What are lumens, lux, and candelas?
Lumens, lux, and candelas are the three most commonly used units for measuring lighting. They are all related but represent entirely different things.
- Lumens (lm) — a unit of luminous flux, or the total amount of light emitted by a source in all directions.
- Lux (lx) — a measure of illuminance: how much light is received per unit of surface area (1 lux = 1 lm/m²).
- Candelas (cd) — the SI unit of luminous intensity: light emitted from a source per unit solid angle (steradian).
- Foot-candles (fc) — the imperial equivalent of lux: 1 foot-candle = 10.764 lux.
How to calculate lumens from candelas
Candelas measure light per steradian, while lumens measure total emitted light. To convert, multiply candelas by the solid angle Ω (in steradians) that the source covers:
lumens = candelas × ΩThe solid angle Ω depends on the apex angle θ (the angle between the axis of maximum luminosity and the 50 % luminosity axis):
Ω = 2π × [1 − cos(θ / 2)]For a light source that emits uniformly in all directions (omnidirectional), Ω = 4π ≈ 12.566 sr.
Example: A spotlight with 500 cd and an apex angle of 60° gives:
Ω = 2π × [1 − cos(30°)] = 2π × [1 − 0.866] ≈ 0.842 sr
Lumens = 500 × 0.842 ≈ 421 lm
Lux to lumen conversion
Lux measures illuminance on a surface, while lumens measure the total light output of the source. The relationship is:
lux = lumens / area (m²)
lumens = lux × area (m²)Example: A room of 20 m² lit to 300 lux requires:
Lumens = 300 × 20 = 6,000 lm
Convert lux to foot-candles
The foot-candle (fc) is the imperial unit of illuminance. One foot-candle equals the illumination produced by one lumen spread over one square foot:
1 foot-candle = 10.764 lux
foot-candles = lux / 10.764
lux = foot-candles × 10.764Example: 500 lux = 500 / 10.764 ≈ 46.4 fc
Typical illuminance values
| Environment | Lux | Foot-candles |
|---|---|---|
| Moonlight | 1 lux | 0.09 fc |
| Living room (ambient) | 50–150 lux | 5–14 fc |
| Office work area | 300–500 lux | 28–46 fc |
| Supermarket | 500–750 lux | 46–70 fc |
| Surgery room | 10,000–20,000 lux | 930–1,860 fc |
| Direct sunlight | 100,000 lux | 9,290 fc |
American vs. metric units
This calculator supports both measurement systems:
- Metric system: lux (lm/m²), square metres (m²)
- American (imperial) system: foot-candles (lm/ft²), square feet (ft²)
Area entered in ft² is automatically converted to m² for lux calculations, and the equivalent in foot-candles is also shown.
Steradians explained
A steradian (sr) is the 3-D equivalent of a radian. A full sphere subtends 4π ≈ 12.566 sr. For a cone with apex half-angle α:
Ω = 2π × (1 − cos α)Our calculator uses the apex angle θ, which is twice the half-angle: α = θ / 2.