Analyze spatial loads, torques, and rigid body moments. Verify balance using coordinate based vector calculations. Download polished reports with charts for classwork and design.
Use up to 6 applied forces and 3 applied couples. The page keeps a single column flow, while the form fields use a 3 column, 2 column, and 1 column responsive layout.
This calculator evaluates translational and rotational balance for a 3D rigid body. Every force contributes directly to the resultant force vector. Each force also generates a moment about the selected reference point using the cross product of position vector and force vector.
Applied couples are added directly to the resultant moment because they are free vectors. If both the resultant force and resultant moment are zero within tolerance, the body is in static equilibrium.
Use the sample button to load this equilibrium case automatically.
| Load | Px | Py | Pz | Fx | Fy | Fz |
|---|---|---|---|---|---|---|
| F1 | 2 | 0 | 0 | 0 | 0 | 50 |
| F2 | -2 | 0 | 0 | 0 | 0 | -50 |
| F3 | 0 | 3 | 0 | 15 | 0 | 0 |
| F4 | 0 | -3 | 0 | -15 | 0 | 0 |
| F5 | 0 | 0 | 4 | 0 | 10 | 0 |
| F6 | 0 | 0 | -4 | 0 | -10 | 0 |
| Applied couple | Mx | My | Mz |
|---|---|---|---|
| C1 | 80 | 200 | 90 |
A strong lab report should include the setup, force locations, sign convention, measured distances, calculated torques, uncertainty discussion, and a conclusion on whether clockwise and counterclockwise moments balanced within experimental error.
Typical sample problems start with a free body diagram, then resolve all forces into x, y, and z components, choose a moment reference point, write six equilibrium equations, and solve for the unknown reactions or balancing loads.
Typical answers explain that net torque becomes zero at equilibrium, torque sign depends on the chosen axis convention, and small residual values usually come from measurement errors, friction, alignment error, or imperfect force application.
That statement is false. A rigid body can have zero resultant force and still rotate if a pure couple remains. Static equilibrium needs both zero resultant force and zero resultant moment.
A rigid body is in equilibrium only when all three force components sum to zero and all three moment components sum to zero about the same reference point: ΣFx = ΣFy = ΣFz = 0 and ΣMx = ΣMy = ΣMz = 0.
It checks whether the entered 3D force system and applied couples satisfy rigid body equilibrium by testing the resultant force vector and resultant moment vector against your tolerance.
Zero resultant force prevents translation. Zero resultant moment prevents rotation. A rigid body is only fully balanced when both conditions are satisfied together.
Yes. You can compute moments about any convenient point. For a body in true equilibrium, the balance conclusion remains consistent, though individual moment terms can change with the reference point.
No. A pure couple is a free vector, so it contributes directly to the resultant moment without needing an application point in this calculator.
Yes. A remaining nonzero couple can still rotate the rigid body. That is why the calculator also checks ΣM = 0.
It is the exact negative of the current resultant force. Applying that vector would cancel translation imbalance for the entered load system.
Yes. It is useful for engineering statics checks on brackets, rigid frames, fixtures, and machine parts wherever you need a quick 3D balance verification.
Use a tolerance that matches your units, rounding, and measurement accuracy. Smaller tolerances are stricter, while larger tolerances are better for noisy lab or hand entered values.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.