Force Calculator

Calculate net force, Newton’s second law, force components, equilibrium, and acceleration with free-body diagrams, vector breakdowns, and step-by-step physics explanations.

Background

Force is a push or pull that can change an object’s motion. This calculator works as a physics force hub: students can add multiple forces, resolve x- and y-components, check equilibrium, calculate acceleration, and connect the math to a clear free-body diagram.

Analyze forces

Choose a force mode

Start simple with F = ma, or build a full free-body diagram with several forces.

Object settings

Mass

Used to calculate acceleration from net force.

Mass unit

Angle convention

Add forces

Add each force by magnitude and angle. The calculator resolves each force into x/y components and finds the net force.

Force label

Magnitude

Angle

Angle unit

Use this before entering your own free-body diagram from scratch.

Quick-add force presets

Add common force arrows quickly, then edit or remove them as needed.

Friction helper

Optional integration: estimate a friction force using f = μN, then add it as a force arrow.

Coefficient, μ

Normal force, N

Friction direction angle

Tip: friction points opposite actual or possible sliding. For a push to the right on a flat surface, friction often points left (180°).

Newton’s Second Law

Use F = ma. Enter any two values to solve the third.

Force, F

Mass, m

Acceleration, a

Resolve one force into components

Calculate F_x = F cos θ and F_y = F sin θ.

Force magnitude

Angle

Angle unit

Equilibrium check

Use the force builder above, then check whether ΣF_x = 0 and ΣF_y = 0.

Tip: equilibrium means net force is approximately zero, so acceleration is zero.

Unknown force solver

Add all known forces above. The calculator finds the missing force that would make ΣF_x = 0 and ΣF_y = 0.

Unknown force label

Target condition

This is ideal for tension, support force, missing applied force, and balanced free-body diagram problems.

Supported formats

10 kg 20 N at 0° 50 N at 30° fractions like 1/2 scientific notation negative angles

Use positive force magnitudes and choose direction with the angle.
Use standard physics angles unless your class uses compass-style directions.
For a free-body diagram, add one force per arrow.
Net force points in the same direction as acceleration.
Hover force arrows in the diagram to see magnitude, angle, and components.

Options

Show step-by-step solution

Show free-body diagram

Show component table

Show student-friendly interpretation

Show common mistakes

Quick examples (click to see result)

Result

Copied!

No result yet. Add forces or enter values, then click Calculate Force.

How to use this calculator

Choose net force, Newton’s Second Law, force components, or equilibrium mode.
For net force problems, add each force with magnitude and angle.
Enter mass if you want acceleration from net force.
Click Calculate Force to see the resultant, components, free-body diagram, and steps.
Use quick examples to see common physics homework setups.

How this calculator works

Each force is treated as a vector with magnitude and direction.
The calculator resolves each force into horizontal and vertical components.
It adds all x-components and all y-components to find the net force.
If mass is known, it uses Newton’s Second Law to calculate acceleration.
It checks whether the forces balance, which means the object is in translational equilibrium.

Formula & Equations Used

Newton’s Second Law: F_net = ma

Horizontal force component: F_x = F cos θ

Vertical force component: F_y = F sin θ

Net horizontal force: ΣF_x

Net vertical force: ΣF_y

Net force magnitude: F_net = √((ΣF_x)² + (ΣF_y)²)

Net force direction: θ = atan2(ΣF_y, ΣF_x)

Acceleration: a = F_net / m

Equilibrium condition: ΣF = 0

Missing equilibrium force: F_unknown = −ΣF_known

Friction helper: f = μN

Example Problems & Step-by-Step Solutions

Example 1: Net force in one dimension

A box has a 20 N force to the right and a 12 N force to the left.

ΣF_x = 20 - 12 = 8 N

The net force is 8 N to the right.

Example 2: Newton’s Second Law

A 10 kg object accelerates at 2 m/s².

F = ma = 10 × 2 = 20 N

The net force is 20 N.

Example 3: Force components

A 50 N force acts at 30° above the positive x-axis.

F_x = 50 cos 30° ≈ 43.3 N

F_y = 50 sin 30° = 25 N

Force concepts students often mix up

Force is a vector: both size and direction matter.
Net force is not every force added as positives: opposite directions subtract through components.
Zero net force does not always mean zero velocity: it means zero acceleration.
Acceleration points with net force: not necessarily with velocity.
Free-body diagrams show forces on one object: avoid mixing forces acting on different objects.

FAQs

What is net force?

Net force is the vector sum of all forces acting on an object. It determines the object’s acceleration.

What formula does a force calculator use?

The central formula is Newton’s Second Law, F_net = ma. For 2D problems, forces are also broken into x- and y-components.

What does equilibrium mean?

Equilibrium means the net force is zero, so the object has no acceleration.

Why do force directions matter?

Forces are vectors. A force to the left can cancel a force to the right, and angled forces must be resolved into components.

Vectors, Scalars, & Displacement