Luminous Intensity Converter — candela, lumen, lux, nit

The luminous intensity converter above handles the four photometric quantities that are routinely confused with one another: luminous intensity in candela, luminous flux in lumens, illuminance in lux, and luminance in candela per square metre. They describe different things. Intensity is light per unit solid angle, flux is total light output, illuminance is light arriving at a surface, and luminance is light leaving a surface toward your eye.

Arb Digital publishes this converter as part of a free technical reference library. Every factor is derived from the SI definition of the candela and the exact geometric relationships between the units, so foot-candles, phots, stilbs and lamberts are all computed from first principles rather than copied from a rounded table.

What This Luminous Intensity Converter Does

Choose a quantity and the tool loads only its units. Intensity mode covers candela, millicandela and kilocandela alongside the historical candlepower, Hefner candle, carcel unit and violle. Flux mode covers lumen and its multiples. Illuminance mode covers lux, kilolux, phot, milliphot, nox and the foot-candle. Luminance mode covers candela per square metre, better known as the nit, plus stilb, apostilb, lambert, foot-lambert, candela per square foot and candela per square inch.

The four supporting panels show the SI unit, a practical submultiple, the imperial or centimetre-gram-second unit most likely to appear in older documentation, and one related quantity. In intensity mode that last panel calculates the illuminance a point source of your intensity would produce at the distance you enter, which is the most common real question people arrive with: how many lux will this lamp give me over there.

How to Use It

1. Pick the quantity. A lamp datasheet quoting total output is lumens. A beam figure or an LED datasheet is usually candela. A meter reading at a desk is lux. A display specification is nits.
2. Enter the value in whatever unit you have it. All four lists are filtered to that quantity, so a nonsensical cross-quantity conversion cannot be made by accident.
3. Choose the from and to units, and read the headline plus the full conversion sentence beneath it.
4. Set the distance if you are working in intensity mode and want the illuminance at a given range from a point source.
5. Read the four panels for the SI value, a submultiple, the legacy unit and the related quantity, then use Swap to confirm the inverse.

The Formula and How It Is Calculated

Every unit is stored as a multiplier to the SI unit for its quantity, so the conversion is result = value × factor(from) ÷ factor(to). The candela is one of the seven SI base units, defined by fixing the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² hertz at exactly 683 lumens per watt. Everything else in photometry follows from it geometrically.

The lumen is a candela-steradian: a source of one candela radiating uniformly into one steradian of solid angle delivers one lumen. The lux is a lumen per square metre. The candela per square metre is intensity divided by the emitting area. Because a full sphere contains 4π steradians, an isotropic one-candela source emits 4π lumens, about 12.566. And for a point source, illuminance follows the inverse square law, E = I ÷ d², so a 1000 cd source produces 250 lux at 2 metres. The definitions are set out in the BIPM SI Brochure, with unit conversion practice covered in NIST Special Publication 811.

Candela, Lumen, Lux and Nit: Four Different Questions

The clearest way to keep these apart is to ask what each one is a property of. Luminous flux in lumens is a property of the source: total visible light emitted in all directions. Luminous intensity in candela is a property of the source in one direction: how concentrated that flux is into a particular cone. Illuminance in lux is a property of a receiving surface: how much light lands on it. Luminance in nits is a property of a surface as seen: how much light leaves it toward the observer.

This is why a 100-lumen torch with a tight beam can be blinding while a 1000-lumen bare bulb is merely bright. The torch concentrates its smaller flux into a narrow solid angle, producing far higher intensity along the axis. It is also why comparing an LED datasheet figure in millicandela against a lamp rating in lumens tells you nothing without knowing the beam angle. Converting between them requires the solid angle, which the angle converter can help you reason about in degrees and steradians.

Lux Versus Foot-Candles: A Ratio About Area, Not Light

One foot-candle is one lumen per square foot; one lux is one lumen per square metre. Since a square metre contains 10.7639 square feet, one foot-candle equals 10.7639 lux exactly, that factor being 1 divided by 0.09290304. Nothing about the light changes; the same flux is simply being divided by a larger or smaller area.

The rough conversion of 10 lux per foot-candle is used constantly in lighting practice and is accurate to about 7%, which is usually fine for a design sketch and not fine for a compliance measurement. The bigger trap is that lighting recommendations are written in one unit or the other depending on region, and a specification of 500 lux and one of 50 foot-candles are not the same requirement despite looking equivalent. 50 foot-candles is actually 538 lux. Areas can be converted directly in the area converter.

The Apostilb Family and the Hidden Factor of Pi

Luminance is the messiest corner of photometry, because two competing families of units exist. One family divides intensity by area directly: candela per square metre, candela per square foot, and the stilb at one candela per square centimetre. The other family, the apostilb, lambert and foot-lambert, was designed so that a perfectly diffusing surface illuminated to one lux has a luminance of exactly one apostilb. That convenience buries a factor of π inside the unit.

The result is that one apostilb is 1/π candela per square metre, about 0.3183, and one foot-lambert is about 3.4263 cd/m² rather than the 10.7639 you might expect by analogy with foot-candles. Converting a foot-lambert as though it were a candela per square foot overstates the luminance by a factor of π, roughly 3.14, and that specific mistake appears in a surprising number of published tables. This converter computes both families from their definitions so the π lands where it should.

Lumens Are Not Watts, and Efficacy Is Not Efficiency

Photometric units are weighted by the response of human vision. The candela definition fixes 683 lumens per watt at 540 THz, which is green light near the peak of daytime visual sensitivity. Move to deep red or deep violet and the same radiant watt produces a small fraction of the luminous output, and beyond the visible range it produces none at all despite carrying real energy.

Two consequences matter in practice. First, luminous efficacy in lumens per watt is not a percentage efficiency; it is a ratio between a visually weighted quantity and a physical one, and its theoretical ceiling is 683 lm/W only for pure monochromatic green light. A practical white source cannot approach that because white light necessarily includes wavelengths the eye responds to weakly. Second, a photometric conversion carries no information about infrared or ultraviolet output, so a lamp comparison based on lumens says nothing about the radiant heat it produces. Radiant power belongs in the power converter and radiant energy in the energy converter.

Historical Candle Units and Why They Are Approximate

Before the candela was defined, luminous intensity was tied to physical reference lamps: the Hefner candle burning amyl acetate, the carcel unit burning colza oil at a set rate, and the violle, defined by the light from a square centimetre of platinum at its freezing point. Their modern equivalents, roughly 0.903, 9.74 and 20.17 candela respectively, are measured comparisons, not exact definitions, and different sources quote slightly different values.

They appear in the table below marked as approximate for exactly that reason. Candlepower is a different case: in modern usage it is treated as numerically equal to the candela, though early twentieth-century documents using the international candle differ by a couple of percent. If you are reading a genuinely historical specification, treat any candle-based figure as carrying at least a percent or two of uncertainty before you convert it.

Full Photometric Conversion Table

Common Mistakes to Avoid

• Comparing candela to lumens directly — the two differ by the solid angle of the beam, so a narrow-beam source can have high intensity and low total flux.
• Converting foot-lamberts as if they were candela per square foot — the apostilb family carries a hidden factor of pi, so the mistake inflates the answer by about 3.14.
• Using 10 lux per foot-candle in a compliance measurement — the exact factor is 10.7639, and the 7% shortfall matters when a specification is being verified.
• Treating lumens per watt as an efficiency percentage — it is a ratio between a visually weighted quantity and a physical one, with a monochromatic ceiling of 683.
• Forgetting the inverse square law — doubling the distance from a point source cuts illuminance to a quarter, not a half.

Related Free Tools From Arb Digital

Lighting calculations pull in several other unit families. Convert throw distances in the length converter, illuminated surfaces in the area converter, beam angles and steradians in the angle converter, electrical draw in the power converter, and consumption over time in the energy converter. Wide-ranging magnitudes are easier to read through the scientific notation converter, and the general unit converter covers the rest.

Frequently Asked Questions

This converter handles photometric units only. Lighting design, workplace illumination levels, and product compliance claims should be verified against the applicable standard and a calibrated measurement.