Net Force Calculator
Add two forces that pull at an angle to each other. Enter both magnitudes (N, lbf, or kN) and the angle between them in degrees, and get the resultant's magnitude and its direction measured from the first force — the parallelogram rule done for you.
Example: with Force 1 30 · Force 2 40 · Angle between the forces (degrees) 60 · Force unit N (newtons) → Net (resultant) force: 60.83 N.
- Direction34.72° from force 1, toward force 2
- Converted13.67 lbf
Computed by the calculator below using its default values. Change any input to see your own numbers.
R = √(F₁² + F₂² + 2F₁F₂cos θ) — the law of cosines applied to the force parallelogram. At 90° it reduces to the Pythagorean theorem.
Forces add like arrows, not like numbers
Two people pulling a crate with 30 N and 40 N do not automatically produce 70 N. Forces are vectors — magnitude plus direction — so they add tip-to-tail. The resultant follows the law of cosines: R = √(F₁² + F₂² + 2F₁F₂cos θ), where θ is the angle between the pulls. Only when the forces are perfectly aligned (θ = 0°) do you get the full 70 N; at 60° apart the same two pulls deliver 60.8 N, and directly opposed they fight down to 10 N.
The direction matters as much as the size. This tool reports the resultant's angle from force 1 using φ = atan2(F₂ sin θ, F₁ + F₂ cos θ) — the line the crate actually moves along if nothing else acts on it.
From net force to motion
Newton's second law only cares about the net force: F_net = ma. If the resultant here is zero, the object is in equilibrium — it sits still or keeps coasting at constant velocity, which is how tug-of-war stalemates and steadily cruising cars are the same physics. For more than two forces, add them pairwise (combine two, then combine the result with the next) or split everything into x and y components; the two-force parallelogram rule is the building block either way.
How it’s calculated
R = √(F₁² + F₂² + 2·F₁·F₂·cos θ), with θ the angle between the two forces (0° = same direction, 180° = opposite). Direction from force 1: φ = atan2(F₂ sin θ, F₁ + F₂ cos θ), reported in degrees. The math is unit-agnostic; conversions shown use 1 lbf = 4.4482216153 N exactly.
Treats both forces as acting at a single point on a rigid body — offset lines of action also create torque, which this tool does not compute.
Two equal 100 N forces — resultant vs. angle
| Angle between | Resultant |
|---|---|
| 0° | 200 N |
| 30° | 193.2 N |
| 60° | 173.2 N |
| 90° | 141.4 N |
| 120° | 100 N |
| 150° | 51.8 N |
| 180° | 0 N |
Computed with R = √(F₁²+F₂²+2F₁F₂cos θ); note the elegant 120° case, where the resultant equals each force.
Common mistakes
- Adding magnitudes arithmetically when the forces aren't parallel — 30 + 40 = 70 N is only true at exactly 0°.
- Entering the angle each force makes with the x-axis instead of the angle between the forces.
- Dropping the direction: a net force of 60.8 N is half an answer; the object accelerates along the resultant's line.
- Mixing units — combining a newton value with a pounds-force value without converting one of them first.
Frequently asked questions
What is the net force formula for two forces at an angle?
R = √(F₁² + F₂² + 2F₁F₂cos θ), where θ is the angle between them. At 90° the cosine term vanishes and it becomes the Pythagorean theorem: R = √(F₁² + F₂²).
Why is my resultant smaller than the two forces combined?
Because the pulls partly work against each other. Any angle above 0° wastes some of each force on sideways components that cancel; past 120° (for equal forces) the resultant drops below either individual force.
How do I add three or more forces?
Combine any two with this rule, then combine that resultant with the next force, and so on — or resolve every force into x and y components, sum each axis, and take R = √(ΣFx² + ΣFy²).
What does zero net force mean?
Equilibrium. The forces balance, so the object keeps doing whatever it was doing — staying at rest or moving in a straight line at constant speed (Newton's first law). It does not mean nothing is pushing.
What units should I use?
Any single force unit works since the formula scales linearly — this tool handles newtons, pounds-force, and kilonewtons, converting at 1 lbf = 4.4482 N. Just don't mix units between the two inputs.