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Calculate and Draw the Intersection of two Straight Lines

Calculator for the intersection point of two straight lines and the angle between them from the linear equations. The two linear equations are y₁ = mx₁ + b and y₂ = nx₂ + c. The variables m and n are the gradients, b and c are the up or down shifts. If both lines have the same gradient, so if m=n, then they are parallel and no intersection and angle exist.

1. line y₁ = x₁ +

2. line y₂ = x₂ +

Angle between α = °

Intersection point: x = , y =

Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Please enter for both linear equations m and b as well as n and c. The angle and the intersection point will be calculated and both lines will be drawn.

Formulas:
α = | atan(m) − atan(n) |
x = (c−b) / (m−n)
y = m*x + b

Example: the lines x+2 and 3x+4 intersect in the point (-1;1) in an angle of 26.565°. For x+2, put a 1 in the first line before x₁.

If two straight lines lie in a plane and are not parallel to each other, then they intersect at exactly one point. This point of intersection and the angle between these two straight lines are calculated here. In fact, when two straight lines intersect, exactly four angles are created. The two opposite angles are the same size. Two angles lying next to each other add up to 180 degrees; if you name the other angle β, then β=180°-α applies. If both straight lines are perpendicular to each other, then all four angles are the same size, namely 90 degrees.
To calculate the angle, you need the arctangent atan, i.e. the inverse function of the tangent. Since straight lines have no direction, this angle cannot be negative, so the absolute value |...| is taken. The angle is independent of the shift up or down, which is only relevant for calculating the point of intersection.
This calculation only refers to the plane. If two straight lines lie in space, then they can also be skewed to each other, i.e. are neither parallel to each other nor do intersect.

Last updated on 03/11/2026. Author: Jürgen Kummer

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