Lighting Formulas | Lumens, Lux & Foot-Candles

This reference organizes the lighting formulas most often used for room layouts, fixture counts, illuminance conversions, and preliminary power planning. It is intended for fast screening and calculator-supported design work, not as a substitute for fixture photometrics, manufacturer data, or project-specific lighting criteria.

Quick Answer

What are the key lighting formulas?

For a 500 lux office target over 20 m x 15 m, using 4,000 lm lamps with CU 0.7 and LLF 0.8 requires about 67 fixtures before layout spacing is checked.

Calculate	Formula
Lumens Required	Lumens = Area × Lux Required
Number of Lamps	N = (Lux × Area) / (Lumens/Lamp × CU × LLF)
Lux to Foot-candles	FC = Lux × 0.0929
Watts/sq ft	W/ft² = Total Watts / Area

→ Use the Lighting Calculator for instant calculations.

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Lighting Units and Conversions

Key Lighting Units

Unit	Symbol	Definition
Lumen (lm)	Φ	Total light output from source
Lux (lx)	E	Lumens per square meter
Foot-candle (fc)	FC	Lumens per square foot
Candela (cd)	I	Light intensity in a direction

Conversion Formulas

Convert	Formula
Lux → Foot-candles	FC = Lux × 0.0929
Foot-candles → Lux	Lux = FC × 10.764
Lumens → Lux	Lux = Lumens / Area (m²)
Lux → Lumens	Lumens = Lux × Area (m²)

Quick Conversion Table

Lux	Foot-candles
50	4.6
100	9.3
200	18.6
300	27.9
500	46.5
750	69.7
1000	92.9

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Recommended Light Levels

By Application (IES Standards)

Space Type	Lux	Foot-candles
Residential
Living room	150-300	15-30
Kitchen	300-750	30-75
Bedroom	100-200	10-20
Bathroom	300-500	30-50
Commercial
Office (general)	300-500	30-50
Office (detailed work)	500-750	50-75
Retail (general)	300-500	30-50
Retail (accent)	750-1500	75-150
Industrial
Warehouse	100-200	10-20
Manufacturing	300-750	30-75
Precision work	750-1500	75-150
Other
Corridors	50-100	5-10
Stairs	100-150	10-15
Parking	50-100	5-10

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Lumen Method Calculations

Basic Formula

Number of Lamps = (E × A) / (Φ × CU × LLF)

Where:

• E = Required illuminance (lux)
• A = Area (square meters)
• Φ = Lumens per lamp
• CU = Coefficient of Utilization (0.3-0.8)
• LLF = Light Loss Factor (0.6-0.9)

Coefficient of Utilization (CU)

CU depends on:

• Room dimensions (Room Cavity Ratio)
• Surface reflectances
• Luminaire type and distribution

Typical CU Values:

Room Type	Reflectances	CU
Light office	High	0.7-0.8
Standard office	Medium	0.5-0.6
Warehouse	Low	0.4-0.5
Industrial	Very low	0.3-0.4

Light Loss Factor (LLF)

LLF = RSDD × LLD × BF × LSD

Where:

• RSDD = Room Surface Dirt Depreciation (0.85-0.95)
• LLD = Lamp Lumen Depreciation (0.7-0.9)
• BF = Ballast Factor (0.85-1.0)
• LSD = Lamp Survival Rate (0.9-0.95)

Typical LLF Values:

Environment	LLF
Clean office	0.8
Standard commercial	0.7
Industrial	0.6
Dirty/harsh	0.5

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Lamp Selection Data

LED Lamp Efficacy

Lamp Type	Lumens/Watt	Typical Lumens
LED A19 (60W equiv)	80-100	800-1000 lm
LED PAR38	70-90	1000-1500 lm
LED T8 4ft	130-150	2000-2400 lm
LED High Bay	130-180	15,000-30,000 lm
LED Panel 2×4	100-130	4000-6000 lm
LED Troffer 2×4	110-140	4000-5500 lm

Legacy Lamp Reference

Lamp Type	Watts	Lumens	Efficacy
Incandescent	60W	800 lm	13 lm/W
CFL	13W	800 lm	62 lm/W
T8 Fluorescent	32W	2800 lm	88 lm/W
T5 Fluorescent	28W	2900 lm	103 lm/W
Metal Halide	400W	36,000 lm	90 lm/W

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Watts per Square Foot

Estimating Power Requirements

Total Watts = Area (sq ft) × Watts per sq ft

Typical Watts per Square Foot (LED)

Application	W/sq ft	W/sq m
Residence	1.0-1.5	10-15
Office	0.8-1.2	8-12
Retail	1.5-2.5	15-25
Warehouse	0.5-1.0	5-10
Industrial (general)	1.0-2.0	10-20
Industrial (detailed)	2.0-3.5	20-35
Classroom	1.0-1.5	10-15
Hospital	1.5-2.0	15-20

NEC Lighting Load Values

Per NEC Table 220.12:

Occupancy	VA/sq ft	VA/sq m
Dwelling	3.0	32
Hospital	2.0	22
Hotel	2.0	22
Office	3.5	38
Retail	3.0	32
School	3.0	32
Warehouse	0.5	5

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Worked Examples

Example 1: Office Lighting

Given:

• Office: 20m × 15m = 300 m²
• Required: 500 lux
• LED panels: 4,500 lumens each
• CU = 0.65, LLF = 0.75

Solution:

N = (E × A) / (Φ × CU × LLF)
N = (500 × 300) / (4,500 × 0.65 × 0.75)
N = 150,000 / 2,194
N = 68.4 → 70 fixtures

Layout: 7 rows × 10 columns = 70 LED panels

Example 2: Warehouse Lighting

Given:

• Warehouse: 100m × 50m = 5,000 m²
• Required: 150 lux
• LED high bay: 20,000 lumens each
• CU = 0.45, LLF = 0.65

Solution:

N = (150 × 5,000) / (20,000 × 0.45 × 0.65)
N = 750,000 / 5,850
N = 128 fixtures

Layout: 8 rows × 16 columns = 128 high bays

Example 3: Lumens to Foot-candles

Given: 400 lux at desk surface

Find: Equivalent in foot-candles

Solution:

FC = Lux × 0.0929
FC = 400 × 0.0929
FC = 37.2 foot-candles

Example 4: Power Estimate

Given:

• Retail space: 4,000 sq ft
• Estimate: 2.0 W/sq ft

Solution:

Total Watts = 4,000 × 2.0 = 8,000 W = 8 kW

With 4,500 lumen LED panels at 40W each:

Fixtures needed = 8,000 / 40 = 200 panels

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Lighting Layout Guidelines

Spacing Criteria

Maximum spacing between fixtures:

Spacing ≤ 1.5 × Mounting Height

For uniform illumination:

Spacing ≤ 1.0 × Mounting Height

Grid Layout Formula

Rows = √(N × (Length/Width))
Columns = N / Rows

Example: 48 fixtures in 30m × 20m room

Rows = √(48 × (30/20)) = √72 = 8.5 → 8 rows
Columns = 48 / 8 = 6 columns

Edge Spacing

Distance from wall to first fixture:

Wall spacing = Row spacing / 2

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Energy Efficiency Metrics

Lighting Power Density (LPD)

LPD = Total Lighting Watts / Area

Target LPD for energy compliance:

• Office: ≤0.9 W/sq ft (≤10 W/m²)
• Retail: ≤1.3 W/sq ft (≤14 W/m²)
• Warehouse: ≤0.5 W/sq ft (≤5 W/m²)

Efficacy Calculation

Efficacy (lm/W) = Total Lumens / Total Watts

Modern targets:

• LED general: >100 lm/W
• LED high bay: >130 lm/W
• LED troffer: >110 lm/W

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Common Mistakes to Avoid

Mistake	Why It's Wrong	Correct Approach
Ignoring light loss factor	Overestimates actual light	Use LLF 0.7-0.8
Using wrong area units	Lux uses m², FC uses ft²	Convert consistently
Forgetting CU	Undersizes system	Include room efficiency
Peak lumens vs maintained	LED output decreases	Use L70 rated lumens

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Related Calculators

Calculator	Use When...
Lighting Calculator	Lumen requirements
Lux Calculator	Illuminance levels
Lighting Level Chart	Target lux/FC checks
Energy Cost Calculator	Operating costs
LED Savings Calculator	Retrofit analysis

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Summary

Key Formulas:

• Lumens: Lumens = Lux × Area (m²)
• Lamps: N = (Lux × Area) / (Lumens × CU × LLF)
• Lux to FC: FC = Lux × 0.0929
• Power: Watts = Area × W/sq ft

Typical Values:

• Office: 300-500 lux, 0.8-1.2 W/ft²
• Retail: 300-750 lux, 1.5-2.5 W/ft²
• Warehouse: 100-200 lux, 0.5-1.0 W/ft²

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FAQ

How many lumens per square foot do I need?

For general office: 30-50 lumens/sq ft. For retail: 50-75 lumens/sq ft. For warehouse: 10-25 lumens/sq ft. Multiply by area to get total lumens.

What's the difference between lux and foot-candles?

Both measure illuminance (light hitting a surface). Lux uses metric (lumens/m²), foot-candles use imperial (lumens/ft²). 1 FC = 10.764 lux.

How do I calculate watts per square foot?

Divide total lighting wattage by floor area. For LED, typical values are 0.5-2.0 W/sq ft depending on application and required light levels.

What is coefficient of utilization?

CU is the percentage of lamp lumens that reach the work surface. It depends on room shape, surface colors, and fixture type. Typical range: 0.3-0.8.

How do I account for light depreciation?

Use Light Loss Factor (LLF) of 0.6-0.8 in calculations. This accounts for lamp aging, dirt accumulation, and maintenance cycles. Lower LLF for dirty environments.