Calculate Luminance

Online calculator and formulas for luminance in cd/m²

Luminance calculator (JavaScript)

Core relation

Luminance is defined as L = I/A with I as luminous intensity in candela and A as effective area in square meters.

cd
m²
Result

Example calculations

Example 1: Luminance from I and A

Given: I = 150 cd, A = 0.5 m²

\[L=\frac{I}{A}=\frac{150}{0.5}=300\,cd/m^2\]

Result: L = 300 cd/m²

Example 2: Intensity from L and A

Given: L = 300 cd/m², A = 0.5 m²

\[I=L\cdot A=300\cdot0.5=150\,cd\]

Result: I = 150 cd

Example 3: Area from I and L

Given: I = 150 cd, L = 300 cd/m²

\[A=\frac{I}{L}=\frac{150}{300}=0.5\,m^2\]

Result: A = 0.5 m²

Formulas and comprehensive description

Luminance L describes how bright a luminous or illuminated surface appears to an observer. It links luminous intensity to effective area and is a key quantity in display technology, automotive lighting, architectural lighting, and visual ergonomics.

Luminance
\[L=\frac{I}{A}\]
Luminous intensity
\[I=L\cdot A\]
Area
\[A=\frac{I}{L}\]
Unit
\[cd/m^2\]
Practical relevance
High luminance values appear very bright, but may also cause glare. In monitors, headlights, and signage, it is important to evaluate not only peak luminance, but also uniformity, contrast, and viewing angle behavior.

Detailed Description

What is Luminance?

Luminance L is a measure of perceived brightness of a surface from a particular viewing direction. It indicates how much light is emitted or reflected from a surface element in a specific direction, relative to the visible surface area. Unlike illuminance (amount of light falling on a surface), luminance describes light leaving from a surface. It is the photometric quantity that best correlates with how we perceive brightness.

Definition and Formula

Luminance is defined as the ratio of luminous intensity to projected (effective) area:

\[L = \frac{I}{A}\]
  • L – luminance (cd/m²)
  • I – luminous intensity (candela, cd)
  • A – projected (effective) area (m²)
Luminance vs. Illuminance
Quantity Symbol Unit Meaning
Illuminance E lx (Lumens/m²) Light that FALLS ON a surface
Luminance L cd/m² Light that LEAVES FROM a surface (reflected or self-emitted)
Luminous intensity I cd Total light energy in one direction
Luminous flux Φ lm Total visible light energy
Derivation

For a small surface element dA that emits luminous intensity I in a particular direction:

  • Luminous intensity: \[I = \frac{d\Phi}{d\Omega}\] (luminous flux per solid angle)
  • Luminance: \[L = \frac{dI}{dA \cdot \cos(θ)}\] (luminous intensity per projected area)
  • The factor cos(θ) accounts for the fact that only the perpendicular component of the area is relevant
Typical Luminance Values
Light Source / Object Luminance (cd/m²)
Dark night sky 0.001
Full moon 0.25
Paper in sunlight 100 – 1000
Typical monitor (white) 100 – 300
Smartphone display 200 – 500
Traffic signal (red LED) 500 – 3000
Car headlight (reflector) 1000 – 5000
Street light (sodium high-pressure lamp) 5000 – 10000
Incandescent bulb (filament) 100000 – 500000
Sun disk 1600000000
Dependence on Viewing Angle

Luminance depends on the viewing angle. A diffuse surface (Lambertian radiator) exhibits constant luminance in all directions (Lambert's cosine law). A specularly reflecting surface, however, has high luminance only in a specific direction.

Glare and Visual Ergonomics

Excessively high luminance can cause glare, especially when:

  • High luminance contrasts exist in the visual field (e.g., bright monitor in dark background)
  • Eyes fixate on high-gloss surfaces for extended periods
  • The viewing angle is unfavorable
  • For older people, whose eyes are more sensitive to glare
Practical Applications
  • Display technology: Monitors, TVs, smartphone displays – luminance determines visibility
  • Automotive lighting: Headlights, rear lights, brake lights – must meet specified luminance values
  • Traffic signage: Signs and traffic signals must be sufficiently bright at night
  • Architectural lighting: Facade and interior lighting – planning based on luminance requirements
  • Digital photography: Sensors respond to scene luminance
  • Workplace lighting: Ergonomically safe luminance ranges for visual display terminals
  • Film projection: Quality and brightness depend on projector luminance
Important Properties
  • Directional dependence: Luminance varies depending on viewing direction
  • Area dependence: A larger area with same intensity yields lower luminance
  • Perceptual relevance: Luminance is the best measure for visual perception of brightness
  • Distance independence: Luminance does not change with observation distance (neglecting atmosphere)
  • Conservation quantity: By the conservation theorem, luminance is preserved in optical systems (ideally)
Note: Lambert's Law
A diffuse (matte) surface that radiates according to Lambert's cosine law has constant luminance independent of viewing angle. This is an idealized assumption that holds well for many matte surfaces. While intensity decreases with angle, the luminance remains constant.
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