Angle Between Vectors Calculator
Calculate the angle between two vectors in 2D or 3D space. Get the result in both degrees and radians with full step-by-step solution using the dot product formula.
Vector a
Vector b
How to Use the Angle Between Vectors Calculator
- Enter the numbers or values in the input fields.
- The result is calculated and displayed automatically.
- Review the step-by-step solution or detailed breakdown.
- Copy the result or adjust inputs for a new calculation.
Schnellreferenz
| Von | Nach |
|---|---|
| 2 + 3 | 5 |
| 12 × 12 | 144 |
| √144 | 12 |
| 2¹⁰ | 1,024 |
| π | 3.14159 |
| e | 2.71828 |
Anwendungsfälle
- •Checking homework or exam answers quickly and accurately.
- •Verifying manual calculations in professional or academic work.
- •Learning mathematical concepts with instant visual feedback.
- •Performing quick computations during meetings or presentations.
Formel
The angle between two vectors is found using the dot product: cos(θ) = (a·b) / (|a|·|b|), then θ = arccos(cos(θ)). The result is always between 0° and 180°.
Häufig gestellte Fragen
How is the angle between vectors calculated?
The angle θ between vectors a and b is computed as θ = arccos((a·b) / (|a|·|b|)), where a·b is the dot product and |a|, |b| are the magnitudes of the vectors.
What does it mean if the angle is 90°?
An angle of 90° (π/2 radians) means the vectors are perpendicular (orthogonal). Their dot product is zero.
Can the angle be greater than 180°?
No. The angle between two vectors using the dot product formula is always in the range [0°, 180°]. To distinguish direction, you would need additional context (e.g., a signed angle in 2D).