Illuminance Calculator
Calculate illuminance in Lux (lx) and Foot-Candles (fc) from luminous flux and surface area, or luminous intensity and distance using the optical Inverse Square Law.
Input Parameters
Step-by-Step Mathematical Solution
How to Calculate Illuminance (Lux)
Illuminance (E) in lux equals the luminous flux (Φ) in lumens divided by the surface area (A) in square meters: E = Φ ÷ A. One lux equals one lumen per square meter (1 lx = 1 lm/m²). For point sources radiating light over a distance d, illuminance follows the Inverse Square Law: E = I ÷ d², where I is luminous intensity in candela (cd) and d is the distance in meters. To convert lux to foot-candles (fc), divide lux by 10.764.
Radiometry vs. Photometry: Understanding the Distinction
Radiometry quantifies electromagnetic radiation across the entire spectrum — from ultraviolet to infrared — in objective physical units like watts (W) for radiant flux and watts per square meter (W/m²) for irradiance. Photometry, by contrast, weights only the visible portion of the spectrum (approximately 380–780 nm) according to the human eye's spectral sensitivity curve, defined by the CIE standard photopic observer function V(λ), which peaks at 555 nm (yellow-green light).
The core photometric quantities form a clear physical hierarchy:
| Quantity | Symbol | SI Unit | Physical Definition |
|---|---|---|---|
| Luminous Flux | Φv | Lumen (lm) | Total visible light emitted in all directions |
| Luminous Intensity | Iv | Candela (cd) | Light emitted per unit solid angle in a given direction |
| Illuminance | Ev | Lux (lx = lm/m²) | Light flux arriving on a surface per unit area |
| Luminance | Lv | cd/m² (nit) | Perceived surface brightness leaving or reflecting from an area |
Illuminance (Ev) answers the practical question: "How much visible light actually reaches this work surface?" This makes it the central metric in architectural lighting design, OSHA workplace safety standards, school classroom codes, and photographic light metering.
The Fundamental Illuminance Equation & SI Unit System
When light from a source is distributed uniformly across a flat surface, illuminance is defined by the basic quotient:
Where Ev is illuminance in lux (lx), Φv is total luminous flux in lumens (lm), and A is the surface area in square meters (m²). One lux represents exactly one lumen spread evenly over one square meter of area.
Imperial Foot-Candles: In the United States, architectural specifications frequently specify light in foot-candles (fc), defined as one lumen per square foot (1 fc = 1 lm/ft²). Since 1 meter equals 3.28084 feet, one square meter contains approximately 10.7639 square feet. Hence:
Inverse Square Law: Mathematical Derivation & Proof
The Inverse Square Law of Illumination is a fundamental geometric law governing all radiant point sources. Consider an isotropic light source with intensity I (candela) radiating uniformly into space. At a distance d, the emitted luminous flux passes through the spherical surface area A = 4πd².
Geometric Proof: The total flux radiated into the surrounding sphere is $\Phi = I \times 4\pi$ (since a complete sphere encompasses $4\pi$ steradians). The surface illuminance is therefore:
Consequence of the Squared Distance: Doubling your distance from a luminaire (d → 2d) reduces the illuminance arriving on your surface to one-fourth (25%) of its initial level. Tripling distance cuts illuminance to one-ninth (11.1%). This rapid geometric falloff explains why task lighting must be situated directly near reading materials or workstations.
Beam Angles, Solid Angles & Steradian Calculations
Lamps with optical reflectors, track spotlights, and LEDs concentrate luminous flux into directional cones rather than radiating isotropically. The angular width is defined by the beam angle (θ), measured at the points where intensity drops to 50% of the center-beam maximum.
To compute center-beam illuminance, we evaluate the solid angle (Ω) in steradians (sr) for a cone with half-apex angle $\theta/2$:
Once solid angle is determined, luminous intensity follows as I = Φ / Ω, and center-beam illuminance at throw distance d is evaluated as E = I / d². The diameter of the illuminated circular beam spot at distance d is:
IES Architectural Indoor Lighting Recommendations
The Illuminating Engineering Society (IES) and CIE publish baseline illuminance guidelines tailored to visual task difficulty, occupational safety, and energy efficiency:
| Environment & Task | Target Illuminance (Lux) | Target (Foot-Candles) | Compliance Standard |
|---|---|---|---|
| Corridors, Hallways & Stairwells | 50 – 100 Lux | 5 – 10 fc | IES RP-28 |
| Residential Living Rooms & Bedrooms | 150 – 300 Lux | 14 – 28 fc | IES RP-11 |
| Commercial Office Desks & Classrooms | 300 – 500 Lux | 28 – 46 fc | IES RP-1 / EN 12464-1 |
| Detailed Drafting, CAD & Retail Showrooms | 500 – 750 Lux | 46 – 70 fc | IES RP-2 |
| Precision Laboratories & Electronics Inspection | 750 – 1,000 Lux | 70 – 93 fc | IES RP-7 |
| Operating Theaters & Surgical Cavities | 1,000 – 2,000 Lux | 93 – 186 fc | CIE S 012 / IEC 60601 |
Real-World Applications: Architecture, Photography & Safety
Architectural Luminaire Planning
Lighting engineers apply the Zonal Cavity Lumen Method to determine how many light fixtures are needed for a space: N = (E × A) / (UF × MF × Φ), where utilization factors (UF ~ 0.4–0.6) and maintenance factors (MF ~ 0.7–0.8) model room wall reflectances and dust accumulation.
Photography & Light Metering
Incident handheld light meters measure illuminance in lux to calculate camera Exposure Values: EV100 = log2(E / 2.5). An office surface reading 500 lux translates to EV 7.6, dictating an exposure of approximately f/4 at 1/60s at ISO 100.
Indoor Agriculture & Horticultural Lux
While horticultural research prioritizes Photosynthetic Photon Flux Density (PPFD in μmol/m²/s), lux meters serve as accessible field proxies for white LED spectrums, where 1 μmol/m²/s corresponds to roughly 70 lux. Leafy greens thrive at 10,000–18,000 lux.
Ergonomics & Eyestrain Prevention
Illuminance ratios across visual fields are strictly audited in ergonomics. Excessive luminance contrast between dark computer monitors and surrounding desk surfaces induces pupillary fatigue, requiring uniform task illuminance of 300 to 500 lux.
Step-by-Step Worked Numerical Solutions (3 Tiers)
Problem: An open office ceiling luminaire emits 4,000 lumens distributed uniformly over a 10 m² desk cluster. Determine the resulting illuminance in Lux and Foot-Candles.
Problem: A directional halogen desk lamp has a luminous intensity of 1,200 candela. Calculate the illuminance at distances of 1.0 meter and 2.0 meters.
Problem: An LED gallery spotlight produces 1,500 lumens with a narrow 30° beam angle mounted 3.0 meters above a sculpture. Compute center-beam illuminance and coverage diameter.
Common Pitfalls & Photometric Anti-Patterns
A 10,000-lumen stadium floodlight spread over a 500 m² parking lot produces merely 20 lux. Lumens measure total source output; lux measures light density arriving at your task. Always compute area dispersion.
Moving a light fixture from 2 meters to 4 meters does not halve the illuminance — it quarters it (dropping by 75%). Never estimate distance falloff linearly.
Calculations assume ideal absorption. In enclosed rooms, white drywall reflects up to 80% of incident light, whereas dark wood absorbs 85%, significantly shifting effective ambient lux.
The Inverse Square Law (1/d²) strictly applies to point sources. For large 2x4 ft LED troffers or diffuse softboxes at close range (d < 5 × width), light falloff is shallower (closer to 1/d).