EngineeringFormulaEngineering Mechanics
Net Force Calculator
Calculate the resultant net force from opposing forces in one axis or from right/left/up/down force components in two dimensions.
Net force is the vector sum of all external forces acting on an object or system. This calculator supports two common setups: a one-dimensional collinear case, where forces act along one chosen axis in opposite directions, and a two-dimensional orthogonal case, where forces are resolved into right, left, up, and down components. If your applied forces are angled, resolve them into components first before using the 2D mode.
F+ · Total force acting along the positive direction of the chosen one-dimensional axis.
F− · Total force acting opposite the positive direction of the chosen one-dimensional axis.
Enter magnitudes by direction, and use 0 when a direction has no force. If a force acts at an angle, resolve it into horizontal and vertical components before using Orthogonal 2D mode.
Solution
Enter the opposing one-axis forces to calculate the resultant net force.
Fnet = Fpos - Fneg
Formula Sheet
- FnetNet Force
- FxNet Horizontal Component
- FyNet Vertical Component
- F+Positive-Direction Force
- F−Negative-Direction Force
- FrRightward Force
- FlLeftward Force
- FuUpward Force
- FdDownward Force
- θResultant Direction Angle
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| Fnet | Net Force | Resultant external force after all included forces are added as vectors. | N, kN, lbf |
| Fx | Net Horizontal Component | Sum of the horizontal force components after rightward and leftward forces are combined. | N, kN, lbf |
| Fy | Net Vertical Component | Sum of the vertical force components after upward and downward forces are combined. | N, kN, lbf |
| F+ | Positive-Direction Force | Total force acting along the positive direction of the chosen one-dimensional axis. | N, kN, lbf |
| F− | Negative-Direction Force | Total force acting opposite the positive direction of the chosen one-dimensional axis. | N, kN, lbf |
| Fr | Rightward Force | Total force component acting toward the positive x-direction. | N, kN, lbf |
| Fl | Leftward Force | Total force component acting toward the negative x-direction. | N, kN, lbf |
| Fu | Upward Force | Total force component acting toward the positive y-direction. | N, kN, lbf |
| Fd | Downward Force | Total force component acting toward the negative y-direction. | N, kN, lbf |
| θ | Resultant Direction Angle | Direction of the 2D resultant, measured counterclockwise from the positive x-axis. |
How to Use This Calculator
- 01Choose the mode first: Collinear for a one-axis problem, or Orthogonal 2D for right/left/up/down component summation.
- 02Enter force magnitudes by direction. Do not type negative values here - direction is already represented by the field labels. If one direction has no force acting in it, enter 0.
- 03Select Calculate to see the net-force magnitude in SI units, along with the direction and the intermediate component sums when relevant.
- 04If your original forces are not already horizontal or vertical, resolve them into components before using Orthogonal 2D mode.
How the Formula Works
In any Newtonian mechanics problem, the net external force is the vector sum of all external forces. Along one chosen axis, that means subtracting the total force in one direction from the total force in the opposite direction. If the two totals are equal, the net force is zero and the forces are balanced along that axis.
In two dimensions, force components are summed separately along the x- and y-directions. Once the horizontal and vertical resultants are known, the overall net-force magnitude is found from the Pythagorean relation Fnet = √(Fx² + Fy²). The direction must respect the correct quadrant, so this calculator determines it from both components together rather than from a simple single-quadrant inverse-tangent shortcut.
Worked Example 01
Collinear net force along one axis
Known
- Positive-Direction Force (F+): 80 N
- Negative-Direction Force (F−): 50 N
Formula
Fnet = Fpos - Fneg
Substitution
Fnet = 80 - 50
Result
Fnet = 30 N toward the positive axis
The opposing force only partially cancels the positive-direction force, leaving 30 N unbalanced.
Worked Example 02
Orthogonal resultant from rightward and upward forces
Known
- Rightward Force: 30 N
- Leftward Force: 0 N
- Upward Force: 40 N
- Downward Force: 0 N
Formula
Fnet = √(Fx² + Fy²)
Substitution
Fx = 30 - 0, Fy = 40 - 0, Fnet = √(30² + 40²)
Result
Fnet = 50 N at 53.1° from +x
The 30-40-50 triangle gives a 50 N resultant, directed 53.1° counterclockwise from the positive x-axis.
Worked Example 03
Balanced forces in two dimensions
Known
- Rightward Force: 15 N
- Leftward Force: 15 N
- Upward Force: 20 N
- Downward Force: 20 N
Formula
Fnet = √(Fx² + Fy²)
Substitution
Fx = 15 - 15, Fy = 20 - 20
Result
Fnet = 0 N
When both horizontal and vertical components cancel completely, the net force is zero and the object is in translational equilibrium.
Applications
- 01Free-body diagram checks in introductory engineering mechanics and dynamics
- 02Determining whether an object is in translational equilibrium
- 03Summing horizontal and vertical force components before applying Newton's second law
Assumptions
- 01Only external forces that matter to the chosen free body are included in the sum.
- 02Collinear mode assumes all included forces act along one chosen axis.
- 03Orthogonal 2D mode assumes forces are already resolved into horizontal and vertical components.
Where This Model Stops
- 01Does not resolve arbitrary angled forces directly - resolve them into components first before using Orthogonal 2D mode.
- 02Does not model full 3D force systems, moments, or rotational equilibrium.
References
- [1]5.1 Forces
OpenStax University Physics Volume 1
Defines net external force as the vector sum of all external forces and shows component-based summation.
- [2]5.2 Newton's First Law
OpenStax University Physics Volume 1
Explains that zero net force corresponds to constant velocity or rest, i.e. translational equilibrium.
Frequently Asked Questions
How is this different from the Force Calculator?
This calculator sums individual forces to find the resultant net force. The separate Force Calculator uses Newton's second law F = ma to relate net force, mass, and acceleration once that resultant force is already known.
Can I enter angled forces directly?
Not in this version. If a force is applied at an angle, first resolve it into horizontal and vertical components, then enter those component magnitudes into Orthogonal 2D mode.
Why are negative numbers not allowed in the inputs?
Because the direction is already represented by separate fields such as right vs left or positive vs negative axis. Enter magnitudes only, and let the calculator handle the vector subtraction.
Should I leave a direction blank if there is no force there?
No. Enter 0 for any direction that has no force acting in it. That keeps the setup explicit and avoids ambiguity about whether a value was intentionally zero or simply omitted.