Luminous Intensity Converter

Lighting specifications can look inconsistent until the geometry is made explicit. A signal LED may be rated in candela, a lamp in lumens, and a work surface in lux. This calculator converts among Candela (cd), Lumen (lm), and Lux (lx) by using the same assumptions in the form: a distance in meters and an emission solid angle in steradians. Enter a nonnegative Value, choose the From unit and To unit, then provide Distance and Emission solid angle. The result panel reports the selected conversion and all three supported equivalents.

Candela is the SI base unit for luminous intensity, the visible-light intensity in a particular direction. Lumen is luminous flux, the visible light passing through or emitted into a solid angle. Lux is illuminance, the luminous flux received per unit area. Those are related, but they are not interchangeable unless a geometry is specified. That is why this converter asks for distance and solid angle instead of using a single fixed factor.

Luminous intensity formulas

The calculator converts every entry to candela first:

$\text{candela from candela} = \text{value}$

$\text{candela from lumen} = \frac{\text{lumen}}{\text{solid angle}}$

$\text{candela from lux} = \text{lux} \text{ } \times \text{ } \text{distance}^{2}$

Then it converts candela to the requested target:

$\text{lumen} = \text{candela} \text{ } \times \text{ } \text{solid angle}$

$\text{lux} = \frac{\text{candela}}{\text{distance}^{2}}$

The default solid angle is a full sphere, calculated as 4π steradians and shown in the input as about 12.566 sr. Distance defaults to 1 m. Both distance and solid angle must be positive, and the displayed result is rounded to three decimal places.

Example: converting candelas to other intensity units

Convert 800 lm to candela using the default full-sphere solid angle of 12.566 sr. The conversion method divides lumens by solid angle:

$\frac{800}{12.566} = 63.664$

The calculator displays about 63.664 cd. If the target is lux at the default distance of 1 m, the same candela value is divided by 1 squared:

$\frac{63.664}{1^{2}} = 63.664$

So the all-units list shows about 63.664 lx for the default distance. If you change distance to 2 m while keeping the same candela, the lux value becomes about 15.916 lx because the denominator is 4. The lumen result remains tied to the solid angle, not distance.

Reference table

Domains that use these units

Electronics and indicators often use candela or millicandela because an LED’s brightness is directional. A small indicator can have a high on-axis candela value without emitting many total lumens if the viewing angle is narrow.

Architectural and workplace lighting often uses lumens for lamp output and lux for illumination on desks, floors, or task surfaces. Lux depends on distance, angle, diffusion, reflectance, and fixture layout, so a unit conversion is only a starting point.

Photography, imaging, and displays use related light measurements but may add exposure time, aperture, luminance, spectral response, or calibration curves. Keep this converter focused on the cd, lm, and lx relationships it actually computes.

Safety and signaling can depend on visibility at distance, beam spread, fog, color, flashing patterns, and regulations. A simple lumen-to-candela conversion does not prove that a beacon, lamp, or warning indicator meets a required standard.

Pitfalls and related calculators

The most common mistake is converting lumens to lux without area or distance context. Another is comparing two candela ratings without checking beam angle. A narrow beam can have a high candela value but illuminate a small area; a wide beam can spread more lumens across a larger angle. Also remember that the form assumes a simplified geometry, not a full photometric distribution.

Use the length converter if your distance is in feet or centimeters before entering meters. The power converter can help compare electrical input ratings, while the electric current converter is useful for LED driver current. If a lighting document uses frequency for flicker or modulation, the frequency converter can keep those units consistent.

When documenting a conversion, record the geometry beside the answer. Writing only “800 lm equals 63.664 cd” hides the 12.566 sr assumption, and writing only “40 cd equals 10 lx” hides the 2 m distance. Those assumptions are not decoration; they are the reason the conversion is possible. Keeping them with the result makes the calculation reproducible for another designer, reviewer, or technician.

Sources

• NIST, SI Units — SI unit framework including candela.
• BIPM, SI base units — international reference for the candela as an SI base unit.
• NIST, Guide for the Use of the International System of Units — SI usage guidance for units and symbols.