What this calculator does
The resultant force is the single force that has the same effect as two or more individual forces acting together. Working out how to find resultant force means combining each force's horizontal and vertical pull (or push) into one net magnitude and one net direction.
The resultant force formula splits each force into components using its angle, adds the components for each axis separately, then recombines them: Rx = F1cosθ1 + F2cosθ2, Ry = F1sinθ1 + F2sinθ2, and R = √(Rx² + Ry²), with direction θ = atan2(Ry, Rx). This calculator takes each force as a magnitude and an angle, which is how most textbook and real-world force problems are stated, rather than as raw x and y components.
The formula
Each force is resolved into horizontal and vertical components using its magnitude and angle from the positive x-axis. The components are summed separately for each axis, then the resultant magnitude comes from Pythagoras on the summed components, and the resultant angle from the arctangent of the summed components.
| Term | Meaning |
|---|---|
| Resultant force | The single equivalent force that replaces two or more forces acting on the same point. |
| Magnitude | The size (strength) of a force, in newtons. |
| Direction (θ) | The angle a force acts along, measured from a chosen reference direction, usually the positive x-axis. |
| Component | The horizontal (x) or vertical (y) part of a force found using cosine and sine of its angle. |
The inputs explained
| Field | What to enter |
|---|---|
| Force 1 magnitude (N) | The magnitude of the first force. |
| Force 1 direction (°) | The direction of the first force, in degrees from the positive x-axis, measured counterclockwise. |
| Force 2 magnitude (N) | The magnitude of the second force. |
| Force 2 direction (°) | The direction of the second force, in the same angle convention as the first. |
When to use it
Two ropes pulling an object at different angles
If two ropes pull the same object at known tensions and angles, the resultant force formula gives the single net pull the object actually feels, which determines its direction of movement.
Checking whether forces cancel out
Entering two forces of equal magnitude at opposite angles shows the resultant collapsing toward zero, confirming the object is in equilibrium along that pair of forces.
Combining wind and thrust on a moving object
A thrust force and a crosswind force acting at an angle to each other combine into a resultant that shows the actual direction of travel, not just the intended one.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the resultant force changes as the angle between two forces widens
A fixed 50 N force along the x-axis, combined with a 30 N force at increasing angles to it.
| Angle of force 2 | Resultant magnitude | Resultant direction |
|---|---|---|
| 0° | 80.00 N | 0.0° |
| 30° | 77.45 N | 11.2° |
| 60° | 70.00 N | 21.8° |
| 90° | 58.31 N | 31.0° |
| 120° | 43.59 N | 36.6° |
| 150° | 28.32 N | 32.0° |
How the resultant force changes as the second force grows
A fixed 50 N force along the x-axis, combined with a perpendicular force of increasing size.
| Magnitude of force 2 | Resultant magnitude | Resultant direction |
|---|---|---|
| 10 N | 50.99 N | 11.3° |
| 20 N | 53.85 N | 21.8° |
| 30 N | 58.31 N | 31.0° |
| 40 N | 64.03 N | 38.7° |
| 50 N | 70.71 N | 45.0° |
| 60 N | 78.10 N | 50.2° |
Questions
How do I find resultant force from more than two forces?
Resolve every force into x and y components using its own angle, add all the x components together and all the y components together, then apply Pythagoras and arctangent to that combined pair, exactly as this calculator does for two forces.
Is resultant force the same as net force?
Yes, they describe the same thing: the single equivalent force representing the combined effect of every individual force acting on an object.
What does it mean if the resultant force is zero?
A zero resultant means the forces are perfectly balanced and the object is in equilibrium along those forces, meaning it will not accelerate as a result of them, though it may still be moving at constant velocity.
Why use magnitude and angle instead of x and y components directly?
Many real problems state forces as a strength and a direction (a rope tension and its angle, a wind speed and its bearing) rather than as ready-made components, so resolving from magnitude and angle matches how the numbers are usually given.
For forces already given as raw x and y (or x, y, z) components rather than magnitude and angle, see the vector addition calculator. To work with a single force's effect over a stopping distance, see the impact force calculator.