How this calculation works
Find the smaller angle between two lines without calculating slopes.
THE FORMULA
θ = atan2(|AD−BC|, |AC+BD|)A worked example
The lines x=0 and x+y=0 meet at a 45° angle.
Good to know
Each line must have at least one nonzero coefficient.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the smaller angle between two lines without calculating slopes.
The primary result is labeled “Smaller angle (°)”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Each line must have at least one nonzero coefficient.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
The lines x=0 and x+y=0 meet at a 45° angle.
Which rule does this calculator apply?
θ = atan2(|AD−BC|, |AC+BD|)