Vector Addition

Calculate the resulting vector when adding two coplanar vectors using trigonometric methods. Supports calculation of resultant magnitude and angles between vectors and resultant using the cosine and sine rules.

Vector Addition Calculator

Add two coplanar vectors using trigonometric calculation with the cosine and sine rules.

Vector Quantities: Can be used for forces, velocities, or any other vector quantities.

Formulas:

  • Resultant magnitude: FR = √(F₁² + F₂² - 2·F₁·F₂·cos(180° - θ))
  • Angle to vector 1: α = sin⁻¹(F₁·sin(180° - θ) / FR)
  • Angle to vector 2: β = sin⁻¹(F₂·sin(180° - θ) / FR)
Calculator

Inputs

Results

Resultant Magnitude-- units
Angle to Vector 1-- degrees
Angle to Vector 2-- degrees