Angle Between Lines Calculator
Calculate the acute angle between two lines given their slopes.
About Angle Between Lines Calculator
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
Worked example
With the default values below, Angle Between Lines Calculator returns Acute Angle of 90.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Slope of Line 1 (m₁)
- 2
- Slope of Line 2 (m₂)
- -0.5
Results
- Acute Angle
- 90.0000 °
- Perpendicular?
- Yes
Step by step
- 1Product of slopes
- 2Since 1 + m₁m₂ = 0, lines are perpendicular= 90°
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.