Math

Instant, private, and free

Angle Between Two Vectors Calculator.

Calculate the angle between two 3D vectors (use zero z components for 2D vectors).

On-device calculationNo signup
01

Set your values

Results update as you type.

Angle: 90 °

Angle

0.000000°
Dot product: 0

Dot product

0.000000

Results update automatically as you type.

Use Cases

Check if vectors are orthogonal

Determine if two vectors are perpendicular by checking if the angle is 90 degrees. This is useful in physics and geometry.

Example: Vector A = (1,0,0), Vector B = (0,1,0) → angle = 90°

Find the angle between directions

In 3D graphics or robotics, find the angle between two direction vectors to understand orientation differences.

Example: Vector A = (1,1,0), Vector B = (0,1,1) → angle ≈ 60°

Frequently Asked Questions

How do I use this calculator for 2D vectors?
For 2D vectors, simply enter the x and y components for both vectors and set the z components to 0. The calculator will compute the angle in the xy-plane.
What formula does the calculator use?
It uses the dot product formula: cos(θ) = (A·B) / (|A||B|), where A·B is the sum of products of corresponding components, and |A| and |B| are the magnitudes. The angle is then arccos of that value.
Can the angle be negative?
No, the angle between two vectors is always between 0 and 180 degrees (or 0 and π radians). The calculator returns the smaller angle between them.

Tips & Common Mistakes

Tips

  • Ensure both vectors are non-zero; otherwise, the angle is undefined.
  • For 2D vectors, set z components to 0 to get accurate results.
  • Double-check your component signs; negative components affect the dot product and angle.
  • The calculator returns the angle in degrees by default; you can convert to radians by multiplying by π/180.

Common Mistakes to Avoid

  • Forgetting to set z components to 0 for 2D vectors, leading to incorrect angles.
  • Entering components in the wrong order (e.g., swapping x and y) which changes the vector direction.
  • Assuming the angle is always acute; the calculator gives the smaller angle, which can be obtuse (up to 180°).

Last updated: August 13, 2026