Calculator Inputs
Use the settings card plus up to six force vectors.
Example Data Table
These sample values match the prefilled rows above.
| Force | Magnitude (N) | Angle (deg) | x (m) | y (m) | Approx. Fx (N) | Approx. Fy (N) |
|---|---|---|---|---|---|---|
| F1 | 120 | 0 | 0 | 0 | 120.0000 | 0.0000 |
| F2 | 85 | 65 | 1.2 | 0.4 | 35.9226 | 77.0362 |
| F3 | 60 | 180 | -0.5 | 0 | -60.0000 | 0.0000 |
| F4 | 95 | -35 | 0.8 | -0.6 | 77.8194 | -54.4898 |
| Expected resultant summary | ΣFx ≈ 173.7420 | ΣFy ≈ 22.5464 | ||||
Expected magnitude ≈ 175.1988 N, direction ≈ 7.3939°, and net moment about the origin ≈ 81.1742 N·m.
Formula Used
1) Resolve each force into Cartesian components
Fx = F cos(θ)
Fy = F sin(θ)
2) Sum all x and y components
ΣFx = Fx1 + Fx2 + ... + Fxn
ΣFy = Fy1 + Fy2 + ... + Fyn
3) Compute the resultant magnitude and direction
R = √[(ΣFx)² + (ΣFy)²]
θR = atan2(ΣFy, ΣFx)
4) Compute the equilibrant direction
θE = θR + 180°
5) Compute the net moment about the origin
Mi = xiFyi − yiFxi
ΣM0 = M1 + M2 + ... + Mn
6) Equivalent line distance of the resultant
d = ΣM0 / R
These formulas let you analyze both the net force and the rotational effect of the complete force system.
How to Use This Calculator
- Choose degrees or radians in the settings card.
- Enter a force unit label such as N, kN, or lbf.
- Enable each force row you want included.
- Provide magnitude and angle for every active force.
- Add x and y coordinates when you need moments.
- Set decimal precision and equilibrium tolerance as needed.
- Press Calculate Resultant Force.
- Review the summary cards, detailed table, and vector plot.
- Use the CSV or PDF buttons to export the report.
FAQs
1) What does the resultant force represent?
It is the single vector that has the same overall translational effect as all entered forces acting together.
2) What is the equilibrant?
The equilibrant has the same magnitude as the resultant but points in the exact opposite direction. It balances the net force.
3) Why are x and y positions included?
They let the calculator compute each force moment about the origin. This helps analyze rotational tendency, not just translation.
4) Can I use radians instead of degrees?
Yes. Select radians in the angle mode setting. The calculator then reads every input angle as radians.
5) Why is atan2 used for the angle?
atan2 uses both resultant components, so it returns the correct direction in every quadrant and handles sign changes properly.
6) What does static equilibrium mean here?
It means the force sums are near zero and the net moment is also near zero, within the tolerance you set.
7) Can this handle negative angles?
Yes. Negative angles are valid. They rotate clockwise from the positive x-axis when interpreted in standard vector notation.
8) What is the signed line distance value?
It estimates where the equivalent resultant line of action lies relative to the origin. The sign reflects direction based on the net moment.