# Resultant Force Calculator (Net Force)

URL: https://speedycalculator.com/calculators/physics/resultant-force/
Last updated: 2026-10-30

> The net force calculator adds up to ten forces given by magnitude and direction, giving the resultant force, its direction and its x and y components.

## Inputs

- Number of forces
- Force F₁ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₁ (°, rad, arcmin, arcsec, mrad)
- Force F₂ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₂ (°, rad, arcmin, arcsec, mrad)
- Force F₃ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₃ (°, rad, arcmin, arcsec, mrad)
- Force F₄ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₄ (°, rad, arcmin, arcsec, mrad)
- Force F₅ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₅ (°, rad, arcmin, arcsec, mrad)
- Force F₆ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₆ (°, rad, arcmin, arcsec, mrad)
- Force F₇ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₇ (°, rad, arcmin, arcsec, mrad)
- Force F₈ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₈ (°, rad, arcmin, arcsec, mrad)
- Force F₉ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₉ (°, rad, arcmin, arcsec, mrad)
- Force F₁₀ (N, kN, MN, mN, lbf, kgf, dyn)
- Angle θ₁₀ (°, rad, arcmin, arcsec, mrad)

## Results

- x component Fₓ
- y component F_y
- Net force
- Direction (from +x, counter-clockwise)

## Formula

```
Fₓ = Σ Fᵢ cos θᵢ,  F_y = Σ Fᵢ sin θᵢ,  |F| = √(Fₓ² + F_y²)
```

## Explanation

The net (resultant) force is the vector sum of all forces acting on an object. It determines the acceleration through Newton's second law; if it is zero, the object is in equilibrium.

### How to use the Resultant Force Calculator

- **Number of forces**
- **Force F₁**
- **Angle θ₁**
- **Force F₂**
- **Angle θ₂**
- **Force F₃**
- **Angle θ₃**
- **Force F₄**
- **Angle θ₄**
- **Force F₅**
- **Angle θ₅**
- **Force F₆**
- **Angle θ₆**
- **Force F₇**
- **Angle θ₇**
- **Force F₈**
- **Angle θ₈**
- **Force F₉**
- **Angle θ₉**
- **Force F₁₀**
- **Angle θ₁₀**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose how many forces act and give each a magnitude and an angle measured counter-clockwise from the positive x-axis.

### Inputs explained

FieldWhat to enterNumber of forcesChoose one: 1, 2, 3, 4 …Force F₁Units: N, kN, MN, mN, lbf, kgf …Angle θ₁Units: °, rad, arcmin, arcsec, mradForce F₂Units: N, kN, MN, mN, lbf, kgf …Angle θ₂Units: °, rad, arcmin, arcsec, mradForce F₃Units: N, kN, MN, mN, lbf, kgf …Angle θ₃Units: °, rad, arcmin, arcsec, mradForce F₄Units: N, kN, MN, mN, lbf, kgf …Angle θ₄Units: °, rad, arcmin, arcsec, mradForce F₅Units: N, kN, MN, mN, lbf, kgf …Angle θ₅Units: °, rad, arcmin, arcsec, mradForce F₆Units: N, kN, MN, mN, lbf, kgf …Angle θ₆Units: °, rad, arcmin, arcsec, mradForce F₇Units: N, kN, MN, mN, lbf, kgf …Angle θ₇Units: °, rad, arcmin, arcsec, mradForce F₈Units: N, kN, MN, mN, lbf, kgf …Angle θ₈Units: °, rad, arcmin, arcsec, mradForce F₉Units: N, kN, MN, mN, lbf, kgf …Angle θ₉Units: °, rad, arcmin, arcsec, mradForce F₁₀Units: N, kN, MN, mN, lbf, kgf …Angle θ₁₀Units: °, rad, arcmin, arcsec, mrad

### What each result means

- **Net force** = sqrt([x component Fₓ]^2 + [y component F_y]^2)
- **Direction (from +x, counter-clockwise)** = mod(deg(atan2([y component F_y], [x component Fₓ])), 360)

### Example values

How the main result changes when **Force F₁** changes and everything else stays at the example values above:

Force F₁ (N)Net force (N)515.81147.516.77051018.027812.519.52561521.21322025

## Worked example

Inputs — Number of forces: 2; Force F₁: 10 N; Angle θ₁: 0 °; Force F₂: 15 N; Angle θ₂: 90 °.

Results — x component Fₓ = 10 N; y component F_y = 15 N; **Net force = 18.0278 N**; Direction (from +x, counter-clockwise) = 56.31 °.

## Key terms

- **Resultant**: The single force equivalent to several forces.

## FAQ

**What does a net force of zero mean?**
The object is in equilibrium: at rest or moving at constant velocity.

**How do I add two perpendicular forces?**
√(F₁² + F₂²).

**Which way is 90°?**
Straight up (positive y), counter-clockwise from the positive x-axis.

**Can forces be added as plain numbers?**
Only if they act along the same line.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)