What does net force mean in Newton’s Second Law?

Net force (ΣF) is the vector sum of all forces acting on an object. Newton’s Second Law uses net force: Fnet = m·a.

Can I use the Advanced (2D) mode without mass?

Yes. Choose the option to compute the net force vector only (ΣF) to get Fx, Fy, magnitude, and direction without mass.

How is the direction angle calculated?

Direction is computed using atan2(Fy, Fx) (or atan2(ay, ax) for acceleration), measured from the +x axis in degrees.

Newton’s Second Law Calculator

Solve F = m·a fast. Use Basic (1D) to solve for force, mass, or acceleration. Use Advanced (2D Vectors) to sum forces into Fₓ, Fᵧ, compute aₓ, aᵧ, magnitude, direction, and view a simple vector diagram + FBD summary.

Background

Newton’s Second Law relates net force, mass, and acceleration: F_net = m·a. In 2D, the same rule applies component-wise: Fₓ = m·aₓ, Fᵧ = m·aᵧ, and magnitudes/directions come from vector math.

Enter known values

Mode

Basic solves one unknown. Advanced lets you sum vectors and (optionally) compute acceleration from mass.

Solve for

Provide the other two values. We’ll compute the missing one.

Units

Values

Tip: acceleration is a signed value in 1D (use negative for opposite direction).

Compute

Choose ΣF only for pure vector addition, or Acceleration to compute aₓ, aᵧ, |a|, θ.

Mass (needed only for acceleration)

If you pick “ΣF only”, mass can be blank.

Provide forces as

Angles are measured in degrees from +x axis (standard math convention). Negative angles are allowed.

Net force components

We’ll compute |F| and direction θ, and optionally acceleration if mass is provided.

Options:

Round to sensible significant figures

Step-by-step working

Vector diagram (with projections)

FBD summary table (forces → components)

Quick picks:

Chips prefill fields and run the calculation.

Result:

No results yet. Enter inputs and click Calculate.

How to use this calculator

Pick a mode: Basic (1D) for one unknown, or Advanced (2D) for vectors.
Enter values: fill the inputs (or tap a Quick pick).
Click Calculate: get the result, steps, and optional visuals.
Reset: clears inputs and results.

How this calculator works

Basic (1D): uses F = m·a and rearranges for the missing variable.
Advanced (2D): sums forces into Fₓ, Fᵧ, then computes magnitude and direction.
If mass is provided: computes acceleration components aₓ = Fₓ/m, aᵧ = Fᵧ/m.

Formula & Equations Used

Newton’s Second Law: F_net = m·a

Rearrangements: a = F/m, m = F/a

2D components: Fₓ = m·aₓ, Fᵧ = m·aᵧ

Vector magnitude: |F| = √(Fₓ² + Fᵧ²), |a| = √(aₓ² + aᵧ²)

Direction: θ = atan2(Fᵧ, Fₓ) (and similarly for acceleration)

From magnitude + angle: Fₓ = F·cosθ, Fᵧ = F·sinθ

Example Problems & Step-by-Step Solutions

Example 1 — Solve force (Basic)

Given m = 12 kg and a = 2.5 m/s².
F = m·a = 12·2.5 = 30 N.

Example 2 — Net force vector (Advanced ΣF only)

Given Fₓ = 30 N and Fᵧ = 40 N.
|F| = √(30² + 40²) = √(2500) = 50 N, direction θ = atan2(40, 30) ≈ 53.13°.

Example 3 — Acceleration from forces (Advanced)

Given m = 10 kg and net force components Fₓ = 30 N, Fᵧ = 40 N.
aₓ = 30/10 = 3.0 m/s², aᵧ = 40/10 = 4.0 m/s².
|a| = √(3² + 4²) = 5.0 m/s², direction ≈ 53.13°.

Frequently Asked Questions

Q: What does “net force” mean?

It’s the vector sum of all forces acting on the object (ΣF). That’s the force used in F = m·a.

Q: Can I use this without mass in Advanced mode?

Yes. Choose “Net force vector only (ΣF)” to compute Fₓ, Fᵧ, |F|, and direction without mass.

Q: What direction convention does the angle use?

Angles are measured in degrees from the +x axis, using atan2 (standard math convention). Negative angles are allowed.

Vectors, Scalars, & Displacement