Quiz: Net Force Calculator

Enter two forces by magnitude and direction (angle from the positive x-axis) to find the net force's magnitude and direction using vector addition, plus the resulting acceleration if you provide the object's mass.

Quick Facts

Newton's Second Law
F_net = m·a
Net force equals mass times acceleration; rearranged, a = F_net / m.
Vector Addition
F_net = ΣF
Forces are vectors — add x- and y-components separately, then recombine with the Pythagorean theorem.
Equilibrium
F_net = 0
When net force is zero, an object stays at rest or keeps moving at constant velocity (Newton's First Law).

Your Results

Calculated
Net Force Magnitude
-
|F_net| = √(Fx² + Fy²)
Net Force Direction
-
θ = atan2(Fy, Fx), from +x axis
Force Components (Fx, Fy)
-
Sum of x- and y-components
Resulting Acceleration
-
a = F_net / mass (Newton's 2nd law)

Ready

Enter two forces with magnitude and direction, then press Calculate.

How to Calculate Net Force

The net force on an object is the single equivalent force created by adding every individual force acting on it as a vector — magnitude and direction both matter, not just size. You can't simply add force magnitudes together unless the forces act along exactly the same line; forces pointing in different directions must be broken into perpendicular components first. This calculator resolves two forces — each given as a magnitude and an angle measured from the positive x-axis — into their x- and y-components, sums those components to get the net force vector, and, if you provide the object's mass, applies Newton's second law to find the resulting acceleration.

Breaking each force into components

Every force F at angle θ (measured counter-clockwise from the positive x-axis, so 0° points right/east and 90° points up/north) has an x-component of F·cos(θ) and a y-component of F·sin(θ). Summing the x-components of all forces gives the net x-component (ΣFx), and summing the y-components gives the net y-component (ΣFy). The magnitude of the net force then follows from the Pythagorean theorem, |F_net| = √(ΣFx² + ΣFy²), and its direction is θ_net = atan2(ΣFy, ΣFx).

From net force to acceleration

Newton's second law states F_net = m·a, so once you know the net force and the object's mass, the resulting acceleration is a = F_net / m, pointing in the same direction as the net force. If the net force works out to zero, the object is in equilibrium: per Newton's first law, it either stays at rest or continues moving in a straight line at constant velocity, with no acceleration.

Frequently Asked Questions

What is net force?
Net force is the single force that has the same effect as all the individual forces acting on an object combined. It is found by adding every force as a vector — accounting for both magnitude and direction — rather than simply adding their sizes.
How do you find net force when forces act at different angles?
Break each force into x- and y-components using F·cos(θ) and F·sin(θ), add the x-components together and the y-components together, then recombine the totals with the Pythagorean theorem: |F_net| = √(ΣFx² + ΣFy²). The direction is θ_net = atan2(ΣFy, ΣFx).
What does it mean if the net force is zero?
A net force of zero means the object is in equilibrium. By Newton's first law, it will remain at rest if it was already at rest, or continue moving in a straight line at constant speed if it was already moving — no acceleration occurs.
How is net force related to acceleration?
Newton's second law connects the two directly: F_net = m·a. Dividing the net force by the object's mass gives its acceleration (a = F_net / m), which always points in the same direction as the net force.

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