Vector Calculator — Magnitude, Angle, Add & Dot Product (2D)
Use this free vector calculator to work with two-dimensional vectors. Enter the components of A and B and choose an operation — add, subtract, dot product, magnitude, direction angle, or scalar multiple — and you’ll get the result, the angle between the vectors, and an arrow diagram.
How to use the vector calculator
- Enter the components of vector A (and B when needed).
- Choose an operation.
- Read the result, the magnitudes and angles, and see the vectors drawn from the origin.
Key formulas
Magnitude: |A| = √(aₓ² + aₔ²). Dot product: A · B = aₓbₓ + aₔbₔ. Angle between vectors: θ = cos⁻¹((A · B)/(|A| |B|)). Direction of A from the positive x-axis uses the arctangent of its components.
Frequently asked questions
How do you find the magnitude of a vector?
Use the Pythagorean theorem on the components: |A| = √(aₓ² + aᵧ²). For (3, 4) the magnitude is 5.
What is the dot product?
A·B = aₓbₓ + aᵧbᵧ. It’s a single number that, together with the magnitudes, gives the angle between the vectors.
How do you find the angle between two vectors?
θ = cos⁻¹((A·B)/(|A||B|)). The calculator computes it in degrees.
Read the full lesson: learn the method step by step.
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