Example Data Table
| Case | Input type | Main input | Extra force | Expected use |
|---|---|---|---|---|
| Bracket load | Components | Fx 120, Fy 80, Fz 40 N | 0, -20, 10 N | Find resultant and moment |
| Cable pull | Two points | 150 N from A(0,0,0) to B(3,4,2) | None | Resolve cable tension |
| Inclined force | Azimuth and elevation | 2 kN, azimuth 35, elevation 20 | 0.3, 0.1, -0.2 kN | Check member projection |
Formula Used
Component vector: F = <Fx, Fy, Fz>.
Magnitude: |F| = sqrt(Fx² + Fy² + Fz²).
Axis angle components: Fx = F cos(α), Fy = F cos(β), Fz = F cos(γ).
Azimuth and elevation: Fx = F cos(e) cos(θ), Fy = F cos(e) sin(θ), Fz = F sin(e).
Two point direction: u = (B - A) / |B - A|, then F = magnitude × u.
Resultant: R = sum of all force vectors.
Unit vector: uR = R / |R|.
Projection on axis a: scalar = R · ua. Vector projection = scalar × ua.
Moment about a point: M = r × R.
How to Use This Calculator
Select the unit first. Choose the main force input method. Fill only the fields needed for that method. Add optional component forces when several loads act together. Enter an axis if you need a projection. Enter a position vector when a moment is required. Set a tolerance for equilibrium checks. Press calculate to show the result above the form. Use the export buttons to save the same result as CSV or PDF.
3D Force Vector Guide
Why 3D Force Vectors Matter
Three dimensional force work appears in many physics tasks. It also appears in statics, machine design, robotics, and structural checks. A force rarely acts only along one neat axis. Most loads pull or push through space. That means the force needs x, y, and z components.
This calculator helps you resolve that force. You may enter components directly. You may also enter a magnitude with direction angles. Another option uses azimuth and elevation. A line between two points can define the force direction too. These choices support common textbook and field problems.
Understanding the Output
The magnitude shows the overall strength of the force. The unit vector shows pure direction. Direction cosines show how strongly the force aligns with each coordinate axis. Axis angles convert those cosines into clear angles. These values make vector diagrams easier to check.
The resultant section is useful when several forces act together. Add optional force components. The tool sums each axis component. Then it finds the final magnitude and direction. If the resultant is near zero, the system may be close to equilibrium. Always compare this result with the chosen tolerance.
Projection and Moment Uses
The projection tool is helpful for cables, rods, braces, and inclined members. Enter any axis vector. The calculator finds the part of the resultant acting along that axis. It also reports the projected vector. This is useful when only the force along a member matters.
The moment option adds another layer. Enter a position vector from the reference point to the force point. The cross product gives the moment vector. Its magnitude tells how strongly the force tends to rotate the body. Check sign direction with your coordinate convention.
Accuracy Tips
Use careful units. The calculator can accept newtons, kilonewtons, or pounds force. Internally, it converts values for consistent math. Round results only after solving. Small angle errors can produce visible component changes.
Record the sign of each component. A wrong sign can reverse the answer. Sketch the axes first. Then match every input with that sketch before submitting the form each time.
This page is best for learning, checking homework, and preparing quick reports. It does not replace code requirements or professional judgment. For safety critical systems, verify loads, constraints, and coordinate axes before using any result.
FAQs
What is a 3D force vector?
It is a force written with x, y, and z components. It describes both strength and direction in three dimensional space.
Can I enter force by magnitude and direction?
Yes. Use axis angles, azimuth with elevation, or a line between two points. The calculator converts that input into components.
What are alpha, beta, and gamma angles?
They are the angles between the force vector and the x, y, and z axes. Their direction cosines should be consistent.
What does the unit vector mean?
The unit vector shows direction only. Its magnitude is one, so it is useful for building force vectors from a known magnitude.
How is the resultant force calculated?
Each x component is added together. The same is done for y and z. The final vector is the resultant force.
What is force projection?
Projection is the part of a force that acts along a selected axis. It is useful for cables, braces, and member forces.
Why is my equilibrium result not balanced?
The resultant magnitude is larger than your tolerance. Check signs, units, missing forces, and coordinate directions before changing the tolerance.
Can this replace an engineering review?
No. It is a calculation aid. Safety critical work needs verified loads, correct assumptions, and qualified professional review.