In our daily lives, light is ever-present—from the lamps in our homes to the displays on our mobile phones, from the sunlight outdoors to the neon lights at night. It surrounds us in myriad forms. To describe the properties of light, certain specialised physical units are indispensable, with lumens, lux, nits, and candelas being four of the most crucial.Though seemingly abstract, these units are intrinsically linked to our perception of light and its practical applications. From selecting bulbs of appropriate brightness to designing display effects for screens, and even in specialised fields such as photography and lighting engineering, these units play an indispensable role.

However, many people often find these four concepts confusing, struggling to clearly distinguish their respective meanings and applications. Therefore, clarifying the concepts of these four units and defining the optical properties they describe is of great significance for us to better understand and utilise light.

1. Lumen is a unit of measurement for light, similar to the watt, but its measurement takes into account the sensitivity of the human eye. When examining the specifications of a light source, lumens measure the total output of the light source, regardless of the direction in which the light is emitted.

2. Lux denotes the number of lumens received per square metre. In everyday parlance, we might refer to it as ‘illuminance’, though within the optical profession it is termed ‘illuminance’. It indicates the quantity of light falling upon a given surface.

3. Nit is the number of lumens per square metre per steradian, which we might refer to as ‘brightness’ in everyday terms, though within the industry it is termed ‘luminance’. If an illuminance of 1 lux falls upon an ideal diffuse-reflecting surface, it produces a luminance of 1 nit.

4. A candela is the number of lumens per steradian. It is used for point light sources, enabling the calculation of the amount of light received by any illuminated surface, regardless of its location.

In other words, the candela measures luminous intensity through an imaginary sphere centred on the light source. For an isotropic point source, one candela equals one lumen per steradian. A complete sphere surrounding the light source encompasses 4π (approximately 12.6) steradians. Consequently, an isotropic light source emitting 12.6 lumens produces a luminous intensity of 1 candela.This does not entirely apply to typical lasers, but for light sources such as short-arc xenon lamps, it constitutes a reasonable approximation. Nevertheless, the candela can still be defined for a portion of a divergent beam. For instance, if your laser emits 1 lumen within a range of merely 0.1 steradians, its luminous intensity would be 10 candelas.

The foot-candle is a unit of illuminance. The Illuminating Engineering Society of North America defines it in ANSI/IES RP-16-1996, Terminology of Lighting Engineering, as ‘the surface density of luminous flux incident on a point on a surface’.

In layman’s terms, illuminance is the amount of light reaching a point on a real or imaginary surface. (This point need not be located on a physical surface.)

One foot-candle equals one lumen per square foot (where the lumen is the unit of measurement for luminous flux or the quantity of light).

The luminous intensity of a candle flame (or equivalently, its candela) is approximately 1 candela. If you place the candle one foot away from a surface, the illuminance on that surface at this distance will be approximately one foot-candle due to the candle’s illumination. At 2 feet, the illuminance would be 1/4 foot-candle; at 3 feet, it would be 1/9 foot-candle, and so on, conforming to the inverse square law for point light sources.

Brightness is a psychophysical phenomenon that cannot be measured directly. The term “photometric brightness” was once used to denote luminance, but it is no longer employed in scientific or engineering contexts.

Definition of the lumen: The luminous flux of monochromatic light at a frequency of 540 terahertz (or a wavelength of approximately 555.5 nanometres) with a power of 1/683 watts. It is worth noting that the lumen is a derived unit based on the candela (1 candela equals 1 lumen per steradian), whereas the candela is a base unit (it represents the ‘beam candela power’ of 1/683 watts per steradian for monochromatic light at a frequency of 540 terahertz). For light with wavelengths other than 555.5 nanometres, the number of lumens per watt of radiated energy differs. For wavelengths not 555.5 nanometres, the lumens per watt correspond to 683 multiplied by the photopic luminous efficiency function value for that wavelength, then divided by the photopic luminous efficiency function value at 555.5 nanometres (I believe this value is very close to 1, but not exactly 1).

Lumens per watt serves as an indicator of efficiency in converting electrical energy into light energy. Multiplying this value by the wattage consumed by an LED yields its luminous flux (in lumens). Typical red, orange, yellow, or yellow-green LEDs exhibit a voltage drop of approximately 2 volts, consuming around 0.04 watts at a standard current of 20 milliamps. In contrast, blue, white, or non-yellowish green LEDs typically have a voltage drop of 3.5 volts at 20 milliamps, resulting in a power consumption of 0.07 watts.

The candela is the number of lumens per steradian, also known as the ‘luminous-candle power’. (In practice, as noted earlier, the candela is the fundamental metric unit, while the lumen is defined in terms of the candela.) Consequently, the lumen equals the candela multiplied by the solid angle covered by the beam. Ideally, the candela equals the lumen divided by the solid angle covered by the beam — assuming all light is contained within the beam and the ‘candela power’ within the beam is constant.

You might well ask, what is sphericity? Sphericity is 1/(4π) of the entire sphere, or 1/(2π) of a hemisphere, equating to approximately 3283 ‘square degrees’. The formula for calculating sphericity based on beam angle is as follows: Sphericity = 2 × π × (1 – cos(0.5 × beam angle))

Therefore, if you calculate the spherical angle covered by the beam and multiply it by the candela value (or 1/1000th of the millicandela value), you can roughly obtain the luminous flux (in lumens)! However, since the beam is not uniformly distributed and not all light is contained within the beam, this calculation is only approximate. Calculating lumens based on beam angle and candela can easily yield errors ranging from +100% to -50%. For beam angles of 8 degrees or less, the actual lumen output is typically higher than this formula predicts, as the nominal beam does not account for the secondary ‘halo’ beams that often surround the main beam. It should also be noted that some beam angle values are overly optimistic, potentially leading to inflated expectations regarding the actual luminous flux received.

In summary, the four optical units—lumen, lux, nit, and candela—each describe the properties of light from distinct perspectives, collectively forming the essential yardsticks by which we comprehend and measure illumination.

Lumens focus on the total amount of light emitted by a light source, quantifying luminous flux to indicate how much light a source can produce; lux, however, concerns the luminous flux received per unit area by an illuminated object, reflecting the degree to which an object is lit and revealing how brightly a surface is illuminated. The nit, as a unit of luminance, applies to area sources by combining luminous intensity with the emitting area. It is commonly used to describe the visual brightness of luminous surfaces such as displays. The candela, meanwhile, is the core metric for the luminous intensity of point sources. It characterises a light source’s ability to concentrate light in a specific direction, revealing how intensely the source itself emits light.