title: Luminance Converter description: Understand luminance units from candela per square metre to foot-lamberts, how they relate, and what affects conversion accuracy in real-world measurement.
What Is Luminance?
Luminance describes how much light travels from a surface toward an observer in a given direction. It is luminous intensity per unit projected area, and it is the photometric quantity that most closely matches what the human eye perceives as brightness. When you look at a display, a lamp, or the sky, the sensation you register is tied to luminance, not to the total luminous flux leaving the source.
The SI unit of luminance is the candela per square metre (cd/m²). This unit also carries the name nit, from the Latin nitere — to shine. A display calibrated to 500 nits emits 500 cd/m². The terms are interchangeable in consumer electronics, automotive, and professional display specifications.
Luminance spans many orders of magnitude. A moonlit scene registers a few hundredths of a cd/m², an office monitor sits between 200 and 400 cd/m², a fluorescent tube surface reaches several thousand cd/m², and the solar disk exceeds 1.6 × 10⁹ cd/m². Converting across these scales is routine in lighting design, display engineering, and vision science.
Core Units and Their Relationships
The candela per square metre anchors the luminance system. All other luminance units are fixed multiples of it. The candela per square centimetre (cd/cm²) is larger by a factor of 10,000 — one square metre contains exactly 10,000 square centimetres. The kilocandela per square metre (kcd/m²) is a convenience unit equal to 1,000 cd/m², used to keep numbers compact when specifying high-dynamic-range panels and outdoor-readable screens.
The foot-lambert (fL) belongs to the imperial system and remains in use in North America for cinema projection and legacy display documentation. One foot-lambert equals 1/π candela per square foot, which works out to roughly 3.426 cd/m². Conversions involving foot-lamberts require the factor (1/π) × (1 ft²/m²), not a rounded decimal — the π term is intrinsic to the definition of the Lambertian surface used to derive the unit.
Historical units include the apostilb (1/π cd/m², about 0.318 cd/m²), the skot (10⁻³ apostilbs), and the bril (10⁻⁷ apostilbs). These appear in older photometric literature and are rarely encountered in modern practice.
Distinguishing Luminance from Illuminance
Luminance and illuminance are frequently confused because both involve the candela. The distinction is directional. Illuminance (lux, or lm/m²) measures how much luminous flux falls on a surface from all directions. Luminance (cd/m²) measures how much luminous intensity leaves a surface in a specific direction per unit of projected area.
A matte white sheet of paper under desk lighting might receive 500 lux of illuminance. Its luminance, when viewed from a given angle, depends on the reflectance of the paper and the geometry of the viewing path. For a perfect Lambertian reflector with reflectance ρ receiving E lux, the luminance is ρE/π cd/m². The division by π is not a calibration nuance; it is the geometric consequence of distributing incident flux over a hemisphere.
Converting between illuminance and luminance requires knowing the surface's bidirectional reflectance distribution function, or at least assuming Lambertian behaviour. Without that assumption, the two quantities are not directly convertible. A luminance converter must treat illuminance inputs as a separate problem and ask for surface properties before bridging the two domains.
Geometric Factors and Viewing Angle
The phrase "per unit projected area" in the definition of luminance is critical. Projected area is the apparent area of the surface as seen from the direction of observation. If a surface element has area A and is viewed at an angle θ from its normal, the projected area is A cos θ. Luminance is therefore L = I / (A cos θ), where I is the luminous intensity in the direction of observation.
For a Lambertian emitter or reflector, luminance is independent of viewing angle because the intensity falls off as cos θ, exactly cancelling the projected-area term. Many real surfaces approximate Lambertian behaviour over a limited angular range, but departures are common. Glossy screens, metallic finishes, and retroreflective materials all exhibit luminance that varies with viewing angle.
A unit-to-unit luminance converter does not model angular dependence. It assumes the user has already accounted for geometry in the measurement. The conversion factor between cd/m² and cd/cm², for example, is purely a unit rescaling. The user should confirm that the underlying measurement protocol controlled the observation angle.
Calibration and Measurement
Luminance is measured with a luminance meter or a spectroradiometer fitted with a luminance probe. These instruments accept light through a defined aperture and apply a photopic weighting function that models the spectral sensitivity of the human eye under daylight conditions. The CIE 1924 photopic luminosity function V(λ) is the standard weighting curve, and meter calibration is traceable to national measurement institutes through a chain of standard lamps and reference detectors.
Calibration uncertainty limits the practical accuracy of any luminance conversion. A handheld luminance meter may carry an uncertainty of ±2 % to ±5 %. A laboratory-grade spectroradiometer can reduce this to fractions of a percent. The unit conversion itself is exact, so the dominant error in any real-world value comes from the measurement, not from the arithmetic.
Drift in detector response, stray light, and temperature variations all contribute to measurement uncertainty. High-quality meters suppress stray light through baffling and optical design, a concern that is especially acute when measuring dark areas adjacent to bright regions in display testing.
Wavelength Limits and Photometric Weighting
Luminance is a photometric quantity, defined through the spectral sensitivity of the human visual system. The candela, and therefore all luminance units, is weighted by the CIE photopic luminosity function, which peaks at 555 nm and drops to near zero below 380 nm and above 780 nm.
Radiant power outside the visible band contributes nothing to luminance, even if physically present. An infrared laser and a green LED might have identical radiant intensity in W/sr, but only the LED contributes to luminance. This is why luminance converters cannot bridge photometric and radiometric domains without spectral data: converting cd/m² to W/sr/m² requires the spectral power distribution of the source integrated against V(λ).
The CIE 1924 curve underestimates sensitivity at short wavelengths. Newer functions — the CIE 1988 modified 2° observer and the CIE 2006 physiologically based functions — address this, but the 1924 standard remains embedded in the SI definition of the candela. The difference between weighting functions is small for broadband sources but can be significant for narrowband LEDs and laser displays.
Worked Example
A display specification lists peak luminance as 1 cd/cm². Because one square metre equals exactly 10,000 square centimetres, the same luminance expressed in the base SI unit is 1 cd/cm² = 10,000 cd/m². This conversion is exact and carries no approximation.
To express the same value in kilocandela per square metre, divide by 1,000: 10,000 cd/m² = 10 kcd/m². In foot-lamberts, multiply by the exact conversion path: 1 cd/cm² × 10,000 (cd/m² per cd/cm²) × (1 / (π × 0.3048²)) (fL per cd/m²) ≈ 2,918 fL, though retaining the full-precision factor avoids cumulative rounding error.
This example illustrates why the 10,000 factor between cd/cm² and cd/m² is the most important single number in luminance conversion. It appears whenever European and North American display specifications are harmonized, and it is the bridge between the compact cd/cm² convention and the SI-native cd/m² convention.
Accuracy and Limitations
The unit conversions themselves are mathematically exact. One candela per square metre is precisely one nit. One candela per square centimetre is precisely 10,000 cd/m². One kilocandela per square metre is precisely 1,000 cd/m². These numbers follow from the definition of the metre and carry no measurement uncertainty.
The limitations of a luminance converter lie not in the arithmetic but in the domain. The tool converts between luminance units. It does not convert between luminance and illuminance without surface reflectance and geometry data. It does not convert between luminance and radiance without spectral information. It does not model angular luminance variation, and it does not apply photometric weighting corrections for different observer functions.
Users working with narrowband sources, specular surfaces, or non-standard observer conditions should treat converted values as starting points and consult the relevant measurement standards. The conversion is reliable; the interpretation of the result depends on the quality of the input.
Sources
- SI Brochure, 9th edition — BIPM
- NIST Special Publication 811 — Guide for the Use of the International System of Units
Editorial Record
This article was drafted to accompany the SoupCalc Luminance Converter. It draws on the SI Brochure for unit definitions and relationships, and on NIST SP 811 for guidance on expressing photometric quantities. The worked example was chosen to illustrate the most common conversion encountered in display specification harmonization. The distinction between luminance and illuminance was included because it is the single most frequent point of confusion among users of photometric converters. The article was reviewed for technical accuracy against the cited sources. No proprietary measurement equipment or third-party calculator brands are referenced. Author: SoupCalc Editorial Team Last reviewed: August 11, 2026.