Magnitude Calculator

Use our free vector magnitude calculator to compute |𝐯| with step-by-step breakdown, squared magnitude, compare magnitudes with triangle inequality verification, and derive the unit vector.

Math

Mode

𝐯 =

𝐯₂ =

Formula

Compute the magnitude (Euclidean norm) of any vector with a full step-by-step breakdown. Also compare magnitudes of two vectors with triangle inequality verification, and derive the unit vector.

|𝐯| = √(v₁² + v₂² + ... + vₙ²)

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 magnitude, compare, or derive unit vector.
3For compare: enter a second vector.
4Click Calculate.

Examples

|(3,4,5)|

1.|𝐯| = √(9+16+25) = √50 ≈ 7.071

Result: 7.0710678119

Compare (3,4) and (1,2)

1.|𝐯₁|=5, |𝐯₂|=√5≈2.236
2.|𝐯₁+𝐯₂|=√52≈7.211 ≤ 5+2.236 ✓

Result: 5

Frequently Asked Questions

The length or norm of a vector: |𝐯| = √(Σ vᵢ²) (Euclidean norm).

|𝐯₁+𝐯₂| ≤ |𝐯₁| + |𝐯₂| — the direct sum is never longer than the sum of the lengths.

|𝐯|² = Σ vᵢ² — often used in calculations to avoid square roots.

Yes — works for 2D, 3D, and higher-dimensional vectors.

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CalculateMe Team

Last updated: 2026-07-15

Magnitude Calculator

Formula

How It Works

Examples

|(3,4,5)|

Compare (3,4) and (1,2)

Frequently Asked Questions

What is vector magnitude?

What is the triangle inequality?

What is squared magnitude?

Can I compute magnitude for any dimension?

Related Calculators

Magnitude Calculator

Formula

How It Works

Examples

|(3,4,5)|

Compare (3,4) and (1,2)

Frequently Asked Questions

What is vector magnitude?

What is the triangle inequality?

What is squared magnitude?

Can I compute magnitude for any dimension?

Related Calculators