By Zencalcy Editorial TeamLast reviewed About us
When two forces act on the same object at an angle, the net force is their vector sum, not their arithmetic sum. This calculator resolves both forces into x and y components, adds them, and reports the resultant magnitude and the angle it makes with the positive x axis.
Add two forces at an angle and get the resultant magnitude and direction.
R = √(F₁² + F₂² + 2F₁F₂ cos θ) θ_R = atan2(F₁ sin α₁ + F₂ sin α₂, F₁ cos α₁ + F₂ cos α₂)
θ is the angle between the two forces, α₁ and α₂ are their absolute directions. The calculator uses absolute directions, so a force pointing left has an angle near 180°.
| Symbol | Meaning |
|---|---|
| F₁, F₂ | Magnitudes of the two forces, in newtons. |
| α₁, α₂ | Direction of each force from the positive x axis. |
| R | Magnitude of the resultant force, in newtons. |
| θ_R | Direction of the resultant force, in degrees. |
A 10 N force east and a 10 N force north give a resultant of √(10² + 10²) = 14.14 N pointing 45° north of east. The components are 10 N in each direction.
Continue with the Normal Force Calculator, Rocket Equation Calculator, or the Tension Calculator — or browse more dynamics tools and all physics calculators.
Forces add as vectors. At 90° the resultant is the diagonal of the rectangle they form, √2 times one force, which is 14.14 N rather than 20 N.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Content updated: September 2026