Angle between Vectors
Find the smaller angle between two nonzero vectors.
Your numbers
Angle
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
Use θ = acos[(A·B)/(norm(A)norm(B))]. A and B are nonzero vectors, the dot denotes their dot product, and norm means Euclidean magnitude. The angle is displayed in degrees.
Find the smaller angle between two nonzero vectors.
Worked example
- Vector A: x
- 1
- Vector A: y
- 0
- Vector A: z
- 0
- Vector B: x
- 0
- Vector B: y
- 1
- Vector B: z
- 0
- Angle
- 90 °
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 844920788b7b · Example checked: