Lumen to Candela Converter

Convert luminous flux (lumens) and beam angle (full apex angle) into luminous intensity (candela). Understand the relationship between lumens, steradians, and candela for LED design, architectural lighting, and photometric analysis.

lumens (lm)
Total visible light power emitted by the source.
degrees (°)
Apex angle (full cone angle) where intensity drops to 50% (typical definition).
? LED Bulb: 800 lm, 120°
? Spotlight: 1200 lm, 25°
?️ Floodlight: 20000 lm, 90°
?️ Reference: 12 lm, 360° (isotropic)
? Narrow beam: 1500 lm, 10°
Privacy-first photometry: All calculations are performed locally in your browser. No data is stored or transmitted.

Understanding Lumen to Candela Conversion

The conversion from lumens (lm) to candela (cd) requires knowledge of the beam angle or solid angle into which light is emitted. While lumens measure total visible light output, candela quantifies the luminous intensity — the concentration of light in a particular direction. The fundamental relationship is:

Iv (cd) = Φ (lm) / Ω (sr)

Where Ω is the solid angle in steradians (sr). For a conical beam with full apex angle α, the solid angle is:
Ω = 2π (1 − cos(α/2))

This formula assumes a perfectly uniform intensity distribution within the cone (Lambertian or idealised beam). In real LEDs, intensity varies with angle, but for engineering approximations the average candela is computed this way. Pro tip: When a manufacturer gives a “peak candela” rating, it may be higher than the average intensity from this calculator. Use this tool for flood‑style or Lambertian sources; for narrow spots, the average candela is a reliable system design value.

Why Use This Interactive Photometry Tool?

  • Lighting Design: Determine required candela for spotlights, downlights, and street lighting given a target lumen output and desired beam angle.
  • LED Specification: Compare LED products – convert between total lumens (on datasheets) and peak intensity (candela).
  • Educational Clarity: Visualize the beam cone and see how smaller angles dramatically increase candela for the same lumens.
  • Architectural & Stage Lighting: Critical for focusing light onto specific areas – from museum accent lighting to concert trusses.

Derivation & Photometric Foundations

The steradian (sr) is the SI unit of solid angle. For a cone of half-angle θ (θ = α/2), the solid angle is derived by integrating over spherical coordinates: Ω = ∫₀²π ∫₀^θ sinθ' dθ' dφ = 2π (1 − cosθ).
If a light source emits Φ lumens uniformly within that cone, the average intensity I = Φ/Ω. This relation is central to the definition of candela: 1 cd = 1 lm/sr.
The method also applies to non‑uniform distributions by using the on‑axis intensity approximation for narrow beams, but for most practical comparisons, this average intensity is extremely useful.

Compliance with CIE 127:2007 – The standard “Condition A/B” for LED measurement uses a defined solid angle. Our calculator aligns with the average LED intensity concept and is suitable for preliminary optical design.

Real-World Application Example: Track Lighting

Museum Spotlight Design

A curator requires a fixture emitting 900 lumens to illuminate an artwork from 3 meters away, achieving an illuminance of 100 lux. Using the inverse‑square law E = I / d², the needed candela is I = E × d² = 100 × 9 = 900 cd. Using our calculator, a 900 lm source with beam angle of approx. 36° yields Ω = 2π(1−cos18°) ≈ 0.305 sr, I ≈ 2950 cd, too strong; a 400 lm source at 40° gives ~1130 cd, close. This interactive tool empowers designers to iterate quickly.

Lumen to Candela Reference Table (Common Beams)

Lumens (lm) Beam Angle (full) Solid Angle (sr) Candela (cd) Typical Application
800 120° 3.1416 254.6 Standard LED bulb
1200 25° 0.148 8108 Narrow spot (stage)
20000 90° 1.840 10870 High bay floodlight
12 360° (isotropic) 12.566 0.96 Candle (approx.)
3000 60° 0.841 3567 Retail downlight

The Difference Between Lumens, Candela, and Lux

Lumens (Φ) = total light output perceived by the human eye. Candela (I) = intensity in a given direction. Lux (E) = illuminance on a surface: E = I / d² for normal incidence. Understanding these three allows engineers to design efficient lighting systems. This calculator bridges the first two, and you can then compute lux using distance for any project.

Common Mistakes & Clarifications

  • Beam angle definition: Usually the full angle where intensity falls to 50% of maximum. The calculator assumes a uniform cone for average intensity. For precise peak candela, use the half‑intensity angle as the beam edge.
  • Isotropic sources: A true isotropic emitter has Ω = 4π sr, I = Φ/(4π). Our example for candle approximates it, but real candles are not perfectly isotropic.
  • Small angles: When beam angle < 5°, the small‑angle approximation can be used: Ω ≈ π(α/2)² (in steradians when α in radians).

Frequently Asked Questions

Lumens are spread over a smaller solid angle, so the concentration (intensity) increases. Example: 1000 lm at 10° yields many more candela than 1000 lm at 120°.

Yes: Lumens = Candela × Solid angle. Using the same solid angle formula based on beam angle, you can invert the calculation. Our tool focuses on lm→cd, but the formula works both ways.

Real LED profiles vary, but the average intensity method using the beam angle at FWHM (full width half maximum) gives a standard reference used by most lighting manufacturers.

From 4° (ultra‑narrow spot) up to 180° (wide wash). Flood lights are typically 90–120°, while wall washers exceed 120°.

It provides the average luminous intensity inside the defined cone. For precise peak candela (e.g., on‑axis), we recommend using a goniophotometer, but this calculator is widely accepted for concept design.

Trusted Photometric Methodology – Based on standards from the CIE (International Commission on Illumination, CIE 127:2007) and SI unit definitions. The formulas have been verified with lighting engineering handbooks (IESNA Lighting Handbook, 10th Ed.). The interactive beam simulation uses real‑time canvas rendering, demonstrating the spatial distribution of light. Updated May 2026by GetZenQuery tech team.

References: CIE – International Commission on Illumination; “Understanding Photometrics” – Lighting Design Lab; Wikipedia: Candela; IESNA Lighting Handbook.