Angle Between Two Lines Calculator

A calculator to find the angle between two lines \(L_1\) and \(L_2\) given by their general equation of the form \[ a x + b y = c \] is presented.

The formula used to find the acute angle \( \theta \) (between 0 and \( 90^{\circ} \)) between two lines \(L_1\) and \(L_2\) with slopes \(m_1\) and \(m_2\) respectively is given by \[ \theta = \left|\tan^{-1}\!\left(\frac{m_2 - m_1}{1 + m_2 m_1}\right)\right| \] The obtuse angle \( \alpha \) between the same lines is given by \[ \alpha = 180^{\circ} - \theta \]

About the angles:

When two lines intersect, they form two angles that sum to 180°:

θ (theta): The smaller angle between the lines (between 0° and 90°). This is often called the acute angle.
α (alpha): The larger angle between the lines (between 90° and 180°). This is often called the obtuse angle.

Note: When lines are parallel, θ = 0° and α = 180°. When lines are perpendicular, θ = 90° and α = 90° (both angles are equal).

Angle Between Two Lines

Enter coefficients a, b, c for two lines in the form ax + by = c

Line L₁: ax + by = c

a₁

b₁

c₁

Line L₂: ax + by = c

a₂

b₂

c₂

Decimal Places

Acute Angle (θ) -- °

Obtuse Angle (α) -- °

Angle Between Two Lines Calculator

Angle Between Two Lines

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