Free online vector calculator for 2D/3D vectors. Calculate dot product, cross product, magnitude, angle, unit vector, and projection with step-by-step solutions. No registration, your data never leaves your device.
2D/3D Vectors | Dot · Cross · Magnitude · Angle · Unit Vector · Projection | Real-time · Step-by-Step
✓ Zero Deps · Works OfflineSelect 2D or 3D vector dimension, enter component values for each vector, and choose an operation to get instant results. Supports dot product, cross product (3D only), magnitude, angle, unit vector, and projection. All calculations run in your browser — no data is ever uploaded.
The dot product (scalar product) multiplies corresponding components of two vectors and sums them, producing a scalar. Formula: A·B = A₁B₁ + A₂B₂ (+ A₃B₃). A dot product of 0 means the vectors are perpendicular.
The cross product only applies to 3D vectors and produces a new vector perpendicular to both input vectors. Its magnitude equals the area of the parallelogram formed by the two vectors.
Use the formula cos(θ) = (A·B) / (|A| × |B|), then take the arccosine. This tool outputs both radians and degrees.
The projection of vector A onto vector B is the component of A along the direction of B: proj_B(A) = (A·B / |B|²) × B.
No. All calculations happen locally in your browser. Your data never leaves your device. This tool works offline.