What is the net force?
Type each force acting on an object and the direction it pushes or pulls. The net force calculator adds them as vectors and shows the net force, its direction, its x and y parts, and, with a mass, the acceleration.
- Net force
- 50 N
The net force is 50 N: 30 N along x and 40 N along y.
- Direction of the net force
- 53.13°
- x component
- 30 N
- y component
- 40 N
Net force: 50 N. The net force is 50 N: 30 N along x and 40 N along y.
How to calculate
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).
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.
Method: Fx = Σ F cos θ, Fy = Σ F sin θ; net force = √(Fx² + Fy²); direction = atan2(Fy, Fx); acceleration = net force ÷ mass.
- 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
Each example is checked against the calculator on every build.
- Forces 30 0; 40 1.5707963267948966 gives Net force 50 N, Direction of the net force 53.13°, x component 30 N, y component 40 N.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
- Forces 10 0.5235987755982988; 40 4.71238898038469; 5 3.141592653589793; 2 1.5707963267948966, Mass (optional) 8.818 lb gives Net force 33.2024 N, Direction of the net force 276.33°, x component 3.66025 N, y component -33 N, 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°
- Forces 10 0; 10 3.141592653589793, Mass (optional) 4.409 lb gives Net force 0 N, x component 0 N, y component 0 N, 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)
- Forces 444.82216152604997 0; 444.82216152604997 1.5707963267948966 gives Net force 629.074 N, Direction of the net force 45°.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
How it works
Type each force Fᵢ with its direction θᵢ, measured counterclockwise from the +x axis (0° right, 90° up). Every force is converted to newtons (1 lbf = 4.4482216152605 N, 1 kN = 1,000 N) and every angle to radians.
- x component Fx = Σ Fᵢ cos θᵢ
- y component Fy = Σ Fᵢ sin θᵢ
- Net force = √(Fx² + Fy²)
- Direction = atan2(Fy, Fx), turned into the range 0° up to 360° (a negative angle has 360° added).
- Acceleration = net force ÷ mass, in m/s², when a mass is typed (1 lb = 0.45359237 kg).
When θ is within 10⁻⁹ degree of a multiple of 90°, cos θ and sin θ use their exact values (0, 1 or −1), so forces along the axes cancel exactly. When the net force is no more than 10⁻¹² of the sum of the force sizes, it counts as 0: the net force and the acceleration show 0 and the direction is empty.
Forces and components show to 6 significant figures, the direction to 2 decimal places. The maths runs in floating point and rounds for display only.
Assumptions: all forces act on the same object, in one plane.
Rules
- 1 to 20 forces. Each force is from 0 to 10¹² N; each direction from −360° to 360°. The mass is optional, from 10⁻⁹ kg to 10¹² kg. A value outside that shows a message on its field.
Worked examples by hand
30 N right and 40 N up (OpenStax 5.1). Fx = 30, Fy = 40. Net = √(900 + 1,600) = 50 N. Direction = atan(40 ÷ 30) = 53.13°.
Four forces on a 4.0 kg particle (OpenStax Example 5.7). 10 N at 30°, 40 N at 270°, 5 N at 180°, 2 N at 90°. Fx = 10 cos 30° − 5 = 3.6603 N. Fy = 10 sin 30° − 40 + 2 = 5 − 38 = −33 N. Net = √(3.6603² + 33²) = 33.2024 N, direction = 360° − 83.67° = 276.33°. Acceleration = 33.2024 ÷ 4 = 8.3006 m/s², or (0.915, −8.25) m/s². The book prints 0.92 i − 8.3 j and 8.4 m/s² at 276°, rounding the components first.
Balanced forces. 10 N at 0° and 10 N at 180°: Fx = 10 − 10 = 0, Fy = 0, so the net force is 0 and a 2 kg mass does not accelerate.
100 lbf right and 100 lbf up. Net = 100√2 = 141.42 lbf (629.07 N) at 45°.
Other questions people ask
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.