How to Calculate Daylight Factor: CIE Overcast Sky Analysis
← Back to Blog
Building Envelope April 16, 2026 11 min read

How to Calculate Daylight Factor: CIE Overcast Sky Analysis

Introduction

Daylight factor is the basic metric of quantitative daylighting design, yet it is often misapplied because engineers confuse it with absolute illuminance levels or conflate overcast-sky metrics with sunny-day performance. A daylight factor of 2% in an office means that on a heavily overcast day with 5,000 lux of outdoor diffuse light, only 100 lux reaches the measurement point — well below the 300–500 lux minimum recommended for sustained desk work. Understanding where daylight factor falls short requires knowing how the CIE standard overcast sky was derived and why it was chosen as the reference condition, rather than a sunny day or average conditions.

The CIE Standard Overcast Sky, originally formulated by Moon and Spencer in 1942 and adopted by CIE in 1955, is now standardized in ISO 15469:2004 (equivalent to CIE S 011:2003) 'Spatial distribution of daylight — CIE standard general sky'. The model distributes luminance as a function of zenith angle, producing a sky brightest at the zenith and one-third as bright at the horizon (zenith-to-horizon luminance ratio of 3:1). This distribution is used as the reference condition for daylight factor because it is reproducible and geometry-independent, representing a reasonable worst-case lighting condition for overcast-dominated climates like the UK and Northern Europe where the metric was developed. In sun-dominated climates, daylight factor underestimates actual daylighting performance because direct beam radiation contributes dramatically to indoor illuminance but is excluded from the CIE overcast sky model.

What Is Daylight Factor and Why Engineers Need It

Daylight factor (DF) is the ratio of interior illuminance at a specific point to the simultaneous exterior horizontal illuminance under an unobstructed CIE overcast sky, expressed as a percentage. A point with DF=3% receives 3% of the light available outdoors on an overcast day. The metric inherently captures the effects of geometry, glazing transmittance, surface reflectances, and external obstructions, making it a useful tool for comparing daylighting strategies during early design when absolute performance is difficult to predict.

Engineers use DF in two ways. The first is early-design comparison: testing window-to-wall ratios, glazing types, and orientations during schematic phase before committing to climate-based simulation (LEED v4 EQ Daylight credit itself uses spatial Daylight Autonomy / Annual Sunlight Exposure or illuminance simulation, not DF, but DF remains useful for orientation and massing studies that feed those simulations). The second is identification of under-lit zones — points with DF below 1.5% that will require electric lighting even in daytime, regardless of climate. DF retains regulatory force in several jurisdictions. CIBSE Lighting Guide LG10 (UK) recommends 2% average DF as the threshold for adequate daylight in office spaces. BREEAM HEA01 credit uses 2% for living rooms and kitchens, 1.5% for studies and bedrooms. Australian National Construction Code Volume 1 (Section J) uses VLT-based glazing area minimums rather than DF directly. Spain's CTE-DB-HE 4 references EN 17037, which uses median DF of 1.6% for daylight provision.

Understanding the Formula Step by Step

Daylight Factor (%) = (Indoor Illuminance / Outdoor Illuminance) × 100

Indoor Illuminance is the illuminance at the measurement point inside the building, measured in lux (lm/m²) or foot-candles (fc), under simultaneous overcast sky conditions. For physical measurement, this requires an illuminance meter positioned at the reference plane (typically 0.85 m above floor in European practice per EN 12464-1, or 0.76 m / 30 inches in North American IES practice; specify which convention is used when reporting results) while an identical meter records outdoor horizontal illuminance. Outdoor Illuminance is the unobstructed horizontal illuminance at the same moment, measured on a flat horizontal surface outdoors away from shadows and reflections.

The ratio eliminates the dependency on absolute sky brightness, making daylight factor a property of the building geometry and glazing rather than of the weather at any particular moment. Converting to foot-candles: 1 fc = 10.764 lux. LEED v4 EQ Credit Daylight uses spatial Daylight Autonomy (sDA300/50% ≥ 55%) and Annual Sunlight Exposure (ASE1000,250h ≤ 10%) under Option 1, illuminance simulation under Option 2, or measurement under Option 3. None of the three uses DF directly. DF retains regulatory weight in jurisdictions that adopted CIBSE LG10 or BREEAM-style criteria, primarily the UK and parts of Europe. Common DF targets by space type: residential habitable rooms 1.5–2% (BREEAM, EN 17037), general office workplaces 2% minimum and 5% for daylit-rated, classrooms 2% (CIBSE LG5), and atria 5–15% depending on whether daylight is the primary or supplementary lighting source.

Worked Example 1: Open-Plan Office Assessment

A 10 × 12 m open-plan office has a south-facing window wall (15 m² glazing, 65% visible light transmittance). On an overcast morning, the outdoor illuminance is measured at 8,500 lux. Three indoor measurements are taken at varying distances from the window:
- Position A (1.5 m from window): 680 lux → DF = 680/8,500 × 100 = 8.0%
- Position B (4 m from window): 255 lux → DF = 255/8,500 × 100 = 3.0%
- Position C (8 m from window): 51 lux → DF = 51/8,500 × 100 = 0.6%

Position C falls below 1% DF — the zone will require supplemental electric lighting even on moderately bright overcast days. Adding a 2.1 m light shelf and increasing ceiling reflectance from 70% to 85% raises Position C to 1.4% DF in the simulation revision. Position C still requires daylight-sensor-controlled supplemental lighting; the shelf reduces but doesn't eliminate the deep-zone shortfall.

In imperial: Outdoor 790 fc. Position A: 63.2 fc (DF=8.0%), Position B: 23.7 fc (DF=3.0%), Position C: 4.7 fc (DF=0.6%).

Worked Example 2: Classroom Compliance Check

A classroom in the UK measures indoor illuminance of 120 lux at the center while outdoor overcast illuminance is 6,000 lux. DF = 120/6,000 × 100 = 2.0%. UK Building Regulations recommend minimum 2% average daylight factor for classrooms; this measurement sits at the threshold.

The engineer checks three more measurement points: 140 lux (DF=2.3%), 85 lux (DF=1.4%), 160 lux (DF=2.7%). Average DF = (2.0 + 2.3 + 1.4 + 2.7) / 4 = 2.1%, marginally compliant. Adding a 1.5 m × 1.5 m roof light over the center raises the four-point average to 3.2% DF. The improvement comes mostly from the previously low-DF center; perimeter points change less than 0.3 percentage points.

In imperial: Outdoor = 557 fc. Center point: 11.1 fc (DF=2.0%), confirming the calculation converts identically.

When Daylight Factor Falls Short

DF is a single-snapshot overcast-sky metric. It's reproducible and geometry-driven, but it ignores time-of-year, time-of-day, orientation, and direct sun. In sun-dominated climates and for compliance with modern codes, climate-based annual metrics replace DF:

Spatial Daylight Autonomy (sDA). Percentage of analysis area that meets a target illuminance (typically 300 lux) for a defined fraction of occupied hours per year (typically 50%), based on hourly simulation with TMY weather data. LEED v4, IES LM-83, and Well Building Standard all use sDA300/50% ≥ 55% as the target for daylit space.

Annual Sunlight Exposure (ASE). Percentage of analysis area exceeding 1,000 lux of direct sun for 250+ hours per year. ASE flags glare and visual discomfort risk; LEED v4 caps ASE1000,250h at 10% to prevent over-glazed designs that pass sDA but produce uncomfortable spaces.

Useful Daylight Illuminance (UDI). Mardaljevic/Nabil framework that splits annual hours into UDI<100 lux (insufficient daylight, electric lighting needed), UDI100–2000 (useful daylight without glare), and UDI>2000 (excessive, glare or overheating risk). UDI is the most informative metric for design optimization but produces three numbers per point rather than one, slowing comparison.

When to use which. DF for early massing and orientation studies before TMY data is loaded. sDA/ASE for code compliance and final design verification in temperate and sun-dominated climates. UDI for detailed shading and glazing optimization where glare and overheating need explicit treatment alongside daylight sufficiency. Pure DF analysis is appropriate for UK/Northern European climates where overcast skies dominate the working year and direct sun contribution is small.

Try the Daylight Factor Calculator

Calculate daylight factor from indoor and outdoor illuminance measurements with our free online tool supporting both metric and imperial units.

Open Daylight Factor Calculator

Common Engineering Mistakes

The most common error is measuring indoor illuminance on a sunny day rather than under overcast conditions, which inflates daylight factor readings by direct sunbeam contribution and produces results that cannot be compared to CIE overcast sky benchmarks or code requirements. Engineers also frequently position outdoor reference meters in partial shade or near reflective surfaces, understating the outdoor illuminance and producing artificially high daylight factors that misrepresent actual performance. Using daylight factor values from overcast-sky models to predict performance in sun-dominated climates (Middle East, Southwest US, tropical zones) underestimates daylighting potential; climate-specific metrics like Useful Daylight Illuminance (UDI) are more appropriate in these regions.

FAQ

Why is overcast sky used as the reference instead of average or sunny conditions?

Three reasons. Overcast sky is reproducible and geometry-independent (luminance distribution depends only on zenith angle, not on time of year or building orientation). It represents the worst typical lighting condition in temperate climates where the metric was developed. And it eliminates the variability of direct sun, which makes physical measurement and simulation cross-comparable. The trade-off is that DF gives no information about sunny-day performance, glare, or seasonal variation.

Can I measure daylight factor on a partly cloudy day?

Only if the sun is fully obscured by uniform cloud cover during measurement. Bright cloud edges, sun breaking through gaps, or thin overcast all produce non-CIE sky luminance distribution and inflate readings. Best practice: measure on heavily overcast days with diffuse outdoor illuminance between 5,000 and 20,000 lux, take both indoor and outdoor readings within 10–15 seconds of each other, and average multiple measurement runs.

What outdoor illuminance is required for valid DF measurement?

CIE recommends a minimum 5,000 lux outdoor horizontal illuminance to ensure measurement signal-to-noise is acceptable on the indoor meter. Below 5,000 lux, sensor noise and meter resolution start to dominate the indoor reading. Most field measurement protocols (BRE, CIBSE) require 10,000+ lux outdoor for compliance-grade measurements.

Does daylight factor account for glazing solar gain or thermal performance?

No. DF only addresses visible light transmittance (VLT). A high-VLT clear glass and a high-VLT spectrally-selective glass both produce the same DF if VLT values match, even though their solar heat gain coefficients (SHGC) and U-values can differ by 50%+. DF must be paired with SHGC and U-value evaluation in any thermal-comfort or energy-performance analysis.

How does DF relate to spatial Daylight Autonomy (sDA)?

DF is a single-condition metric (overcast); sDA is annual hour-percentage based on TMY weather data. Empirical correlation studies (Reinhart 2010, Mardaljevic 2012) show DF of 2% corresponds to roughly sDA300/50% of 50–60% in temperate climates, with significant scatter. The correlation is climate-dependent: sun-dominated climates produce much higher sDA than DF would predict; overcast-dominated climates produce closer matches. For compliance, calculate sDA directly when the code requires it; do not infer sDA from DF.

What's the difference between point DF and average DF?

Point DF is at a single measurement location. Average DF (typically called DFavg) is the mean across a regular grid of points covering the analysis area, usually at workplane height. Codes that specify minimum DF requirements almost always specify average across the room or zone, not minimum at any single point. A room with DF averaging 2% can have individual points well below 1% in deep zones away from glazing.

How accurate are simulation-based DF predictions versus measured values?

Validated radiosity or Radiance-based simulations typically predict DF within ±15% of measurements when input geometry, glazing VLT, and surface reflectances are accurate. The dominant error sources are surface reflectance assumptions (often estimated rather than measured) and external obstruction modeling. For early-design use, simulation accuracy is more than adequate; for code compliance, follow the validation requirements of the specific code (CIBSE TM37, BRE 209, EN 17037 Annex B).

Conclusion

Daylight factor equals interior illuminance divided by simultaneous exterior illuminance, expressed as a percentage under CIE overcast sky conditions. It captures window geometry, glazing properties, and surface reflectances in a single reproducible metric, independent of weather at the moment of measurement. Common targets land at 2% average DF for offices (CIBSE LG10) and 1.5–2% for habitable rooms (BREEAM, EN 17037), with multi-point measurement revealing the spatial distribution that identifies zones requiring supplemental electric lighting.

Related Calculators