, SMD 2835 Indicator LED (500.0 mcd @ 120° Wide Angle) → 1.57 Lumens. Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Calculate Conical Solid Angle: Omega = 2pi (1 - cos(theta_half))

Luminous Flux in Lumens: Phi = I_v * Omega

Illuminance at Distance d: E = I_v / d^2 (Lux = lm/m^2)

Worked Example

A lighting designer selecting track spotlights converts a 1,000 cd LED with a 60° beam angle into 841.8 Lumens, confirming it delivers 250 Lux of accent illumination on an artwork displayed 2.0 meters away.

Understanding Your Result

Unit conversion precision: round to the same number of significant figures as your original measurement. Converting 6 feet to meters gives 1.8288 m — but if your measurement was approximate (±1 inch), expressing more than 2 decimal places is false precision. For international trade and technical specifications, SI units (meters, kilograms, liters) are the standard. US customary units (feet, pounds, gallons) differ from Imperial UK units: 1 US gallon = 3.785 L vs. 1 UK gallon = 4.546 L.