Lumen to Lux to Candela Calculator
Choose a conversion mode, enter the values you know, and this calculator instantly derives the missing photometric quantities using the correct physics formulas. All six inter-conversions between lumens, lux, and candela are supported, with full step-by-step working and a reference table of real-world illuminance levels.
Formula
Worked example
An LED spotlight rated 800 lm with a 60 deg beam angle: solid angle = 2pi*(1-cos(30 deg)) = 0.842 sr; intensity = 800/0.842 = 950 cd. At 2 m distance, illuminance = 950/4 = 237 lx, comparable to a dimly lit corridor.
The three photometric units and how they relate
Photometry measures visible light from the human eye's perspective, and three quantities describe different aspects of a light source. Luminous flux (lumens, lm) is the total light emitted in all directions - the "power" the eye can use. Luminous intensity (candela, cd) describes how much of that flux is aimed in a particular direction per unit solid angle; a spotlight concentrates flux into a narrow cone, so the same number of lumens produces far more candela than an omnidirectional bulb. Illuminance (lux, lx) is what arrives at a surface - one lux equals one lumen landing on one square metre. The three are linked by area and solid angle: lux = lumens/area and candela = lumens/steradians.
Solid angle and the beam angle formula
A solid angle measures a cone of directions in three-dimensional space, expressed in steradians (sr). A full sphere spans 4pi sr (about 12.57 sr), which is why an omnidirectional bulb emitting 800 lm has a relatively low intensity of about 64 cd. For a cone with an apex (full-cone) angle of theta degrees, the solid angle is: Omega = 2*pi*(1 - cos(theta/2)). A narrow 10-degree spotlight has only 0.024 sr, so 800 lm concentrated into that cone gives 33,000 cd - a dramatic intensity. A 120-degree flood has about 1.84 sr and yields roughly 435 cd from the same bulb.
The inverse-square law for illuminance
When a point source radiates in a cone, the light spreads over an ever-larger area as distance increases. The mathematical consequence is that illuminance (lux) falls as the square of distance: E = I / d^2. Doubling the distance reduces illuminance to one quarter; tripling it reduces it to one ninth. This is why a reading lamp positioned 0.5 m above a book produces sixteen times the illuminance it would at 2 m. The relationship reverses to find intensity from a measured illuminance: I = E * d^2. Both derivations assume a point source and a surface perpendicular to the beam - angled surfaces receive less light by a factor of cos(angle of incidence).
Practical lighting design and foot-candles
Recommended illuminance levels vary widely by task. The Illuminating Engineering Society (IES) advises 300-500 lx for general office work, 750-1,500 lx for demanding tasks such as drafting or assembly, and 50-100 lx for corridors and stairwells. In the United States and some other countries, illuminance is still measured in foot-candles (fc), where 1 fc = 10.764 lx. This calculator converts automatically between lux and foot-candles so you can work in either system. When designing a room's lighting, divide the required lux by the fixture's beam efficiency and multiply by the floor area to estimate the total lumen output needed.
Typical illuminance levels
| Environment / Condition | Typical illuminance (lx) |
|---|---|
| Moonlit night | 0.001 - 0.1 |
| Candlelight at 0.5 m | 1 - 10 |
| Street lighting | 10 - 50 |
| Stairwell / corridor | 50 - 100 |
| Living room (ambient) | 100 - 300 |
| Office (recommended) | 300 - 500 |
| Bright classroom | 500 - 750 |
| Retail display lighting | 750 - 1,500 |
| Operating theatre | 10,000 - 40,000 |
| Overcast daylight | 1,000 - 10,000 |
| Direct sunlight | 32,000 - 100,000 |
Approximate lux values for common environments and lighting conditions.
Frequently asked questions
What is the difference between lumen, lux, and candela?
Lumens (lm) measure total light output from a source regardless of direction - think of it as the overall "brightness budget". Candela (cd) measures intensity in a specific direction per unit solid angle - it tells you how concentrated the beam is. Lux (lx) measures the illuminance received by a surface - one lux is one lumen landing on one square metre. The three are related: lux = lumens/area, and candela = lumens/steradians.
How do I convert lumens to candela?
Divide the luminous flux in lumens by the solid angle in steradians: cd = lm / sr. The solid angle depends on the beam's apex angle (theta): sr = 2 * pi * (1 - cos(theta/2)). For example, 800 lm in a 60-degree beam: sr = 2*pi*(1-cos(30 deg)) = 0.842 sr, so the intensity is 800/0.842 = 950 cd.
How do I convert lux to lumens?
Multiply illuminance by the area being lit: lm = lux * area in square metres. If a 2 m x 3 m room (6 m²) is lit to 400 lx, the source must emit at least 400 * 6 = 2,400 lm. This assumes the light is evenly distributed over the surface - in practice, fixtures lose some light to walls and fittings, so choose a higher lumen rating.
What does the inverse-square law mean for lighting?
Illuminance (lux) from a point source drops in proportion to the square of the distance: E = I / d². If you move a lamp from 1 m to 2 m away from a desk, the illuminance falls to 25% (one quarter) of its original value, not half. This is why small changes in fixture position have a large effect on how bright a surface appears.
What is a foot-candle and how does it relate to lux?
A foot-candle (fc) is the illuminance produced by one lumen falling on one square foot. Because a square foot is smaller than a square metre, one foot-candle equals 10.764 lux. Foot-candles remain common in North American lighting specifications and photography exposure settings. Multiply foot-candles by 10.764 to convert to lux, or divide lux by 10.764 to get foot-candles.
What is a steradian and how is it calculated from a beam angle?
A steradian (sr) is the SI unit of solid angle - it is the three-dimensional equivalent of a radian. A full sphere spans 4*pi steradians. For a cone with apex angle theta, the solid angle is Omega = 2*pi*(1 - cos(theta/2)). A narrow 10-degree spotlight has about 0.024 sr; an omnidirectional source covers the full 4*pi sr (about 12.57 sr). Candela = lumens / steradians, so concentrating flux into a smaller solid angle raises intensity.
How many lumens do I need to light a room?
Multiply the floor area (in square metres) by the recommended illuminance for the task. For general living spaces, 100-300 lx is typical; for offices, 300-500 lx. A 20 m² office at 400 lx needs at least 20 * 400 = 8,000 lm total - spread across multiple fixtures to avoid shadows. Add 20-30% extra to account for fixture inefficiency and light absorbed by walls and ceiling.