The net (resultant) force is the vector sum of all forces acting on an object. It determines the acceleration through Newton’s second law; if it is zero, the object is in equilibrium.
How to use the Resultant Force Calculator
- Number of forces
- Force F₁
- Angle θ₁
- Force F₂
- Angle θ₂
- Force F₃
- Angle θ₃
- Force F₄
- Angle θ₄
- Force F₅
- Angle θ₅
- Force F₆
- Angle θ₆
- Force F₇
- Angle θ₇
- Force F₈
- Angle θ₈
- Force F₉
- Angle θ₉
- Force F₁₀
- Angle θ₁₀
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose how many forces act and give each a magnitude and an angle measured counter-clockwise from the positive x-axis.
Inputs explained
| Field | What to enter |
|---|---|
| Number of forces | Choose one: 1, 2, 3, 4 … |
| Force F₁ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₁ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₂ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₂ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₃ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₃ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₄ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₄ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₅ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₅ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₆ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₆ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₇ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₇ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₈ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₈ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₉ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₉ | Units: °, rad, arcmin, arcsec, mrad |
| Force F₁₀ | Units: N, kN, MN, mN, lbf, kgf … |
| Angle θ₁₀ | Units: °, rad, arcmin, arcsec, mrad |
What each result means
- Net force = sqrt([x component Fₓ]^2 + [y component F_y]^2)
- Direction (from +x, counter-clockwise) = mod(deg(atan2([y component F_y], [x component Fₓ])), 360)
Example values
How the main result changes when Force F₁ changes and everything else stays at the example values above:
| Force F₁ (N) | Net force (N) |
|---|---|
| 5 | 15.8114 |
| 7.5 | 16.7705 |
| 10 | 18.0278 |
| 12.5 | 19.5256 |
| 15 | 21.2132 |
| 20 | 25 |
Formula
Fₓ = Σ Fᵢ cos θᵢ, F_y = Σ Fᵢ sin θᵢ, |F| = √(Fₓ² + F_y²)
Worked example
Inputs — Number of forces: 2; Force F₁: 10 N; Angle θ₁: 0 °; Force F₂: 15 N; Angle θ₂: 90 °.
Results — x component Fₓ = 10 N; y component F_y = 15 N; Net force = 18.0278 N; Direction (from +x, counter-clockwise) = 56.31 °.
Key terms
- Resultant
- The single force equivalent to several forces.
Frequently asked questions
What does a net force of zero mean?
The object is in equilibrium: at rest or moving at constant velocity.
How do I add two perpendicular forces?
√(F₁² + F₂²).
Which way is 90°?
Straight up (positive y), counter-clockwise from the positive x-axis.
Can forces be added as plain numbers?
Only if they act along the same line.