Lux (lx)
Light arriving at a surface. One lumen per square metre. The SI standard for illuminance.
E = Ξ¦ / 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 / dΒ²
Inverse square law β illuminance vs distance
Lux β Footcandles
Most common illuminance conversion. Used constantly in international specs.
lux β
46.5footcandles
fc β
538.2lux
Formula
fc = lux Γ· 10.764lux = fc Γ 10.764
Lux from lumens + area
How many lumens does it take to hit a target lux over a given area?
lumens
mΒ²
200lux
18.6footcandles
Formula
E (lux) = Ξ¦ (lm) Γ· A (mΒ²)Lux from candela at distance
Point source illuminance. At 2Γ distance, lux drops to ΒΌ. This is the inverse square law.
candela
metres
111.1lux (nadir, perpendicular)
10.3footcandles
Formula
E = I (cd) Γ· dΒ² (mΒ²)Off-axis: E = I Γ cos(ΞΈ) Γ· dΒ²
Lumen (lm)
Total light output from a source in all directions. The quantity on the bulb box.
Ξ¦ (phi)
Lm/mΒ² = Lux
When lumens land on a surface, they become lux. Spread the same lumens over a larger area and lux falls.
E = Ξ¦ / A
Lumens in a cone
A focused beam captures only part of the total lumen output. The cone formula calculates how much.
Ξ¦ = 2Ο I (1βcosΞΈ/2)
Same lumens, different areas β lux changes
Lumens from lux + area
How many lumens are needed to achieve a target illuminance over a space?
target lux
mΒ²
6000lumens required
Formula
Ξ¦ (lm) = E (lux) Γ A (mΒ²)Lumens in a beam cone
Total flux within a cone of a given beam angle, assuming uniform candela intensity I.
candela
beam angle Β°
βlumens in cone
Formula
Ξ¦ = 2Ο Γ I Γ (1 β cos(ΞΈ/2))Lumens β area at target lux
Given a fixture’s lumen output, what area can it illuminate at a target level?
lumens
target lux
4.0mΒ² coverable
43.1sq ft
Formula
A = Ξ¦ (lm) Γ· E (lux)Candela (cd)
Luminous intensity β brightness in a specific direction. Does not depend on distance.
I (intensity)
CBCP
Center Beam Candlepower β peak intensity at the center of a spotlight beam. The “punch” number.
cd at 0Β°
Steradian (sr)
Solid angle unit. Full sphere = 4Ο sr. A hemisphere = 2Ο sr. Used in candela-to-lumen conversion.
I = Ξ¦ / Ξ©
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) Γ dΒ² (mΒ²)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 = Ξ¦ Γ· (4Ο) = Ξ¦ Γ· 12.5664Ο = full sphere in steradians
Off-axis illuminance
Illuminance on a tilted surface. At 30Β° off-axis at 3m, what lux hits the surface?
candela
metres (to surface)
angle Β°
βlux on tilted surface
Formula
E = I Γ cos(ΞΈ) Γ· dΒ²These conversions are specific to photometric planning β 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 Β°
height (m)
2.18metres diameter
7.2feet diameter
Formula
D = 2 Γ h Γ tan(ΞΈ Γ· 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
ΞΈ = 2 Γ atan(D Γ· (2 Γ h)) Γ (180/Ο)Spacing-to-mounting-height ratio
S/MH ratio determines if fixtures are spaced for good uniformity. Ideal range: 0.8β1.2 for general.
spacing (m)
mounting height (m)
1.33S/MH ratio
Interpretation
<0.5 Heavy overlap Β· 0.5β0.8 Tight Β· 0.8β1.2 Ideal Β· 1.2β1.5 Marginal Β· >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 dβ
dβ (m)
dβ (m)
125lux at dβ
Formula
Eβ = Eβ Γ (dβ Γ· dβ)Β²lm/W
Lumens per watt β how efficiently electricity is converted to light. Higher is better.
Ξ· = Ξ¦ / PIncandescent
8β16 lm/W. Most energy wasted as heat. A 60W bulb produces ~800 lm and 54W of heat.
~12 lm/WLED
80β200+ 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
Ξ¦ (lm) = P (W) Γ Ξ· (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
Ξ· = Ξ¦ (lm) Γ· 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 β P_new / P_old) Γ 100| Technology | Typical efficacy | Energy wasted as heat | Status |
|---|---|---|---|
| Incandescent | 8β16 lm/W | ~90% | Largely phased out |
| Halogen | 15β25 lm/W | ~85% | Being phased out |
| CFL compact fluorescent | 40β70 lm/W | ~75% | Declining |
| T8 fluorescent tube | 70β100 lm/W | ~60% | Being replaced by LED |
| Metal halide | 60β100 lm/W | ~70% | Being replaced by LED |
| LED residential (standard) | 80β120 lm/W | ~50% | Current standard |
| LED commercial (quality) | 120β170 lm/W | ~40% | Best practice |
| LED (high-performance) | 170β220+ 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 Γ·
volts
0.50amps drawn
Formula
P (W) = V Γ 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 Γ h Γ· 1000Annual electricity cost
Running cost of a lighting circuit over a year.
watts
hrs/day
Β’/kWh rate
$93.44per year
Formula
Cost = W Γ h Γ 365 Γ rate Γ· 100000Typical illuminance levels by application
| Application | Typical lux | Footcandles | Notes |
|---|---|---|---|
| Moonlight | 0.1 lux | 0.01 fc | Natural reference |
| Corridor / stairwell | 50β100 lux | 5β9 fc | Safety minimum |
| Bedroom / relaxed living | 100β200 lux | 9β18 fc | Ambient only |
| Living room (standard) | 150β300 lux | 14β28 fc | General living |
| Office β general | 300β500 lux | 28β46 fc | EN 12464-1 office |
| Kitchen (task surfaces) | 400β700 lux | 37β65 fc | Countertop work |
| Retail (general) | 500β1000 lux | 46β93 fc | Product display |
| Retail (accent/display) | 1000β3000 lux | 93β278 fc | Sparkle and focus |
| Drawing / detailed work | 750β1500 lux | 70β139 fc | EN 12464-1 drawing |
| Operating theatre | 10,000β100,000 lux | 930β9300 fc | Surgical field |
| Outdoor β overcast day | 1,000β10,000 lux | 93β930 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 Γ sr |
| Lux | lx | Illuminance (lm/mΒ²) | 1 lux = 1 lm/mΒ² |
| Footcandle | fc | Illuminance (lm/ftΒ²) | 1 fc = 10.764 lux |
| Candela | cd | Luminous intensity | 1 cd = 1 lm/sr |
| Candela per mΒ² | cd/mΒ² | Luminance (surface brightness) | 1 cd/mΒ² = 1 nit |
| Nit | nt | Luminance (display/surface) | 1 nit = 1 cd/mΒ² |
| Steradian | sr | Solid angle | Full sphere = 4Ο sr β 12.57 sr |
| Lumen per watt | lm/W | Luminous efficacy | Higher = more efficient |
Key formulas
Illuminance (lux)
E = Ξ¦ / A (lm Γ· mΒ²)
E = I / dΒ² (cd Γ· mΒ²)
E = IΒ·cos(ΞΈ) / dΒ² (off-axis)
1 fc = 10.764 lux
E = I / dΒ² (cd Γ· mΒ²)
E = IΒ·cos(ΞΈ) / dΒ² (off-axis)
1 fc = 10.764 lux
Beam geometry
D = 2hΒ·tan(ΞΈ/2) (beam diameter)
ΞΈ = 2Β·atan(D/2h) (beam angle)
Eβ = EβΒ·(dβ/dβ)Β² (inv. square)
S/MH ideal: 0.8β1.2
ΞΈ = 2Β·atan(D/2h) (beam angle)
Eβ = EβΒ·(dβ/dβ)Β² (inv. square)
S/MH ideal: 0.8β1.2
Flux & intensity
Ξ¦ = E Β· A (lm = lux Γ mΒ²)
I = Ξ¦ / 4Ο (isotropic)
Ξ¦_cone = 2ΟΒ·IΒ·(1βcosΞΈ/2)
Ξ· = Ξ¦ / P (lm/W)
I = Ξ¦ / 4Ο (isotropic)
Ξ¦_cone = 2ΟΒ·IΒ·(1βcosΞΈ/2)
Ξ· = Ξ¦ / P (lm/W)