Unit Vector Calculator

Use our free unit vector calculator to normalize any vector to a unit vector, compute direction cosines and angles, verify unit vector status, and see the full step-by-step normalization process.

Math

Mode

𝐯 =

Formula

Normalize any non-zero vector to a unit vector (length 1). Shows the full step-by-step normalization, direction cosines, direction angles in degrees, and can verify whether a vector is already a unit vector.

𝐯̂ = 𝐯/|𝐯| = (v₁/|𝐯|, v₂/|𝐯|, ..., vₙ/|𝐯|)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter 𝐯 as comma-separated numbers.
2Select mode: compute unit vector, verify, or direction cosines.
3Click Calculate.

Examples

Unit vector of (3,4,5)

1.|𝐯| = √50 ≈ 7.071
2.𝐯̂ = (3/7.071, 4/7.071, 5/7.071) ≈ (0.424, 0.566, 0.707)

Result: 1

Direction of (1,1,0)

1.𝐯̂ = (0.707, 0.707, 0)
2.Direction angles: 45°, 45°, 90°

Result: 1

Frequently Asked Questions

A vector with magnitude 1, pointing in the same direction as the original.

Divide each component by the vector's magnitude: 𝐯̂ = 𝐯/|𝐯|.

The components of the unit vector — they represent cosines of the angles with each axis.

No — the zero vector has no direction and cannot be normalized.

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CalculateMe Team

Last updated: 2026-07-15

Unit Vector Calculator

Formula

How It Works

Examples

Unit vector of (3,4,5)

Direction of (1,1,0)

Frequently Asked Questions

What is a unit vector?

How is a unit vector computed?

What are direction cosines?

Can I normalize the zero vector?

Related Calculators

Unit Vector Calculator

Formula

How It Works

Examples

Unit vector of (3,4,5)

Direction of (1,1,0)

Frequently Asked Questions

What is a unit vector?

How is a unit vector computed?

What are direction cosines?

Can I normalize the zero vector?

Related Calculators