Solve 3D torque using force and position vectors. Get components, magnitude, and direction in seconds. Export results and compare practical examples for better design.
| Pivot | Force Point | Force Vector | Torque Vector | |τ| |
|---|---|---|---|---|
| (0, 0, 0) | (2, 1, 0) | (0, 5, 10) | (10, -20, 10) | 24.495 N·m |
| (1, 0, 0) | (4, 2, 1) | (3, 8, 2) | (-4, -3, 18) | 18.682 N·m |
| (0, 0, 0) | (0.5, 0.2, 0.1) | (120, 40, 15) | (-1, 4.5, -4) | 6.103 N·m |
Torque in three dimensions is the vector cross product of the position vector and the applied force vector.
τ = r × F
r = (rx, ry, rz)
F = (Fx, Fy, Fz)
τx = ryFz − rzFy
τy = rzFx − rxFz
τz = rxFy − ryFx
|τ| = √(τx² + τy² + τz²)
r · F = rxFx + ryFy + rzFz
θ = cos-1((r · F) / (|r||F|))
Lever arm = |τ| / |F|
Keep force and distance units consistent. The output torque unit is force unit multiplied by length unit.
Torque describes the turning effect of a force. In real engineering work, many loads act in three dimensions. A simple two dimensional shortcut may miss an important component. That can change shaft loading, fastener stress, and support reactions. A 3D torque calculator helps engineers see the full rotational effect around a pivot.
This calculator uses a pivot point, a force application point, and a force vector. The pivot and force point create the position vector. That vector starts at the pivot and ends at the force location. The force vector shows both direction and magnitude. The cross product of these two vectors produces the torque vector. Each torque component reveals rotation about a specific axis.
The torque vector contains x, y, and z components. A positive or negative sign follows the right hand rule. The magnitude shows the total turning effect. The angle between the position vector and force helps explain efficiency. A ninety degree force creates maximum torque for a given distance. The perpendicular lever arm also shows how far the force acts from the pivot line.
Mechanical engineers use torque analysis for brackets, levers, gears, and rotating shafts. Civil engineers review moments on joints, supports, and frames. Robotics designers use 3D moments to study arm motion and actuator loads. Automotive teams check suspension parts, wheel forces, and steering linkages. Aerospace work also depends on accurate moment calculations in spatial coordinates.
This tool speeds up design checks and reduces manual errors. It also helps students understand vector mechanics. You can compare examples, export results, and verify component directions quickly. For consistent results, always use matching units and measured coordinates. A clear 3D torque result supports safer designs and better engineering decisions.
3D torque is the rotational effect of a force in space. It is a vector, not just one number. It shows turning tendency about the x, y, and z axes.
The pivot defines the reference point for rotation. Torque depends on the distance and direction from that point to the force application location.
Torque becomes zero. A force acting along the same line as the position vector has no perpendicular distance, so it produces no turning effect.
Yes. You can use any consistent pair of units. The output torque unit will follow the same combination, such as N·mm or N·m.
A negative component means rotation in the opposite axis direction under the right hand rule. It does not mean the torque is invalid.
The magnitude combines all three torque components into one total vector length. A single component only shows rotation about one axis.
The lever arm is the perpendicular distance from the pivot to the force line. It is computed as torque magnitude divided by force magnitude.
Yes. It is useful for students and engineers who need fast vector torque checks, worked examples, and a clear view of cross product results.
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.