Net Force Calculator

Net Force Calculator adds 2 to 10 forces at any angle to find the resultant force, its direction and both x and y components, with full steps, a force diagram and the acceleration.

Net Force Calculator for 2 to 10 Forces

Net force in simple words is the one force that is left after every push and pull on an object has been added together. It is also called the resultant force. Two people pushing a box the same way add up, and two pushing against each other partly cancel.

The Net Force Calculator adds from 2 to 10 forces that act on one object in a plane. Pick the count under Number of Forces, then give each force a size and an angle. Sizes can be in newtons, kilonewtons, pounds-force or kilograms-force, and they can be mixed.

Angles run counterclockwise from the +x axis, so 0° points right, 90° up, 180° left and 270° down. Each force is entered as a positive size. To reverse a force, add 180° to its angle. Angles can also be typed in radians.

The starting entries are 40 N at 30° and 25 N at 120° on a 5 kg mass. The main result reads 47.17 N Up and to the Right. The mass is not needed for the net force itself, and it is there so the tool can give the acceleration as well.

Net Force Formula

OpenStax University Physics defines the net external force as the vector sum of all forces acting on an object. Forces have direction, so they cannot be added like plain numbers unless they lie along one line.

$$\vec{F}_{net} = \vec{F}_{1} + \vec{F}_{2} + \dots + \vec{F}_{n}$$

To calculate net force at any angles, split each force into an x part and a y part. Add all the x parts together, then add all the y parts together. A force pointing left or down gives a negative part.

$$\Sigma F_{x} = F_{1} \cos(\theta_{1}) + F_{2} \cos(\theta_{2}) + \dots$$

$$\Sigma F_{y} = F_{1} \sin(\theta_{1}) + F_{2} \sin(\theta_{2}) + \dots$$

The size of the net force then comes from the Pythagorean theorem, with the two sums as the legs of a right triangle. This is the line the Net Force Calculator prints under its main result.

$$F_{net} = \sqrt{(\Sigma F_{x})^{2} + (\Sigma F_{y})^{2}}$$

For the starting entries the x parts are 34.64 N and −12.5 N, which sum to 22.14 N. The y parts are 20 N and 21.65 N, which sum to 41.65 N. The square root of 22.14² + 41.65² is 47.17 N.

A resultant force in xyz works the same way with one more term. Add the z parts into ΣF_z and put its square under the root with the other two. The Net Force Calculator works in the x-y plane, which covers most textbook and free-body problems.

Net Force Formula Examples on One Line

When all the forces lie along one line, the formula reduces to adding and subtracting. This is the method taught in Class 8 science. Forces in the same direction add, and forces in opposite directions subtract, with the net force pointing the way of the larger one.

The third row is the OpenStax example of two skaters pushing a third at right angles. In the tool, a force to the right is entered at 0°, a force to the left at 180° and an upward force at 90°.

How to Find the Direction of Net Force

The direction comes from the inverse tangent of the y sum over the x sum. The result must then be placed in the correct quadrant, because tan⁻¹ alone cannot tell up-right from down-left.

$$\theta = \tan^{-1}\left(\frac{\Sigma F_{y}}{\Sigma F_{x}}\right)$$

For the starting entries, tan⁻¹(41.65 ÷ 22.14) is 62.01°. Both sums are positive, so the angle stays in the first quadrant. If ΣF_x were negative, 180° would be added. The tool does this placement for you and reports an angle from 0° to 360°.

The second result card gives the direction as 62.01° From the +x Axis and as 1.082 rad. It also lists where a balancing force would point, here 242°. One more force of 47.17 N at 242° would bring the net force to zero.

How to Find Net Force of 3 Forces

Three forces follow the same steps as two, with one more term in each sum. Set Number of Forces to 3 and the tool adds a third force of 15 N at 200° to the starting pair.

This is the Each Force Split Into x and y panel for those three forces. The net force is 37.4 N at 77.58°. The last column shows how much each force helps along the net direction. The third force has a negative entry, so it works against the other two.

The Step-by-Step Working panel in the Net Force Calculator writes out the same sums line by line, with the cosine and sine of each angle. It then gives the magnitude, the direction and the acceleration, so the working can be checked against a hand solution.

What Is the 3 Force Rule?

The three force rule covers an object held at rest by exactly three forces. Drawn head to tail, the three arrows must close into a triangle. If they do not close, the gap that is left is the net force.

Three forces of 10 N at 0°, 120° and 240° are a clean case. Their x parts are 10, −5 and −5 N, and their y parts are 0, 8.66 and −8.66 N. Both sums are zero, and the tool reports 0 N Balanced Forces.

Net Force from a Free-Body Diagram

A free-body diagram is a sketch of every external force on one object. OpenStax describes drawing the object as a point at the origin, with each force as an arrow pointing away from it. Forces the object exerts on other things are left out.

To calculate net force from a free-body diagram, read each arrow’s size and its angle from the +x axis. Enter those pairs in the Net Force Calculator, one per force. A weight arrow goes in at 270°, a normal force on level ground at 90°, and friction opposite to the motion.

The Force Diagram panel draws the same picture back as a graph. Each force is a thin arrow from the origin, scaled to its size, and the net force is the thick arrow labeled F_net. It is a quick check that every angle was entered the right way round.

Any type of force can go into the sum, including weight, normal force, friction, tension, applied pushes, air resistance and spring force. The Normal Force Calculator and the Friction Calculator supply two of the arrows that are hardest to read off a problem. The Hooke’s Law Calculator gives the pull of a stretched spring.

Can Net Force Be Zero?

Yes, and it happens whenever the forces balance. A book lying on a table has a net force of zero. So does a lamp hanging from a ceiling, and so does a car cruising at a steady speed on a straight road. Each object is in equilibrium.

Net force is not always zero, though. A non-zero net force is an unbalanced force, and it always changes the object’s velocity. A falling ball, a car pulling away from a light and a sled slowing on snow each have one.

When the entries cancel exactly, the Net Force Calculator shows the note Forces Are Balanced. The object stays at rest or keeps moving at a constant velocity, which is Newton’s first law. With unbalanced entries the note reads Unbalanced Forces.

Difference Between Force and Net Force

A force is a single push or pull. The net force is the combined effect of all of them, and only the net force decides how the object moves. A large force can be on an object that is not moving at all, as long as another force cancels it.

The third result card puts a number on this. For the starting entries the two magnitudes add up to 65 N, but the net force is 47.17 N. The card lists 27.43% as lost to cancelling. With the third force added the sum is 80 N, and 53.26% is lost.

From Net Force to Acceleration

The law of force that links net force to motion is Newton’s second law. It says the acceleration of an object equals the net force on it divided by its mass. The acceleration points the same way as the net force.

$$a = \frac{F_{net}}{m}$$

The fourth card of the Net Force Calculator applies it. A net force of 47.17 N on 5 kg gives 9.434 m/s², which is 30.95 ft/s² or 0.962 g. Double the mass and the same net force gives half of that.

To calculate Newton’s force when the forces are not known, turn the law around and multiply mass by acceleration. The Newton’s Second Law Calculator solves F = m × a for any one of the three. The Acceleration Calculator finds a from a change in speed.

Three formulas for force come up most often in school physics. The first is F = m × a for net force and the second is W = m × g for weight. The third is F = Δp ÷ Δt, which treats force as a rate of change of momentum. The Force Calculator covers those along with pressure and spring forms.

Net force also explains why an action-reaction pair never cancels. The two forces of a pair act on different objects, so they never appear in the same sum. The Newton’s Third Law Calculator works through that case.

Net Force Units: N, kgf and lbf

The SI unit of net force is the newton. One newton is the net force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N equals 1 kg·m/s². It is about 0.2248 lbf, or the weight of roughly 102 grams.

The kilogram-force is also a unit of force, though it is not an SI unit. It is the weight of 1 kg under standard gravity, which the NIST Guide to the SI sets at exactly 9.80665 N. So 1 kg of force is 9.807 N, and a 60 kg mass weighs 588.4 N.

A force of 30 N is therefore about the weight of a 3 kg bag of rice. To calculate force in kg, divide newtons by 9.80665. To convert a mass to its weight, multiply kilograms by 9.80665, which the kg to Newtons Calculator does in both directions.

The first result card of the Net Force Calculator shows the answer in three of these units at once. The Result Unit option changes the unit of the main result, the components and the split table. The full list of related tools is under Dynamics and Statics Calculators.