How to Calculate Hue Angles

Hue Angle Formula:

\[ H = \arctan2(b^*, a^*) \times \frac{180}{\pi} \]

Hue Angle (H):

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1. What is Hue Angle?

The hue angle is a measurement in color science that represents the actual color attribute (red, yellow, green, blue, etc.) in the CIELAB color space. It's calculated from the a* and b* coordinates, where a* represents the red-green axis and b* represents the yellow-blue axis.

2. How Does the Calculator Work?

The calculator uses the hue angle formula:

\[ H = \arctan2(b^*, a^*) \times \frac{180}{\pi} \]

Where:

\( a^* \) — Red-green coordinate in CIELAB color space
\( b^* \) — Yellow-blue coordinate in CIELAB color space
\( \arctan2 \) — The two-argument arctangent function
\( \frac{180}{\pi} \) — Conversion factor from radians to degrees

Explanation: The arctan2 function calculates the angle between the positive a* axis and the point (a*, b*), providing a result between -180° and +180°, which is then converted to a positive angle between 0° and 360°.

3. Importance of Hue Angle Calculation

Details: Hue angle is crucial in color science for quantifying color appearance, comparing color differences, and ensuring color consistency in various applications including printing, textiles, food quality assessment, and digital imaging.

4. Using the Calculator

Tips: Enter the a* and b* coordinates from CIELAB color measurements. The calculator will compute the corresponding hue angle in degrees. Both coordinates can be positive or negative values.

5. Frequently Asked Questions (FAQ)

Q1: What do different hue angle values represent?
A: 0° = red-purple, 90° = yellow, 180° = bluish-green, 270° = blue. The angle progresses continuously through the color spectrum.

Q2: Why use atan2 instead of regular arctan?
A: atan2 preserves the quadrant information and handles the case when a* = 0 correctly, providing more accurate angle calculation across all four quadrants.

Q3: What is the range of possible hue angle values?
A: The calculated angle ranges from 0° to 360°, representing a complete color circle.

Q4: How is hue angle used in color difference calculations?
A: Hue angle is used in advanced color difference formulas like CIE94 and CIEDE2000, where hue differences contribute to the overall perceived color difference.

Q5: Can hue angle be calculated for any color space?
A: While the concept applies to various color spaces, this specific calculation is for the CIELAB color space, which is perceptually uniform and widely used in color science.