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Total Luminous Flux

Calculate the equivalent solid angle and total luminous flux of a conical light source.

Total Luminous Flux, expressed in lumens (lm), measures the total brightness or intensity of light emitted by a light source. It includes all visible light wavelengths, providing a complete measurement of the source's luminosity.

Evaluating a light source's brightness or luminous efficacy is the main goal of total luminous flux. It enables comparisons between different light sources and helps choose suitable lighting solutions based on their luminous output.

Understanding Total Luminous Flux

Common Symbols and Units

Symbol	Description
$\Phi_v$	Luminous Flux
lm	Lumen — SI unit of luminous flux
cd	Candela — SI unit of luminous intensity
sr	Steradian — SI unit of solid angle

Key Concepts

Concept	Description
Luminous Intensity	The apparent intensity of light emanating from a specific direction, expressed per unit of solid angle
Radiant Flux	The aggregate energy output of electromagnetic radiation — encompassing infrared, ultraviolet, and visible light spectrums
Luminous Efficacy	The ratio of luminous flux to radiant flux

Examples of Luminous Flux

Light Source	Luminous Flux
100W Incandescent Lamp	~1,200 lm
Typical LED Lamp	~800 – 1,000 lm
The Sun	~ $3.8 \times 10^{26}$ lm

Interesting Facts

Luminous flux represents the total energy output across all visible wavelengths, weighted accordingly
Energy emitted outside the visible spectrum does not factor into luminous flux calculations
The relationship between luminous flux and radiant flux gives rise to luminous efficacy

Applications

Lighting Design and Engineering
Energy Efficiency Assessments
Architectural Lighting
Industrial and Commercial Lighting
Automotive Lighting
Photometry and Radiometry
Optical Engineering
Lighting Measurement and Testing

About This Calculator

This online total luminous flux calculator determines how much useful light a source is emitting. Lumens (lm) offer an objective way to quantify the brightness of light. You can also use this converter to convert luminous intensity to luminous flux, giving you the light source's lumen output.

Formulas

$\Omega = 2\pi \times (1 - \cos(\theta))$

$F = \Omega \times I_v$

where:

$\Omega$ = Equivalent Solid Angle (sr)
$\theta$ = Cone Full Angle (degrees)
$F$ = Total Luminous Flux (lm)
$I_v$ = Maximum Luminous Intensity (cd)

Inputs

Maximum Luminous Intensity(cd)

Peak luminous intensity of the light source in candela

Cone Full Angle(°)

Full apex angle of the light cone in degrees

Results

Equivalent Solid Angle0.000e+0srSolid angle subtended by the cone in steradians

Total Luminous Flux0.000e+0lmTotal luminous flux emitted within the cone in lumens