Calculate Luminous Flux

Online calculator and formulas for luminous flux, luminous intensity, and solid angle

Luminous Flux Calculator (JavaScript)

Core relation

Luminous flux is computed by Φ = I · Ω, where I is luminous intensity in candela and Ω is solid angle in steradian.

cd
sr
Result

Example calculations

Example 1: Flux from intensity and solid angle

Given: I = 120 cd, Ω = 2 sr

\[\Phi = I\cdot\Omega = 120\cdot2 = 240\,lm\]

Result: Φ = 240 lm

Example 2: Intensity from flux and solid angle

Given: Φ = 240 lm, Ω = 2 sr

\[I = \frac{\Phi}{\Omega} = \frac{240}{2} = 120\,cd\]

Result: I = 120 cd

Example 3: Solid angle from flux and intensity

Given: Φ = 240 lm, I = 120 cd

\[\Omega = \frac{\Phi}{I} = \frac{240}{120} = 2\,sr\]

Result: Ω = 2 sr

Luminous flux formulas and detailed notes

Luminous flux Φ is the total visible light power emitted by a source. It is weighted by the human eye's sensitivity (photopic vision), which makes it different from pure radiant power in watts. The relation between luminous flux, luminous intensity, and solid angle is fundamental in photometry.

Luminous flux
\[\Phi=I\cdot\Omega\]
Luminous intensity
\[I=\frac{\Phi}{\Omega}\]
Solid angle
\[\Omega=\frac{\Phi}{I}\]
Unit relation
\[1\,lm=1\,cd\cdot sr\]
Comprehensive interpretation
High Φ means more total visible light output.
High I with small Ω means a focused beam (spotlight behavior).
Same Φ spread over larger Ω gives lower I (diffuse emission).
This is why beam angle matters in luminaire design, road lighting, and projector optics.

Detailed Description

What is Luminous Flux?

Luminous flux Φ (Phi) is the measure of the total visible light power emitted by a light source. Unlike pure radiant power in watts, luminous flux is weighted according to the spectral sensitivity of the human eye. This means that light at wavelengths to which the eye is particularly sensitive (green light around 555 nm) is perceived as much brighter than light at wavelengths where the eye is less sensitive (blue or red light). Luminous flux is measured in the unit Lumen (lm).

Luminous Flux, Intensity, and Solid Angle

Luminous flux depends on two factors:

\[Φ = I · Ω\]
  • Φ – luminous flux (lumen, lm)
  • I – luminous intensity (candela, cd) – the light intensity in one direction
  • Ω – solid angle (steradian, sr) – the angular range over which light is emitted
The Solid Angle (Steradian)

The solid angle Ω (measured in steradians, sr) describes the spatial angular range over which a light source radiates:

  • Full sphere: 4π sr ≈ 12.57 sr
  • Hemisphere: 2π sr ≈ 6.28 sr
  • Cone (like a spotlight): Ω = 2π(1 - cos(θ/2)) sr, where θ is the opening angle
  • Small solid angle: Focused, intense light in one direction
  • Large solid angle: Diffusely radiated, widely spread light
Photometric Quantities Overview
Quantity Symbol Unit Meaning
Luminous flux Φ lm Total visible light power
Luminous intensity I cd Luminous flux per solid angle
Illuminance E lx Luminous flux per area (light on a surface)
Luminance L cd/m² Luminous intensity per area (light from a surface)
Solid angle Ω sr Angular range (steradian)
Typical Luminous Flux Values
Light Source Luminous Flux (lm) Remark
LED candle (0.5 W) 30 – 50 Weak light
Incandescent bulb (40 W) 400 – 500 Typical room lighting
Incandescent bulb (60 W) 700 – 800 Brighter incandescent
Incandescent bulb (100 W) 1500 – 1700 Very bright incandescent
LED bulb (10 W, neutral white) 800 – 1000 Energy efficient
LED bulb (15 W, warm white) 1300 – 1500 Good brightness
Fluorescent tube (36 W) 2800 – 3200 Office lighting
Projection lamp (1000 W) 20000 – 30000 Film projector
Halogen floodlight (500 W) 8000 – 10000 Outdoor lighting
Luminous Flux vs. Radiant Power

An important distinction exists between:

  • Radiant power (Watts): The actual electromagnetic energy, independent of wavelength
  • Luminous flux (Lumens): The perceived brightness, weighted by eye sensitivity

Example: An LED with 10 W could produce more visible light than a 10 W incandescent bulb because LEDs are more efficient in the visible range. An infrared lamp with 100 W would have a luminous flux of 0 lm (because infrared is not visible), even though it radiates much energy.

Practical Applications
  • Lighting design: Determining required light amount for rooms, streets, and workplaces
  • Bulb selection: Comparing and choosing LED, halogen, and incandescent bulbs
  • Energy efficiency: Luminous flux per watt shows efficiency (lm/W)
  • Headlight design: Combining luminous flux and solid angle for optimally focused light
  • Photography & film: Assessing available light for captures
  • Displays & projectors: Brightness and luminance depend on luminous flux distribution
Luminous Efficacy

Luminous efficacy is the ratio of luminous flux to power consumption:

  • Incandescent bulb: 10 – 17 lm/W
  • Compact fluorescent (CFL): 40 – 60 lm/W
  • LED (white): 80 – 150 lm/W
  • LED (monochromatic, red): Over 200 lm/W
  • Theoretical maximum: 683 lm/W (monochromatic green light at 555 nm)
Important Properties
  • Perception-based: Luminous flux accounts for human vision function
  • Additive: Luminous flux from multiple sources adds up
  • Wavelength-dependent: Green light contributes more to luminous flux than blue or red light with equal radiant power
  • Distance-independent: The luminous flux of a source does not change with observation distance
  • Measurable and standardized: Luminous flux is measured according to international photometry standards
Note: Photopic vs. Scotopic Vision
Luminous flux is weighted according to photopic vision (vision at normal brightness) with maximum sensitivity at 555 nm. At very low brightness (scotopic vision), the sensitivity shifts to shorter wavelengths (507 nm). This is why green light appears brighter during the day than at night.
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