Net Force Calculator
Calculate the resultant net force from multiple forces at different angles.
Enter up to three forces with magnitude and direction to get the vector sum.
Forces are vectors — they have both magnitude and direction. To find the net (resultant) force on an object, you decompose each force into horizontal (x) and vertical (y) components, sum them separately, then recombine.
For a force F at angle θ (measured from the positive x-axis, counterclockwise):
Fx = F × cos(θ) Fy = F × sin(θ)
Sum all components:
Σ Fx = F1x + F2x + F3x Σ Fy = F1y + F2y + F3y
Net force magnitude: F_net = √(ΣFx² + ΣFy²) Direction: φ = arctan(ΣFy / ΣFx), adjusted for quadrant
Angle convention used here: 0° = right (east), 90° = up (north), 180° = left (west), 270° = down (south). Angles are measured counterclockwise from east.
If the net force is zero, the object is in equilibrium — Newton’s first law says it stays at rest or continues in uniform motion.
Example: three forces of 10 N at 0°, 8 N at 90°, and 6 N at 210°. Fx = 10 + 0 + 6 cos(210°) = 10 − 5.196 = 4.804 Fy = 0 + 8 + 6 sin(210°) = 8 − 3 = 5 F_net = √(4.804² + 5²) = √(23.08 + 25) = √48.08 ≈ 6.93 N
Forces F2 and F3 are optional — enter 0 N if not needed.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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