---
title: "Resultant Force Calculator - Vector Sum"
description: "Calculate resultant force magnitude and direction from multiple force vectors using component addition and Pythagorean theorem."
image: "https://onlineminitools.com/tools/resultant-force-calculator/logo.svg"
---

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# Resultant Force Calculator

Calculate resultant force magnitude and direction from multiple force vectors using component addition and Pythagorean theorem.

      O M T

## What Is Resultant Force?

Force is a vector quantity with both magnitude and direction. When two or three forces act on a body at the same point, their combined effect is a single resultant force found by vector addition. This is the net force that determines acceleration through Newton's second law.

## Vector Addition of Forces

Resolve each force into horizontal and vertical components:

 $$F_x = \sum F_i \cos\theta_i, \quad F_y = \sum F_i \sin\theta_i$$

The resultant magnitude and direction are:

 $$R = \sqrt{F_x^2 + F_y^2}, \quad \theta_R = \arctan\left(\frac{F_y}{F_x}\right)$$

Angles are measured from the positive x axis, counterclockwise. Use \(\mathrm{atan2}(F_y, F_x)\) to get the correct quadrant.

## Worked Example

Two perpendicular 100 N forces at 0° and 90° give \(F_x = 100\,\mathrm{N}\), \(F_y = 100\,\mathrm{N}\), and \(R = 100\sqrt{2} \approx 141.4\,\mathrm{N}\) at 45°. Adding a third force changes both magnitude and direction of the net vector.

Related tools: [Vector Addition Calculator](https://onlineminitools.com/vector-addition-calculator), [Force Calculator](https://onlineminitools.com/force-calculator), and [Magnitude of Acceleration Calculator](https://onlineminitools.com/magnitude-of-acceleration-calculator).

## Frequently Asked Questions

   **How many forces can this calculator combine?**

You can add two or three force vectors. Each force needs a magnitude in newtons and an angle in degrees from the positive x axis.

   **Which angle convention is used?**

Angles are measured counterclockwise from the +x axis. 0° points right, 90° points up, 180° points left, and 270° points down.

   **What if forces act at different points?**

This tool finds the vector sum of forces. If forces act at different locations, you may also need to compute net torque for rotational effects.

   **Can the resultant be zero?**

Yes. If vector components cancel, the net force is zero and the object is in translational equilibrium (no acceleration from those forces).

   **How is resultant force related to acceleration?**

Newton's second law states \(\vec{F}_{net} = m\vec{a}\). The resultant force divided by mass gives the acceleration vector in the same direction.

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### Recent Visits

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