How this calculation works
Find the acute angle between two planes from normal vectors.
THE FORMULA
θ=atan2(‖n₁×n₂‖,|n₁·n₂|)A worked example
Normals (1,0,0) and (1,1,1) give an angle of about 54.74°.
Good to know
Reversing either normal leaves the acute angle unchanged.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Find the acute angle between two planes from normal vectors.
The primary result is labeled “Acute dihedral angle (°)”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Reversing either normal leaves the acute angle unchanged.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
Normals (1,0,0) and (1,1,1) give an angle of about 54.74°.
Which rule does this calculator apply?
θ=atan2(‖n₁×n₂‖,|n₁·n₂|)