Angle Between Two Lines Calculator 📐

The angle between two lines is the smallest angle formed where the lines intersect. It is a fundamental concept in geometry, trigonometry, and vector mathematics — used in physics, engineering, computer graphics, and more.

📐 Why Calculate the Angle Between Two Lines?

• To check if lines are perpendicular (90°)
• To determine if lines are parallel (0°)
• To measure the inclination or orientation between directions or paths

🧠 How It Works (Formulas)

There are two main ways to calculate the angle between lines:

• Slope Formula: Used when you know the slopes of both lines:
  $$\theta = \tan^{-1}\left|\frac{m_2 - m_1}{1 + m_1m_2}\right|$$
• Vector Formula: Used when lines are defined by two points each:
  $$\theta = \cos^{-1}\left(\frac{\vec{u} \cdot \vec{v}}{|\vec{u}||\vec{v}|}\right)$$

📌 Quick Facts:

• 90° means lines are perpendicular
• 0° means lines are parallel
• The angle is always between 0° and 180°

Whether you are solving for physics, design angles, or math homework, this calculator helps you visualize and compute the correct angle instantly.