Correlated Color Temperature (CCT) Calculator

Correlated Color Temperature (CCT) quantifies the color appearance of light sources, crucial for lighting design. It defines how warm or cool a light source appears, measured in Kelvins (K).

This article explores CCT calculation methods, practical tables, formulas, and real-world applications for engineers and lighting professionals.

Artificial Intelligence (AI) Calculator for “Correlated Color Temperature (CCT) Calculator”

  • ¡Hola! ¿En qué cálculo, conversión o pregunta puedo ayudarte?
Pensando ...
Desarrollado con IA: este chat puede contener errores. Por favor, verifique la información importante.
  • Calculate CCT for chromaticity coordinates x=0.3127, y=0.3290
  • Find CCT from RGB values (255, 244, 229)
  • Determine CCT for xy coordinates (0.33, 0.34)
  • Convert CIE 1931 xyY to CCT for x=0.30, y=0.31

Comprehensive Tables of Common Correlated Color Temperature (CCT) Values

Below are detailed tables listing typical CCT values for various light sources, including natural and artificial lighting. These values assist in selecting appropriate lighting for specific applications.

Light SourceTypical CCT (Kelvin)DescriptionCommon Applications
Candlelight~1900 KVery warm, reddish lightAmbiance lighting, decorative
Incandescent Bulb2700 K – 3000 KWarm white lightResidential lighting, hospitality
Halogen Lamp3000 K – 3200 KSlightly cooler than incandescentAccent lighting, retail
Fluorescent Lamp (Warm White)3000 KWarm white fluorescentOffices, schools
Fluorescent Lamp (Cool White)4000 KNeutral white lightCommercial, industrial
Daylight (Overcast Sky)6500 KCool, bluish lightPhotography, color matching
Clear Blue Sky>10000 KVery cool, blue lightScientific research, outdoor lighting
LED (Warm White)2700 K – 3000 KWarm white LED lightResidential, hospitality
LED (Cool White)4000 K – 5000 KNeutral to cool white LEDOffices, retail, industrial

Fundamental Formulas for Correlated Color Temperature (CCT) Calculation

Correlated Color Temperature (CCT) is derived from chromaticity coordinates, typically in the CIE 1931 xy color space. The goal is to find the temperature of the Planckian blackbody radiator whose color most closely matches the given light source.

1. McCamy’s Approximation Formula

One of the most widely used empirical formulas for quick CCT estimation from chromaticity coordinates (x, y) is McCamy’s formula:

CCT = 449 * n3 + 3525 * n2 + 6823.3 * n + 5520.33

where

  • n = (x – 0.3320) / (y – 0.1858)
  • x, y = chromaticity coordinates in CIE 1931 color space

This formula is accurate for CCT values between approximately 2850 K and 6500 K.

2. Robertson’s Method (More Accurate)

Robertson’s method uses isotemperature lines and chromaticity diagrams to interpolate CCT values. It is more complex and typically implemented algorithmically. The method involves:

  • Locating the closest isotemperature line to the given chromaticity point
  • Calculating the perpendicular distance to the Planckian locus
  • Interpolating between known temperature points

Due to its complexity, Robertson’s method is often embedded in software tools rather than calculated manually.

3. Planckian Locus Approximation

The Planckian locus in the CIE 1960 UCS (Uniform Chromaticity Scale) space is often used for precise CCT calculations. The conversion from CIE 1931 xy to CIE 1960 UCS (u, v) coordinates is:

u = (4 * x) / (-2 * x + 12 * y + 3)
v = (6 * y) / (-2 * x + 12 * y + 3)

Once (u, v) are obtained, the CCT can be calculated by finding the closest point on the Planckian locus curve, often using iterative numerical methods.

4. Approximate CCT from CIE 1960 UCS Coordinates

For a given (u, v), the CCT can be approximated by:

CCT = -449 * m3 + 3525 * m2 – 6823.3 * m + 5520.33

where

  • m = (u – ue) / (v – ve)
  • (ue, ve) = coordinates of the epicenter of the Planckian locus (approximately 0.1978, 0.3122)

5. Conversion from RGB to CCT

When starting from RGB values, the process involves:

  • Converting RGB to linear RGB (removing gamma correction)
  • Transforming linear RGB to XYZ tristimulus values using a color space matrix (e.g., sRGB)
  • Calculating chromaticity coordinates (x, y) from XYZ
  • Applying one of the CCT formulas above

Example matrix for sRGB to XYZ conversion:

| X | | 0.4124 0.3576 0.1805 | | R_lin |
| Y | = | 0.2126 0.7152 0.0722 | * | G_lin |
| Z | | 0.0193 0.1192 0.9505 | | B_lin |

Where R_lin, G_lin, B_lin are linearized RGB components.

Detailed Real-World Examples of Correlated Color Temperature (CCT) Calculation

Example 1: Calculating CCT from Chromaticity Coordinates Using McCamy’s Formula

Given chromaticity coordinates:

  • x = 0.3127
  • y = 0.3290

Step 1: Calculate n

n = (x – 0.3320) / (y – 0.1858) = (0.3127 – 0.3320) / (0.3290 – 0.1858) = (-0.0193) / (0.1432) ≈ -0.1348

Step 2: Calculate CCT

CCT = 449 * (-0.1348)3 + 3525 * (-0.1348)2 + 6823.3 * (-0.1348) + 5520.33

Calculations:

  • n3 = -0.00245
  • n2 = 0.01818
  • 449 * (-0.00245) = -1.10
  • 3525 * 0.01818 = 64.07
  • 6823.3 * (-0.1348) = -920.18
  • Sum = -1.10 + 64.07 – 920.18 + 5520.33 = 4663.12 K

Result: The CCT is approximately 4663 K, indicating a neutral white light source.

Example 2: Calculating CCT from RGB Values

Given sRGB values:

  • R = 255
  • G = 244
  • B = 229

Step 1: Normalize RGB to [0,1]

  • R = 255 / 255 = 1.0
  • G = 244 / 255 ≈ 0.957
  • B = 229 / 255 ≈ 0.898

Step 2: Linearize RGB (inverse gamma correction)

For each component c (R, G, B):

  • If c ≤ 0.04045, then c_lin = c / 12.92
  • If c > 0.04045, then c_lin = ((c + 0.055) / 1.055)2.4

Calculations:

  • R_lin = ((1.0 + 0.055) / 1.055)2.4 = 1.0
  • G_lin = ((0.957 + 0.055) / 1.055)2.4 ≈ 0.907
  • B_lin = ((0.898 + 0.055) / 1.055)2.4 ≈ 0.776

Step 3: Convert linear RGB to XYZ

X = 0.4124 * R_lin + 0.3576 * G_lin + 0.1805 * B_lin = 0.4124*1.0 + 0.3576*0.907 + 0.1805*0.776 ≈ 0.4124 + 0.3243 + 0.1400 = 0.8767
Y = 0.2126 * R_lin + 0.7152 * G_lin + 0.0722 * B_lin = 0.2126*1.0 + 0.7152*0.907 + 0.0722*0.776 ≈ 0.2126 + 0.6487 + 0.0560 = 0.9173
Z = 0.0193 * R_lin + 0.1192 * G_lin + 0.9505 * B_lin = 0.0193*1.0 + 0.1192*0.907 + 0.9505*0.776 ≈ 0.0193 + 0.1081 + 0.7377 = 0.8651

Step 4: Calculate chromaticity coordinates (x, y)

x = X / (X + Y + Z) = 0.8767 / (0.8767 + 0.9173 + 0.8651) = 0.8767 / 2.6591 ≈ 0.3297
y = Y / (X + Y + Z) = 0.9173 / 2.6591 ≈ 0.3450

Step 5: Apply McCamy’s formula

  • n = (x – 0.3320) / (y – 0.1858) = (0.3297 – 0.3320) / (0.3450 – 0.1858) = (-0.0023) / (0.1592) ≈ -0.0145
  • CCT = 449 * (-0.0145)3 + 3525 * (-0.0145)2 + 6823.3 * (-0.0145) + 5520.33

Calculations:

  • n3 = -3.05e-06
  • n2 = 0.00021
  • 449 * (-3.05e-06) = -0.00137
  • 3525 * 0.00021 = 0.74
  • 6823.3 * (-0.0145) = -98.92
  • Sum = -0.00137 + 0.74 – 98.92 + 5520.33 ≈ 5422.15 K

Result: The CCT is approximately 5422 K, indicating a cool white light source.

Additional Technical Insights on CCT Calculation

Correlated Color Temperature is a critical parameter in lighting engineering, affecting human perception, mood, and productivity. Accurate CCT calculation enables:

  • Optimized lighting design for residential, commercial, and industrial environments
  • Color matching in manufacturing and quality control
  • Calibration of cameras and displays for color accuracy
  • Assessment of daylight conditions for architectural planning

While McCamy’s formula offers a fast approximation, it is limited to a specific CCT range and may introduce errors outside this range. For high-precision applications, iterative numerical methods or lookup tables based on the Planckian locus are preferred.

Modern software tools integrate these complex algorithms, often combining spectral power distribution (SPD) data with chromaticity coordinates to refine CCT estimations. Additionally, the concept of Duv (distance from the Planckian locus) is used to quantify how far a light source deviates from ideal blackbody radiation, providing further insight into color quality.

References and Further Reading