Resultant Vector Calculator – Find Magnitude, Direction & Force in 2D/3D

Calculate the magnitude and direction of resultant vectors with this free online tool. Supports 2D and 3D vector addition, angle-based inputs, and force calculations. Whether you're using the parallelogram method, polygon technique, or resolving three vectors, this calculator simplifies physics and engineering problems. Ideal for students, teachers, and professionals—no downloads, mobile-friendly, and easy to use.

Resultant Vector Calculator

Theory

The resultant vector is the vector sum of two or more vectors. It can be found by adding the corresponding components of the vectors.

The magnitude of the resultant vector can be calculated using the formula:

$$|R| = \sqrt{R_x^2 + R_y^2 + R_z^2}$$

The direction of the resultant vector can be found using the direction cosines:

$$\cos(\alpha) = \frac{R_x}{|R|}, \cos(\beta) = \frac{R_y}{|R|}, \cos(\gamma) = \frac{R_z}{|R|}$$

Here, $$\alpha$$, $$\beta$$, and $$\gamma$$ are the angles that the resultant vector makes with the x, y, and z axes, respectively.