Vector Calculator

Calculate dot products, cross products, vector operations and more with our free online vector calculator.

Vector a

Vector b

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Understanding Vector Operations

Dot Product

The dot product of two vectors results in a scalar value. It's calculated as: a·b = ax×bx + ay×by + az×bz. This operation is useful in physics for work and force calculations.

Vector Addition

Adding vectors means combining their components: a+b = (ax+bx, ay+by, az+bz). This is commonly used in physics for force combinations and displacement calculations.

Magnitude

The magnitude of a vector is its length, calculated as: ||a|| = √(ax² + ay² + az²). This is essential for normalizing vectors and calculating distances.