Calculator Inputs
Use angles measured counterclockwise from the positive x-axis. Positive moments are counterclockwise.
Formula Used
Resolve each applied force into components:
Fx = F cos(θ), Fy = F sin(θ)
Sum all components:
ΣFx = Σ(Fx), ΣFy = Σ(Fy)
Find the resultant magnitude and direction:
R = √[(ΣFx)² + (ΣFy)²], θR = atan2(ΣFy, ΣFx)
Total moment about the origin:
M = Σ(x·Fy − y·Fx) + Mexternal
Line of action of the resultant:
(ΣFy)x − (ΣFx)y = M
Useful location results:
Perpendicular distance from origin: d = |M| / R
x-axis intercept: x = M / ΣFy when y = 0
y-axis intercept: y = −M / ΣFx when x = 0
These equations assume a rigid body in a two-dimensional coplanar force system.
How to Use This Calculator
- Choose the force unit and length unit.
- Enter any external couple moment if one exists.
- Fill each active force row with magnitude, angle, x position, and y position.
- Measure angles counterclockwise from the positive x-axis.
- Press the calculate button to generate the resultant, moment, intercepts, and graph.
- Use CSV or PDF export to save the results for homework, reports, or design checks.
Example Data Table
| Force | Magnitude (N) | Angle (deg) | x (m) | y (m) |
|---|---|---|---|---|
| F1 | 120 | 90 | 1 | 0 |
| F2 | 80 | 90 | 3 | 0 |
| F3 | 50 | 180 | 0 | 2 |
| Example Resultant | 206.155 N at 104.036° |
|---|---|
| Example Total Moment | 460.000 N·m |
| Example x-axis Intercept | 2.300 m |
| Example Distance to Origin | 2.232 m |
FAQs
1. What does this calculator return?
It returns the net horizontal and vertical components, resultant magnitude, direction angle, total moment about the origin, line-of-action intercepts, closest point coordinates, and a visual graph of the force system.
2. How is the resultant location determined?
The location comes from moment balance. The calculator first finds total moment about the origin, then places the resultant so its moment matches that total exactly.
3. What if the resultant force becomes zero?
If net force is zero and moment is also zero, the system is in equilibrium. If net force is zero but moment remains, the system becomes a pure couple.
4. Can I enter negative angles?
Yes. Negative angles are accepted. They are interpreted using the usual trigonometric convention, so clockwise directions from the positive x-axis work correctly.
5. What do the x-axis and y-axis intercepts mean?
They show where the resultant line of action crosses the reference axes. These values help when locating equivalent loads on beams, plates, or rigid bodies.
6. When should I use the external couple moment field?
Use it when an added free moment acts on the body, such as a turning effect from a wrench, motor, or applied couple not tied to one force location.
7. Why is there a closest point to the origin?
A force line has infinitely many points on it. The closest point gives one unique location and also equals the shortest distance used in the moment relation.
8. Are exported values suitable for reports?
Yes. The CSV export is useful for spreadsheets and checking calculations. The PDF export captures the result summary, graph, and breakdown table for documentation.