Enter Force System Data
Use consistent units throughout. Angles are measured counterclockwise from the positive x-axis.
Formula Used
| Quantity | Formula | Meaning |
|---|---|---|
| Horizontal component | Fx = F cos(θ) | Resolves each force along the x-axis. |
| Vertical component | Fy = F sin(θ) | Resolves each force along the y-axis. |
| Moment about origin | M = xFy − yFx | Computes rotational effect from the force location. |
| Net resultant | R = √[(ΣFx)² + (ΣFy)²] | Gives the combined force magnitude. |
| Resultant direction | θR = atan2(ΣFy, ΣFx) | Returns the net force direction in degrees. |
| Equilibrium condition | ΣFx = 0, ΣFy = 0, ΣM = 0 | Static equilibrium exists when all three sums are zero. |
| Balancing force | Fb = R at angle θR + 180° | Applies an equal and opposite force to cancel the resultant. |
| Balancing couple | Mb = −ΣM | Cancels any remaining net moment. |
How to Use This Calculator
- Choose force and distance units that match your statics problem.
- Enter each force magnitude, angle, and application point coordinates.
- Add any known external couple moment if one acts on the body.
- Set the allowable tolerance used to judge numerical equilibrium.
- Press Solve Equilibrium to calculate component sums, moments, and balancing actions.
- Review the result card above the form, the component table, and the Plotly graph.
- Use the CSV or PDF buttons to export the solved data.
Example Data Table
This example balances the force system by adding an external couple moment of −273.21 N·m.
| Force | Magnitude (N) | Angle (°) | X (m) | Y (m) | Fx (N) | Fy (N) | Moment (N·m) |
|---|---|---|---|---|---|---|---|
| F1 | 100.00 | 0.00 | 0.00 | 0.00 | 100.00 | 0.00 | 0.00 |
| F2 | 100.00 | 120.00 | 2.00 | 0.00 | -50.00 | 86.60 | 173.21 |
| F3 | 100.00 | 240.00 | 0.00 | 2.00 | -50.00 | -86.60 | 100.00 |
| Force totals | 0.00 | 0.00 | 273.21 | ||||
| External couple moment added | -273.21 | ||||||
FAQs
1) What does this equilibrium solver calculate?
It resolves each force into x and y components, sums all forces, computes net moment, finds the resultant, and suggests the balancing force and couple needed for equilibrium.
2) Which angle convention does the calculator use?
Angles are measured in degrees from the positive x-axis, increasing counterclockwise. This is the common engineering convention for planar statics and vector resolution.
3) Why do I need x and y positions?
The application point determines the moment created by each force. Even if the net force is small, an offset force can still create a large rotational effect.
4) What is the balancing force?
The balancing force is equal in magnitude and opposite in direction to the resultant. It removes the net translational effect, but a separate balancing couple may still be required.
5) What does the external couple moment field do?
It lets you include a pure applied moment that does not depend on a force location. Use positive or negative sign based on your chosen rotational convention.
6) Why use a tolerance instead of exact zero?
Real calculations often produce tiny rounding differences. The tolerance defines how close ΣFx, ΣFy, and ΣM must be before the system is accepted as numerically balanced.
7) Can this solve support reactions directly?
This version evaluates known forces and checks balance. You can still use it for reaction problems by entering assumed reactions as unknown trial values from your statics equations.
8) What should I export, CSV or PDF?
CSV works best for spreadsheets and further calculations. PDF is better for reports, sharing solved cases, and keeping a formatted record of the summary and component tables.