Resultant Force Calculator — 2D Vector Addition
Calculate the resultant (net) force when two forces act at different angles: enter the magnitude and direction of each force to get the combined magnitude and direction.
N
°
N
°
Magnitude of the vector sum of both forces
- 1
x-components (Fx)
30 × cos(0°) + 40 × cos(90°) = 30 - 2
y-components (Fy)
30 × sin(0°) + 40 × sin(90°) = 40 - 3
Resultant force
√(30² + 40²) = 50
How does this calculator work?
Resolve each force into components (Fx = F·cosθ, Fy = F·sinθ), sum horizontally and vertically, then find resultant magnitude R = √(Fx² + Fy²) at direction θ = atan2(Fy, Fx). For two perpendicular forces this reduces to the Pythagorean theorem: the default 30 N and 40 N at 90° give exactly 50 N.
Formula
How this is calculated
Forces are vector quantities — they have both magnitude and direction. To combine two forces, each is resolved into its horizontal (x) and vertical (y) components using trigonometry: Fx = F·cosθ and Fy = F·sinθ, where θ is measured counter-clockwise from the positive x-axis (east direction). The x-components are summed and y-components are summed independently, then the resultant magnitude R = √(Fx² + Fy²) and direction θ = atan2(Fy, Fx) are recovered via the Pythagorean theorem and inverse tangent.
This is the parallelogram law of vector addition: the resultant is the diagonal of the parallelogram formed by the two force arrows placed tail-to-tail. For the default values (30 N at 0° and 40 N at 90°), the forces are perpendicular, giving R = √(30² + 40²) = 50 N at θ = atan2(40, 30) ≈ 53.13° — a textbook 3-4-5 right triangle scaled by 10.
This calculator handles two concurrent forces (applied at the same point). For three or more forces, sum all x- and y-components first; you can also use the result of two forces as an input for the next pair. Non-concurrent forces (applied at different points) also require moment analysis, which is outside this calculator.
Frequently asked questions
Angles are measured counter-clockwise from the positive x-axis (east/right direction): 0° = right, 90° = up, 180° = left, 270° (or −90°) = down. You can enter angles outside the 0–360° range — the trigonometry handles them correctly.
Sum all x-components (Fx_total = ΣFᵢcosθᵢ) and all y-components (Fy_total = ΣFᵢsinθᵢ), then R = √(Fx_total² + Fy_total²). Alternatively, use this calculator in steps: combine forces 1 and 2, then treat the resultant as "Force 1" and add Force 3.
The resultant is zero when the x and y components cancel completely — the body is in static equilibrium. Two equal and opposite forces (same magnitude, 180° apart) always cancel. This is Newton's first law: net force zero means no acceleration.
Also known as
TG we-Calculate Editorial Team. (2026). Resultant Force Calculator — 2D Vector Addition [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/resultant-force-calculator
TG we-Calculate Editorial Team. "Resultant Force Calculator — 2D Vector Addition." TG we-Calculate. 2026. https://we-calculate.com/calculator/resultant-force-calculator.
TG we-Calculate Editorial Team, "Resultant Force Calculator — 2D Vector Addition," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/resultant-force-calculator
@misc{wecalculate_resultant_force_calculator, title = {Resultant Force Calculator — 2D Vector Addition}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/resultant-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
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