Angle Between Two Vectors Calculator
Enter two vectors to find the angle between them.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- cos θ = (A · B) ÷ (|A| × |B|)
- θ = arccos(cos θ), shown in degrees and radians
- The cosine is kept within −1 to 1 to avoid rounding errors
For the dot product and lengths on their own, use the dot product calculator.
Worked example
A = (1, 0) and B = (1, 1):
- cos θ = 1 ÷ (1 × 1.4142) = 0.7071
- θ = 45°, an acute angle
Why your number may differ
Floating-point rounding can leave tiny differences, so exactly parallel or perpendicular cases are matched within a very small tolerance.
Frequently asked questions
How do I find the angle between two vectors?
Divide their dot product by the product of their lengths to get the cosine, then take the inverse cosine: θ = arccos(A · B ÷ (|A| × |B|)).
When are two vectors perpendicular?
When their dot product is zero, so the angle is exactly 90°.
What range does the angle have?
From 0° (pointing the same way) to 180° (pointing opposite ways).