# What is the net force?

Adds up to 20 forces, each with a size and a direction, into the net (resultant) force: its size, direction and x and y components, and the acceleration it gives a mass (F = ma).

- Page: https://www.acalculator.org/physics/net-force-calculator
- JSON spec: https://www.acalculator.org/physics/net-force-calculator.json
- Version: 721106235f2c

## Default answer

Example with the default inputs (Forces [Force 6.74426829299132 lbf, Direction 0 °; Force 8.99235772398842 lbf, Direction 90 °]): The net force is 50 N: 30 N along x and 40 N along y.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| forces | Forces | Each force acting on the object, one per row: its size and its direction. |
| m | Mass (optional) | The mass of the object, for the acceleration a = F ÷ m; leave empty to skip it. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| net | Net force | The size of the sum of all the forces. |
| direction | Direction of the net force | Counterclockwise from the +x axis, from 0° up to 360°; empty when the forces cancel. |
| fx | x component | The sum of F cos θ over the forces. |
| fy | y component | The sum of F sin θ over the forces. |
| acceleration | Acceleration | The net force ÷ the mass, in metres per second squared. |

## Method

Fx = Σ F cos θ, Fy = Σ F sin θ; net force = √(Fx² + Fy²); direction = atan2(Fy, Fx); acceleration = net force ÷ mass.

## Assumptions

- All forces act on one object, in one plane; directions are measured counterclockwise from the +x axis.
- Units convert to newtons: 1 lbf = 4.4482216152605 N, 1 kN = 1,000 N.

## Worked examples

1. forces = {"f":30,"a":0} or {"f":40,"a":1.5707963267948966} gives net = 50, direction = 0.927295, fx = 30, fy = 40. Source: OpenStax, University Physics Volume 1, §5.1 Forces: 30.0 N to the right and 40.0 N up give a net force of 50.0 N at 53.1°, https://openstax.org/books/university-physics-volume-1/pages/5-1-forces.
2. forces = {"f":10,"a":0.5235987755982988} or {"f":40,"a":4.71238898038469}, m = 4 gives net = 33.202371, direction = 4.822854, fx = 3.660254, fy = -33, acceleration = 8.300593. Source: OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law, Example 5.7 Several Forces on a Particle, https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law: a = (0.92 i − 8.3 j) m/s² at 276°.
3. forces = {"f":10,"a":0} or {"f":10,"a":3.141592653589793}, m = 2 gives net = 0, fx = 0, fy = 0, acceleration = 0. Source: OpenStax, University Physics Volume 1, §5.1 Forces: 30.0 N to the right and 40.0 N up give a net force of 50.0 N at 53.1°, https://openstax.org/books/university-physics-volume-1/pages/5-1-forces (balanced forces give no net force).
4. forces = {"f":444.82216152604997,"a":0} or {"f":444.82216152604997,"a":1.5707963267948966} gives net = 629.073534, direction = 0.785398. Source: OpenStax, University Physics Volume 1, §5.1 Forces: 30.0 N to the right and 40.0 N up give a net force of 50.0 N at 53.1°, https://openstax.org/books/university-physics-volume-1/pages/5-1-forces.

## FAQ

### How do I calculate the net force?

Split each force into x and y parts (F cos θ and F sin θ), add the x parts and the y parts, then combine: net force = √(Fx² + Fy²). 30 N to the right and 40 N up give √(30² + 40²) = 50 N.

### How do I find the direction of the net force?

Use the angle whose tangent is Fy ÷ Fx, in the right quadrant (atan2). For 30 N right and 40 N up it is 53.13° above the +x axis.

### What if the forces point in the same or opposite directions?

Forces in the same direction add; opposite forces subtract. 10 N right and 10 N left cancel, so the net force is 0 and the object does not speed up.

### How do I get the acceleration from the net force?

Divide by the mass (Newton’s second law, a = F ÷ m). A net force of 33.2 N on a 4.0 kg object gives 8.30 m/s².

### How are directions measured?

Counterclockwise from the +x axis: 0° points right, 90° up, 180° left and 270° (or −90°) down. You can type degrees or radians.

### Can I mix newtons and pounds-force?

Yes. Each force can be in N, kN or lbf; the calculator converts them all to newtons (1 lbf = 4.448 N) before it adds them.

## Sources

- OpenStax, University Physics Volume 1, section 5.1 Forces: the net external force is the vector sum of the forces; 30.0 N to the right and 40.0 N up give 50.0 N at 53.1°. CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/university-physics-volume-1/pages/5-1-forces
- OpenStax, University Physics Volume 1, section 5.3 Newton’s Second Law: F_net = ma; Example 5.7 Several Forces on a Particle. CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law