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Newton's Second Law

General

Newton's Second Law of Motion

The physical law stating that the net force acting on an object equals its mass times its acceleration (F = ma), describing how forces change an object's motion.

Definition

Newton's Second Law of Motion is one of the three foundational laws of classical mechanics formulated by Isaac Newton. It states that the net force acting on an object is equal to the object's mass multiplied by its acceleration. In other words, force is what causes an object's velocity to change, and the amount of acceleration produced depends directly on how much force is applied and inversely on how much mass resists that force.

This relationship explains everyday physical intuition: pushing a shopping cart is easy because it has low mass, while pushing a stalled car takes much more force because of its much greater mass. Newton's Second Law lets you calculate any one of force, mass, or acceleration when the other two are known, which is exactly what the Force Calculator and Acceleration Calculator do.

The law also underlies the concept of Momentum, since force can be equivalently defined as the rate of change of momentum over time — a more general form of the same principle that also applies when mass itself is changing, such as a rocket burning fuel.

Formula

F = m × a

Where F is net force (in newtons, N), m is mass (in kilograms, kg), and a is acceleration (in meters per second squared, m/s²).

Rearranged forms:

a = F ÷ m

m = F ÷ a

Worked Example

A car with a mass of 1,200 kg accelerates from rest to 20 m/s in 10 seconds. First find the acceleration:

a = (20 − 0) ÷ 10 = 2 m/s²

Now apply Newton's Second Law to find the net force required:

F = m × a = 1,200 kg × 2 m/s² = 2,400 N

The engine and drivetrain must produce a net forward force of 2,400 newtons to achieve that acceleration, assuming friction and air resistance are already accounted for in the net force.

Key Things to Know

  • Force is a vector: it has both magnitude and direction, and acceleration always points in the same direction as the net force applied.
  • Net force matters, not individual forces: if multiple forces act on an object, F = ma uses the sum (net) of all forces, not any single force in isolation.
  • Heavier objects need more force to reach the same acceleration: doubling an object's mass requires double the force to produce identical acceleration.
  • Connects directly to Momentum: force can also be expressed as the rate of change of momentum with respect to time, which is the more general version of this law.
  • Applies at everyday speeds, not relativistic ones: for objects moving at a significant fraction of the speed of light, Einstein's relativistic mechanics replaces Newton's classical formula.

Related Calculators

Force Calculator →Calculate force using Newton's second law, F = m × a. Enter mass and acceleration to get the resulting force in newtons instantly, with a step-by-step breakdown shown.
Acceleration Calculator →Calculate acceleration from initial velocity, final velocity, and time. Get instant results in m/s², plus the change in velocity, with a step-by-step breakdown shown.

Related Terms

MomentumLinear Momentum

Frequently Asked Questions

Newton's Second Law says that the harder you push or pull an object (the more force you apply), the faster it speeds up, and the heavier the object, the less it accelerates for the same force. Mathematically, force equals mass times acceleration (F = ma).
Force is measured in newtons (N), where 1 newton is the force needed to accelerate a 1 kilogram mass at 1 meter per second squared (1 N = 1 kg·m/s²). Mass is measured in kilograms and acceleration in meters per second squared.
Newton's First Law describes what happens when there is no net force — an object stays at rest or moves at constant velocity. Newton's Second Law describes what happens when there IS a net force, quantifying exactly how much an object accelerates as a result.
Yes — the formula F = ma can be rearranged to solve for any of the three variables: mass equals force divided by acceleration (m = F/a), and acceleration equals force divided by mass (a = F/m). The Force Calculator and Acceleration Calculator both apply this same relationship.
Yes — for an object in free fall, the only force acting on it (ignoring air resistance) is gravity, so F = ma becomes F = mg, where g is the acceleration due to gravity (about 9.8 m/s² on Earth). This is why all objects, regardless of mass, fall at the same rate in a vacuum.