Calculators/Net Force

Classical Mechanics

Net Force Calculator

Add up to four forces by magnitude and direction to find the net force, its direction, and the resulting acceleration.

Forces

Force 1

Magnitude (N)

Angle (°, 0=right)

Force 2

Magnitude (N)

Angle (°, 0=right)

Force 3

Magnitude (N)

Angle (°, 0=right)

Force 4

Magnitude (N)

Angle (°, 0=right)

Mass (kg) — optional, for acceleration

Examples

Vector diagram

Net Force

50 N

at 53.1°

Fx (sum)

30 N

Fy (sum)

40 N

Acceleration

—

Step-by-step solution

ΣFx = 30·cos(0°) + 40·cos(90°) = 30 N

ΣFy = 30·sin(0°) + 40·sin(90°) = 40 N

F_net = √(Fx² + Fy²) = √(30² + 40²) = 50 N

θ = atan2(Fy, Fx) = 53.1°

Net force equations

Net force (components)

F_net = √(ΣFx² + ΣFy²)

Direction

θ = atan2(ΣFy, ΣFx)

Newton's Second Law

F_net = ma

How to Find Net Force

Net force is what you get when you add every force acting on an object together as vectors — not just their sizes, but their directions too. Two 50 N forces pulling in opposite directions produce zero net force; the same two forces pulling in the same direction produce 100 N.

The standard method is to break every force into horizontal (x) and vertical (y) components using F_x = F·cos(θ) and F_y = F·sin(θ), add all the x-components, add all the y-components, then recombine the two sums into a single magnitude and direction with the Pythagorean theorem and arctangent.

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 — the vector sum of every force applied to it. An object only accelerates according to its net force, not any one force acting alone.

How do you calculate net force with multiple forces?+

Break each force into its x and y components (Fx = F·cosθ, Fy = F·sinθ), add all the x-components together and all the y-components together, then recombine: F_net = √(ΣFx² + ΣFy²), with direction θ = atan2(ΣFy, ΣFx).

What does it mean if the net force is zero?+

Zero net force means the object is in equilibrium — by Newton’s First Law, it continues at constant velocity (including staying at rest) with no acceleration, even though individual forces may still be acting on it.

Can net force be negative?+

The net force’s magnitude (from the formula above) is never negative — magnitude is always ≥ 0. What can be negative is a force’s component along one axis, which simply means it points in the negative direction of that axis.

How is net force related to acceleration?+

By Newton’s Second Law, net force equals mass times acceleration: F_net = ma. Once you know the net force, dividing by the object’s mass gives its acceleration — that’s what the optional mass field above calculates.

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Net Force — The Complete Guide

Every object you can think of usually has more than one force acting on it at once — gravity, friction, a push, air resistance. Net force is the single combined effect of all of them, and it's the only thing that determines how an object actually accelerates, by Newton's Second Law.

Confusing an individual force with the net force is one of the most common mistakes in introductory mechanics. A 500 N push on a heavy crate does nothing if 500 N of friction opposes it exactly — the net force, and therefore the acceleration, is zero.

Worked Example — Two Perpendicular Forces

Problem: A 30 N force pulls east and a 40 N force pulls north on the same object. Find the net force.

Fx = 30 N, Fy = 40 N (already aligned with the axes)

F_net = √(30² + 40²) = √(900 + 1600) = √2500 = 50 N

θ = atan2(40, 30) ≈ 53.1° north of east — this is the classic 3-4-5 triangle.

Worked Example — Three Forces in Equilibrium

Problem: Three 10 N forces act on a ring, spaced 120° apart (0°, 120°, 240°). Find the net force.

By symmetry, every component cancels exactly: ΣFx = 10cos0° + 10cos120° + 10cos240° = 10 − 5 − 5 = 0

ΣFy = 10sin0° + 10sin120° + 10sin240° = 0 + 8.66 − 8.66 = 0 → Net force is exactly zero — the ring is in equilibrium.

Why Direction Matters

Force is a vector, not just a number. Two forces of equal magnitude can produce anywhere from zero net force (pointing exactly opposite) to double the individual magnitude (pointing exactly the same way), with everything in between depending on the angle. This is why engineers resolve every force into components before adding — adding magnitudes directly, ignoring direction, gives the wrong answer except in the special case where all forces happen to point the same way.