Angle Between Lines Calculator
Calculate the acute angle between two lines given their slopes.
Inputs
Acute Angle
90.0000°
Perpendicular?
Yes
Step by step
Product of slopes
m₁ × m₂ = 2 × -0.5 = -1
Since 1 + m₁m₂ = 0, lines are perpendicular
= 90°
How it works
The acute angle between two lines with slopes m₁ and m₂ is found via tan(θ) = |m₁−m₂| / |1+m₁m₂|. If 1+m₁m₂ = 0, the lines are perpendicular (90°).
Formula
Angle Between Lines
tan(θ) = |(m₁ − m₂) / (1 + m₁m₂)|
- m₁
- Slope of first line
- m₂
- Slope of second line
Frequently Asked Questions
What if one line is vertical?
A vertical line has undefined slope. The angle between a vertical line and one with slope m is arctan(|1/m|).
Does this give the acute or obtuse angle?
Always the acute angle (≤ 90°). The obtuse angle is 180° minus the acute angle.