Lux (lx)
Light arriving at a surface. One lumen per square metre. The SI standard for illuminance.
E = Φ / A
Footcandle (fc)
Imperial illuminance. One lumen per square foot. Widely used in US lighting specifications.
1 fc = 10.764 lx
Lux at distance
Illuminance falls as the square of distance. Doubling distance quarters the lux (inverse square law).
E = I / d²
Inverse square law — illuminance vs distance
Lux ↔ Footcandles
Most common illuminance conversion. Used constantly in international specs.
lux →
46.5footcandles
fc →
538.2lux
Formula
fc = lux ÷ 10.764lux = fc × 10.764
Lux from lumens + area
How many lumens does it take to hit a target lux over a given area?
lumens
m²
200lux
18.6footcandles
Formula
E (lux) = Φ (lm) ÷ A (m²)Lux from candela at distance
Point source illuminance. At 2× distance, lux drops to ¼. This is the inverse square law.
candela
metres
111.1lux (nadir, perpendicular)
10.3footcandles
Formula
E = I (cd) ÷ d² (m²)Off-axis: E = I × cos(θ) ÷ d²
Lumen (lm)
Total light output from a source in all directions. The quantity on the bulb box.
Φ (phi)
Lm/m² = Lux
When lumens land on a surface, they become lux. Spread the same lumens over a larger area and lux falls.
E = Φ / A
Lumens in a cone
A focused beam captures only part of the total lumen output. The cone formula calculates how much.
Φ = 2π I (1−cosθ/2)
Same lumens, different areas — lux changes
Lumens from lux + area
How many lumens are needed to achieve a target illuminance over a space?
target lux
m²
6000lumens required
Formula
Φ (lm) = E (lux) × A (m²)Lumens in a beam cone
Total flux within a cone of a given beam angle, assuming uniform candela intensity I.
candela
beam angle °
—lumens in cone
Formula
Φ = 2π × I × (1 − cos(θ/2))Lumens → area at target lux
Given a fixture’s lumen output, what area can it illuminate at a target level?
lumens
target lux
4.0m² coverable
43.1sq ft
Formula
A = Φ (lm) ÷ E (lux)Candela (cd)
Luminous intensity — brightness in a specific direction. Does not depend on distance.
I (intensity)
CBCP
Center Beam Candlepower — peak intensity at the center of a spotlight beam. The “punch” number.
cd at 0°
Steradian (sr)
Solid angle unit. Full sphere = 4π sr. A hemisphere = 2π sr. Used in candela-to-lumen conversion.
I = Φ / Ω
Candela from lux at distance
Back-calculate the required intensity to hit a target illuminance at a given distance.
target lux
metres
1800candela required
Formula
I (cd) = E (lux) × d² (m²)Candela from lumens
Average candela for an isotropic (omnidirectional) source. Real fixtures concentrate light, so CBCP will be higher.
lumens
63.7cd (avg, isotropic source)
Formula
I = Φ ÷ (4π) = Φ ÷ 12.5664π = full sphere in steradians
Off-axis illuminance
Illuminance on a tilted surface. At 30° off-axis at 3m, what lux hits the surface?
candela
metres (to surface)
angle °
—lux on tilted surface
Formula
E = I × cos(θ) ÷ d²These conversions are specific to photometric planning — beam geometry, mounting heights, and spacing. They connect directly to the IES File Reader and Mounting Height Calculator.
Beam diameter at mounting height
How wide is the beam footprint on the floor for a given fixture and ceiling height?
beam angle °
height (m)
2.18metres diameter
7.2feet diameter
Formula
D = 2 × h × tan(θ ÷ 2)Required beam angle from target diameter
What beam angle fixture do you need to achieve a desired footprint at a given height?
target diameter (m)
height (m)
53.1degrees beam angle
Formula
θ = 2 × atan(D ÷ (2 × h)) × (180/π)Spacing-to-mounting-height ratio
S/MH ratio determines if fixtures are spaced for good uniformity. Ideal range: 0.8–1.2 for general.
spacing (m)
mounting height (m)
1.33S/MH ratio
Interpretation
<0.5 Heavy overlap · 0.5–0.8 Tight · 0.8–1.2 Ideal · 1.2–1.5 Marginal · >1.5 Dark gapsInverse square law checker
If you know lux at distance 1, what lux at distance 2? Works for any point source.
lux at d₁
d₁ (m)
d₂ (m)
125lux at d₂
Formula
E₂ = E₁ × (d₁ ÷ d₂)²lm/W
Lumens per watt — how efficiently electricity is converted to light. Higher is better.
η = Φ / PIncandescent
8–16 lm/W. Most energy wasted as heat. A 60W bulb produces ~800 lm and 54W of heat.
~12 lm/WLED
80–200+ lm/W. State-of-the-art chips exceed 220 lm/W in lab conditions.
~120 lm/W typicalLumens from watts + efficacy
Predict a fixture’s lumen output from its wattage and typical technology efficacy.
watts
lm/W efficacy
1540lumens output
Formula
Φ (lm) = P (W) × η (lm/W)Efficacy from lumens + watts
Calculate a fixture’s efficacy. Compare against reference values below to assess quality.
lumens
watts
120.0lm/W
Formula
η = Φ (lm) ÷ P (W)Energy saving from upgrade
Compare old vs new fixture wattage to find energy reduction percentage.
old watts
new watts
85%energy reduction
51 Wwatts saved per fixture
Formula
Saving % = (1 − P_new / P_old) × 100| Technology | Typical efficacy | Energy wasted as heat | Status |
|---|---|---|---|
| Incandescent | 8–16 lm/W | ~90% | Largely phased out |
| Halogen | 15–25 lm/W | ~85% | Being phased out |
| CFL compact fluorescent | 40–70 lm/W | ~75% | Declining |
| T8 fluorescent tube | 70–100 lm/W | ~60% | Being replaced by LED |
| Metal halide | 60–100 lm/W | ~70% | Being replaced by LED |
| LED residential (standard) | 80–120 lm/W | ~50% | Current standard |
| LED commercial (quality) | 120–170 lm/W | ~40% | Best practice |
| LED (high-performance) | 170–220+ lm/W | ~25% | State of the art |
Watts, volts, amps
Ohm’s law for AC power. Enter any two to get the third.
volts
amps
60watts
W ÷
volts
0.50amps drawn
Formula
P (W) = V × I (amps)kWh energy consumption
How much energy does a lighting circuit use? Essential for cost calculation.
total watts
hours per day
1.60kWh per day
584kWh per year
Formula
kWh = W × h ÷ 1000Annual electricity cost
Running cost of a lighting circuit over a year.
watts
hrs/day
¢/kWh rate
$93.44per year
Formula
Cost = W × h × 365 × rate ÷ 100000Typical illuminance levels by application
| Application | Typical lux | Footcandles | Notes |
|---|---|---|---|
| Moonlight | 0.1 lux | 0.01 fc | Natural reference |
| Corridor / stairwell | 50–100 lux | 5–9 fc | Safety minimum |
| Bedroom / relaxed living | 100–200 lux | 9–18 fc | Ambient only |
| Living room (standard) | 150–300 lux | 14–28 fc | General living |
| Office — general | 300–500 lux | 28–46 fc | EN 12464-1 office |
| Kitchen (task surfaces) | 400–700 lux | 37–65 fc | Countertop work |
| Retail (general) | 500–1000 lux | 46–93 fc | Product display |
| Retail (accent/display) | 1000–3000 lux | 93–278 fc | Sparkle and focus |
| Drawing / detailed work | 750–1500 lux | 70–139 fc | EN 12464-1 drawing |
| Operating theatre | 10,000–100,000 lux | 930–9300 fc | Surgical field |
| Outdoor — overcast day | 1,000–10,000 lux | 93–930 fc | Daylight reference |
| Direct sunlight | 100,000 lux | 9,290 fc | Natural maximum |
Lighting unit symbol reference
| Unit | Symbol | Measures | Conversion |
|---|---|---|---|
| Lumen | lm | Total luminous flux | 1 lm = 1 cd × sr |
| Lux | lx | Illuminance (lm/m²) | 1 lux = 1 lm/m² |
| Footcandle | fc | Illuminance (lm/ft²) | 1 fc = 10.764 lux |
| Candela | cd | Luminous intensity | 1 cd = 1 lm/sr |
| Candela per m² | cd/m² | Luminance (surface brightness) | 1 cd/m² = 1 nit |
| Nit | nt | Luminance (display/surface) | 1 nit = 1 cd/m² |
| Steradian | sr | Solid angle | Full sphere = 4π sr ≈ 12.57 sr |
| Lumen per watt | lm/W | Luminous efficacy | Higher = more efficient |
Key formulas
Illuminance (lux)
E = Φ / A (lm ÷ m²)
E = I / d² (cd ÷ m²)
E = I·cos(θ) / d² (off-axis)
1 fc = 10.764 lux
E = I / d² (cd ÷ m²)
E = I·cos(θ) / d² (off-axis)
1 fc = 10.764 lux
Beam geometry
D = 2h·tan(θ/2) (beam diameter)
θ = 2·atan(D/2h) (beam angle)
E₂ = E₁·(d₁/d₂)² (inv. square)
S/MH ideal: 0.8–1.2
θ = 2·atan(D/2h) (beam angle)
E₂ = E₁·(d₁/d₂)² (inv. square)
S/MH ideal: 0.8–1.2
Flux & intensity
Φ = E · A (lm = lux × m²)
I = Φ / 4π (isotropic)
Φ_cone = 2π·I·(1−cosθ/2)
η = Φ / P (lm/W)
I = Φ / 4π (isotropic)
Φ_cone = 2π·I·(1−cosθ/2)
η = Φ / P (lm/W)