CalcRef

Parametric, Polar & Vectors · Vector Operations

Vector Magnitude

∣v⃗∣=v12+v22+v32|\vec{v}| = \sqrt{v_1^2 + v_2^2 + v_3^2}

The magnitude (length) of a vector v = ⟨v₁, v₂, v₃⟩.

Variables

SymbolNameUnit
v1x-component—
v2y-component—
v3z-component—

Worked examples

Find |⟨3, 4⟩|.
  1. √(9 + 16) = √25 = 5

Answer: 5

Find |⟨1, 2, 2⟩|.
  1. √(1 + 4 + 4) = √9 = 3

Answer: 3

Practice this and 135 more formulas in the CalcRef workspace — quizzes, reference tables, a 16-category unit converter, and an expression evaluator.