| Label | Fx (N) | Fy (N) | x (m) | y (m) | Mi (N·m) |
|---|
Use this sample to validate your setup.
| Label | Magnitude (N) | Angle (deg) | x (m) | y (m) |
|---|---|---|---|---|
| F1 | 100 | 0 | 2 | 0 |
| F2 | 80 | 90 | 0 | 1.5 |
| F3 | 60 | 210 | 1 | 1 |
- Fxᵢ = Fᵢ cos(θᵢ), Fyᵢ = Fᵢ sin(θᵢ) (angles from +x, CCW).
- ΣFx = Σ Fxᵢ, ΣFy = Σ Fyᵢ.
- R = √(ΣFx² + ΣFy²).
- θ = atan2(ΣFy, ΣFx) (reported as 0–360° or −180–180°).
- Moment about reference (x₀, y₀): M = Σ((xᵢ−x₀)Fyᵢ − (yᵢ−y₀)Fxᵢ).
- If R ≠ 0, signed offset: d = M / R.
- Equilibrant: same magnitude as R, direction θ + 180°.
- Set the reference point where you want moments reported.
- Choose an input mode: magnitude-angle or force components.
- Add each force with its point of application (x, y).
- Click Calculate to view results above the form.
- Use the export buttons to download CSV or PDF outputs.
Vector Resolution Basics
A coplanar force set is reduced by resolving each load into x and y components. For magnitude-angle input, Fx equals F·cosθ and Fy equals F·sinθ. A 100 N force at 30° produces Fx 86.6 N and Fy 50.0 N. Component entry skips trigonometry and directly contributes to the sums.
Resultant Magnitude And Angle
The calculator totals ΣFx and ΣFy, then computes resultant magnitude R = √(ΣFx² + ΣFy²). Direction uses atan2(ΣFy, ΣFx) to preserve quadrant. With ΣFx = 48.038 N and ΣFy = 50.000 N, R becomes 69.338 N and θ is 46.146°. Angle wrapping can display 0–360° or −180–180° for reporting. Normalize units: keep all forces in newtons and coordinates in meters, so moments remain consistent in N·m throughout.
Moment About Reference
If application coordinates are enabled, each force creates a moment about the reference point (x0,y0). The contribution is Mi = (x−x0)Fy − (y−y0)Fx, positive for counterclockwise rotation. Using the example set, the net moment is about 21.962 N·m. When R is nonzero, the signed offset d = M/R estimates the perpendicular distance from the reference to the resultant line.
Concurrent Versus Nonconcurrent
Some problems treat forces as concurrent at one point, meaning only the net force matters and moments cancel by definition. Selecting “treat all forces as concurrent” forces M to zero and disables line-of-action geometry. For distributed loads, brackets, frames, or any system with separated lines of action, keep coordinates on so the couple effect is captured correctly.
Engineering Checks And Tolerances
Use the breakdown table to sanity-check signs, especially when angles exceed 180° or forces are entered as negatives. A near-zero R with a nonzero M indicates a pure couple, which can drive rotation without translation. Set decimals to match instrument accuracy; for field measurements, 2–3 decimals is typical, while simulation outputs may justify 4–6.
Reporting And Exports
The CSV export stores inputs, per-force components, and final outputs for audits or lab reports. The PDF export includes formatted tables suitable for attaching to design notes. The Plotly vector graph visualizes each force in component space and highlights the resultant as the sum vector, making outliers and dominant directions easy to spot.
1) What does the vector graph show?
It plots each force as a vector from the origin using its (Fx, Fy) components. The resultant vector starts at the origin and ends at (ΣFx, ΣFy).
2) When should I enable coordinate-based moments?
Enable it when forces act at different points on a body. Coordinates capture rotation effects through moments, which are essential for brackets, frames, and nonconcurrent loads.
3) What if the resultant force is nearly zero?
If R is near zero but M is not, the system is a pure couple. If both R and M are near zero, the system is balanced within numerical tolerance.
4) How are angles interpreted?
Angles are measured from the positive x-axis, counterclockwise positive. The tool uses atan2 for the resultant direction and can display it as 0–360° or −180–180°.
5) Can I enter forces as components instead of magnitude and angle?
Yes. Choose the components mode and enter Fx and Fy directly. The calculator still computes magnitude, direction, moments, and exports the full breakdown.
6) What does the signed distance d = M/R mean?
It estimates how far the resultant’s line of action is from the reference point, with sign indicating rotational sense relative to the chosen convention.