Calculator Inputs
Example Data Table
| Case | F1 | Angle 1 | F2 | Angle 2 | Expected Third Force | Expected Angle |
|---|---|---|---|---|---|---|
| Rigging A | 120 N | 0 deg | 80 N | 135 deg | 88.3070 N | 226.1021 deg |
| Bracket B | 65 N | 30 deg | 55 N | 210 deg | 10.0000 N | 30.0000 deg |
| Cable C | 90 N | 90 deg | 110 N | 200 deg | 88.9170 N | 20.9887 deg |
Formula Used
Component equations
Fx = F cos(theta)
Fy = F sin(theta)
Sigma Fx = F1x + F2x + F3x
Sigma Fy = F1y + F2y + F3y
Resultant = sqrt((Sigma Fx)^2 + (Sigma Fy)^2)
Angle = atan2(Sigma Fy, Sigma Fx)
For equilibrium, both component sums must equal zero. If two forces are known, the third equilibrium force is the exact opposite of their resultant. This calculator uses vector resolution, so it handles any coplanar direction set, not only symmetric cases.
How to Use This Calculator
- Select whether you want to solve the missing third force or check three known forces.
- Choose degrees or radians for angle entry.
- Enter magnitudes and directions for the available forces.
- Set a tolerance if you want to test how close the three-force system is to perfect equilibrium.
- Click the calculate button to show results above the form.
- Review component tables, required balancing force, residual resultant, and status message.
- Use the CSV or PDF buttons to save the output.
Frequently Asked Questions
1. What does three-force equilibrium mean?
It means three concurrent coplanar forces balance perfectly. Their vector sum becomes zero, so the body has no net translational effect from those forces.
2. Can I solve for the unknown balancing force?
Yes. Enter two known forces and their angles. The calculator finds the third force needed to cancel their resultant and restore equilibrium.
3. Why does the calculator use components?
Component resolution works for any direction set. It is more general than shortcut triangle rules and directly shows how each force contributes along x and y axes.
4. What is the tolerance field for?
Tolerance sets the maximum residual resultant allowed when checking three known forces. Smaller values mean a stricter equilibrium test.
5. Should I use degrees or radians?
Use whichever matches your data source. The calculator converts angles internally and returns the final direction in the selected unit.
6. Does this calculator include moments?
No. This tool checks only force equilibrium for concurrent coplanar forces. Moment equilibrium requires a separate rotational analysis.
7. Can this help with statics problems?
Yes. It is useful for cables, brackets, rings, supports, and particle statics where three forces act through one point.
8. Why is my system not balanced?
A nonzero residual means the entered third force does not fully cancel the other two. Check angle direction, units, and magnitude values.