Luminance Converter Calculator

What is Luminance?

Luminance is the photometric equivalent of radiance in radiometry. It quantifies the amount of visible light emitted, transmitted, or reflected by a surface per unit area in a given direction. The human eye's sensitivity to light varies with wavelength, so luminance takes into account the spectral sensitivity of the human visual system.

Luminance is measured in units of candela per square meter (cd/m²) in the SI system, but various other units are used in different fields and regions.

L_v = (dI_v)/(dA \cosθ) \textwhere:\\ L_v = \textluminance\\ I_v = \textluminous intensity\\ A = \textarea\\ θ = \textangle between surface normal and direction of light

Common Luminance Units

**Nit (nt):** The most common unit of luminance, equal to 1 candela per square meter. Named after the Latin word "nitere" meaning "to shine."

**Candela per Square Meter (cd/m²):** The SI base unit for luminance. One candela per square meter is the luminance of a surface that emits one candela of luminous intensity per square meter.

**Lambert (L):** A non-SI unit equal to 1/π candela per square meter. Named after Johann Heinrich Lambert.

**Stilb (sb):** Equal to 10,000 candela per square meter. Used in some European countries.

**Foot-Lambert (fL):** An imperial unit equal to 1/π candela per square foot, or approximately 3.426 candela per square meter.

\beginalign* 1\text nit &= 1\text cd/m^2\\ 1\text lambert &= (1)/(π)\text cd/m^2 ≈ 0.318\text cd/m^2\\ 1\text stilb &= 10,000\text cd/m^2\\ 1\text foot-lambert &= (1)/(π)\text cd/ft^2 ≈ 3.426\text cd/m^2 \endalign*

Conversion Principles

To convert between different luminance units, you multiply by the appropriate conversion factor. The conversion factor represents how many of the target units equal one of the source units.

**Conversion Formula:** Luminance in target unit = Luminance in source unit × Conversion factor

**Key Conversion Relationships:** - 1 nit = 1 cd/m² (base relationship) - 1 lambert = 0.318 cd/m² - 1 stilb = 10,000 cd/m² - 1 foot-lambert = 3.426 cd/m²

L_target = L_source × \frac\textconversion factor_source\textconversion factor_target

Applications of Luminance

**Display Technology:** Luminance is crucial in designing and calibrating displays, monitors, and screens. It determines the brightness and visibility of content.

**Lighting Design:** Architects and lighting designers use luminance measurements to ensure proper illumination levels and visual comfort.

**Photography and Videography:** Luminance values help photographers and videographers understand exposure and lighting conditions.

**Safety Standards:** Many safety regulations specify minimum luminance requirements for emergency lighting, road signs, and workplace illumination.

**Astronomy:** Luminance measurements are used to characterize the brightness of celestial objects and atmospheric conditions.

\textTypical luminance values:\\ \beginalign* \textSun &≈ 1.6 × 10^9\text cd/m^2\\ \textClear sky &≈ 8,000\text cd/m^2\\ \textComputer monitor &≈ 100-300\text cd/m^2\\ \textIndoor lighting &≈ 100-500\text cd/m^2\\ \textMoon &≈ 2,500\text cd/m^2 \endalign*

Human Visual System and Luminance

The human eye's response to light is not linear with respect to luminance. The perceived brightness follows a logarithmic relationship, which is why we can see objects in both bright sunlight and dim moonlight.

**Weber-Fechner Law:** The perceived brightness is proportional to the logarithm of the luminance.

**Contrast Sensitivity:** The ability to distinguish between different luminance levels depends on the ratio of luminance differences rather than absolute differences.

**Adaptation:** The human eye adapts to different luminance levels, allowing us to see in both very bright and very dim conditions.

\textPerceived brightness \propto \log(L) \textWeber contrast: C = \fracL_max - L_minL_max + L_min

Worked Example

Inputs

• value: 100
• fromUnit: nit
• toUnit: lambert

Result: 314.16

Explanation

To convert 100 nits to lamberts: 100 ÷ (1/π) = 100 × π = 314.16 lamberts

Second Scenario

Inputs

• value: 120
• fromUnit: nit
• toUnit: lambert

Result: 314.16

Explanation

This scenario uses different inputs (value = 120, fromUnit = nit, toUnit = lambert) to show how changing one variable affects the luminance converter result. Run the calculator above with these values to get the exact updated output with step-by-step work.