Free Online CIE XYZ to CIELAB Color Space Conversion Tool
Convert CIE XYZ tristimulus values to CIELAB (LAB) color space with our free, accurate online calculator. Perfect for designers, photographers, color scientists, and print professionals who need reliable color space conversions.
Our tool uses the industry-standard D65 illuminant and provides instant, precise results with detailed mathematical explanations and comprehensive technical documentation.
Input your CIE XYZ tristimulus values (X, Y, Z) in the converter above
Get immediate LAB color values using D65 illuminant standard
Apply the LAB values in your color management workflow
LAB color space is perceptually uniform, meaning equal distances represent equal perceived color differences. This makes it ideal for color matching, quality control, and calculating color differences (Delta E) in professional applications.
CIE XYZ is the foundation color space defined by the International Commission on Illumination (CIE). It represents colors using three tristimulus values based on human vision response curves and serves as the reference for all other color spaces.
CIELAB (LAB) is a perceptually uniform color space where equal distances represent equal perceived color differences. It's designed to be device-independent and closely match human visual perception for accurate color analysis.
// Step 1: Normalize XYZ values with D65 illuminant X_n = X / 95.047 Y_n = Y / 100.000 Z_n = Z / 108.883 // Step 2: Apply nonlinear transformation f(t) = t > 0.008856 ? t^(1/3) : (7.787 * t + 16/116) f_x = f(X_n) f_y = f(Y_n) f_z = f(Z_n) // Step 3: Calculate LAB values L* = 116 * f_y - 16 a* = 500 * (f_x - f_y) b* = 200 * (f_y - f_z)
XYZ Input: X=41.24, Y=21.26, Z=1.93
LAB Output: L*=53.23, a*=80.11, b*=67.22
Standard sRGB red converted to perceptual LAB coordinates
XYZ Input: X=35.76, Y=71.52, Z=11.92
LAB Output: L*=87.73, a*=-86.18, b*=83.18
Standard sRGB green showing negative a* (green direction)
XYZ Input: X=18.05, Y=7.22, Z=95.05
LAB Output: L*=32.30, a*=79.19, b*=-107.86
Standard sRGB blue showing negative b* (blue direction)
XYZ Input: X=95.05, Y=100.00, Z=108.88
LAB Output: L*=100.00, a*=0.00, b*=0.00
D65 white point reference showing neutral LAB values
0 = Black, 100 = White
Negative = Green, Positive = Red
Negative = Blue, Positive = Yellow
import numpy as np
def xyz_to_lab(X, Y, Z):
"""Convert CIE XYZ to CIELAB using D65 illuminant"""
# D65 illuminant white point
xn, yn, zn = 95.047, 100.000, 108.883
# Normalize XYZ values
x_norm = X / xn
y_norm = Y / yn
z_norm = Z / zn
# Apply nonlinear transformation
def f(t):
return np.power(t, 1/3) if t > 0.008856 else (7.787 * t + 16/116)
fx = f(x_norm)
fy = f(y_norm)
fz = f(z_norm)
# Calculate LAB values
L = 116 * fy - 16
a = 500 * (fx - fy)
b = 200 * (fy - fz)
return L, a, b
# Example usage
xyz = (41.24, 21.26, 1.93) # Red color
lab = xyz_to_lab(*xyz)
print(f"XYZ{xyz} -> LAB({lab[0]:.2f}, {lab[1]:.2f}, {lab[2]:.2f})")function xyzToLab(X, Y, Z) {
// D65 illuminant white point
const xn = 95.047, yn = 100.000, zn = 108.883;
// Normalize XYZ values
const xNorm = X / xn;
const yNorm = Y / yn;
const zNorm = Z / zn;
// Apply nonlinear transformation
const f = (t) => {
return t > 0.008856 ? Math.pow(t, 1/3) : (7.787 * t + 16/116);
};
const fx = f(xNorm);
const fy = f(yNorm);
const fz = f(zNorm);
// Calculate LAB values
const L = 116 * fy - 16;
const a = 500 * (fx - fy);
const b = 200 * (fy - fz);
return { L: L, a: a, b: b };
}
// Example usage
const xyz = { X: 41.24, Y: 21.26, Z: 1.93 }; // Red color
const lab = xyzToLab(xyz.X, xyz.Y, xyz.Z);
console.log(`XYZ(${xyz.X}, ${xyz.Y}, ${xyz.Z}) -> LAB(${lab.L.toFixed(2)}, ${lab.a.toFixed(2)}, ${lab.b.toFixed(2)})`);CIE XYZ is a device-independent color space based on human vision, but it's not perceptually uniform. CIELAB (LAB) is derived from XYZ but designed to be perceptually uniform, meaning equal distances in LAB space represent equal perceived color differences. This makes LAB ideal for color difference calculations and quality control applications.
D65 illuminant represents average daylight at 6500K and is the standard reference white point for sRGB, most computer displays, and many color management systems. Using D65 ensures compatibility with modern digital workflows and international color standards like ISO 12640 and IEC 61966.
Our converter uses the official CIE formulas with double-precision floating-point arithmetic, providing accuracy suitable for professional applications. The conversion follows the exact mathematical specifications defined in CIE Publication 15:2004, ensuring results match those from professional color management software and spectrophotometers.
Yes, this XYZ to LAB converter is completely free to use for both personal and commercial projects. The conversion algorithms are based on public CIE standards, and there are no usage restrictions. However, for critical applications, we recommend validating results with certified reference materials or professional color measurement equipment.
For D65 illuminant: XYZ values typically range from 0-95.047 (X), 0-100 (Y), and 0-108.883 (Z). LAB values range from 0-100 (L* lightness), approximately -128 to +127 (a* green-red axis), and -128 to +127 (b* blue-yellow axis). Values outside these ranges may indicate colors outside the visible spectrum or calculation errors.
This converter uses the D65 illuminant (daylight at 6500K) as the reference white point, which is the international standard for sRGB and most modern display systems. The D65 white point coordinates are X=95.047, Y=100.000, Z=108.883.
Industry Standards: D65 is specified in ISO 3664, ISO 12640, and IEC 61966 standards for color management and display calibration.
Converting to CIELAB provides perceptual uniformity, meaning that equal distances in the LAB color space correspond to equal perceived color differences. This makes LAB ideal for color difference calculations, color matching applications, and quality control processes.
Delta E Calculation: Use LAB values to calculate color differences with formulas like ΔE*ab = √[(ΔL*)² + (Δa*)² + (Δb*)²]
The conversion involves cube root operations and conditional transformations that require careful numerical handling. Our implementation uses double-precision floating-point arithmetic for professional-grade accuracy.
Typical Accuracy: ±0.01 LAB units for most visible colors, suitable for professional color management applications.
While XYZ can theoretically represent colors outside the visible spectrum, practical applications should validate input ranges. Negative XYZ values or values significantly exceeding the D65 white point may indicate measurement errors.
Recommended Ranges: X: 0-100, Y: 0-100, Z: 0-120 for most practical applications.
When integrating XYZ to LAB conversion into larger color management workflows, ensure consistent illuminant usage throughout the pipeline. Mixed illuminants can cause color shifts and inaccurate results.
Best Practice: Document the illuminant used in each conversion step and provide chromatic adaptation when switching between illuminants.
Convert CIELAB colors back to CIE XYZ color space with precise mathematical formulas.
Transform CIE XYZ colors to RGB with sRGB color space conversion and gamma correction.
Convert RGB colors to CIELAB color space for perceptual color analysis and processing.