Vector Calculator - Dot Product, Cross Product, Angle & Projection
Vector Calculator
Add, subtract and multiply 2D and 3D vectors, and find the angle between them
Everything in One Place
Sum, difference, dot and cross product, lengths, unit vectors, projection and the angle between two vectors.
2D and 3D
Switch between plane and space vectors. In 2D the cross product is the single z-component.
Accurate Angles
The angle is found with atan2, which stays accurate for nearly parallel and nearly opposite vectors where arccos loses precision.
Full Privacy
Everything is calculated in your browser.
Dot and Cross Products
The dot product A · B multiplies matching components and adds them. It is a single number that is zero exactly when the vectors are perpendicular, and it gives the angle through cos θ = A · B ÷ (|A||B|). The cross product A × B is a vector perpendicular to both, whose length equals the area of the parallelogram they span.
The projection of A onto B is the part of A that points along B. The unit vector keeps a vector's direction but gives it length 1. A zero vector has no direction, so its unit vector, angle and projection are shown as a dash rather than an invented number.
Key Takeaways
- Relationship check: Tells you when the vectors are perpendicular or parallel.
- Clean numbers: Floating-point dust such as 1e-16 is shown as 0.
- Copyable: Copy a full text summary of every result.