Vector Calculator

Use our free vector calculator to explore vector properties and perform operations: magnitude, unit vector, addition, subtraction, dot product, cross product (3D), scalar multiplication, and angle between vectors.

Math

Mode

𝐚 =

𝐛 =

Scalar n

Formula

A comprehensive vector calculator supporting any dimension for most operations. Compute vector properties, perform arithmetic, and analyze relationships between vectors.

|𝐚| = √(Σ aᵢ²), 𝐚·𝐛 = Σ aᵢbᵢ, 𝐚×𝐛 = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter vectors as comma or semicolon-separated numbers (e.g., 1,2,3).
2Select the desired operation mode.
3For scalar multiplication, enter factor n.
4For cross product, vectors must be 3D.
5Click Calculate.

Examples

Info for 𝐚=(1,2,3)

1.|𝐚| = √(1+4+9) = √14 ≈ 3.742

Result: 3.7416573868

Dot product (1,2,3)·(4,5,6)

1.1·4+2·5+3·6 = 4+10+18 = 32

Result: 32

Frequently Asked Questions

Any dimension for most operations. Cross product requires 3D vectors.

Comma or semicolon separated: 1,2,3 or 1;2;3.

A vector perpendicular to both inputs, only defined in 3D.

A scalar equal to |𝐚||𝐛|cos(θ), indicating how parallel two vectors are.

A vector of length 1 in the same direction: 𝐚̂ = 𝐚/|𝐚|.

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Vector Addition Calculator Vector Subtraction Calculator Unit Vector Calculator Magnitude Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-15

Frequently Asked Questions

Any dimension for most operations. Cross product requires 3D vectors.

Comma or semicolon separated: 1,2,3 or 1;2;3.

A vector perpendicular to both inputs, only defined in 3D.

A scalar equal to |𝐚||𝐛|cos(θ), indicating how parallel two vectors are.

A vector of length 1 in the same direction: 𝐚̂ = 𝐚/|𝐚|.

Vector Calculator

Formula

How It Works

Examples

Info for 𝐚=(1,2,3)

Dot product (1,2,3)·(4,5,6)

Frequently Asked Questions

What dimensions are supported?

How do I enter vectors?

What is the cross product?

What is the dot product?

What is a unit vector?

Related Calculators

Vector Calculator

Formula

How It Works

Examples

Info for 𝐚=(1,2,3)

Dot product (1,2,3)·(4,5,6)

Frequently Asked Questions

What dimensions are supported?

How do I enter vectors?

What is the cross product?

What is the dot product?

What is a unit vector?

Related Calculators