50
50
N
10
kg
5
m/s²
0.05
kN
11.2405
lbf
50
50
N
10
kg
5
m/s²
0.05
kN
11.2405
lbf
Newton's Second Law of Motion is the cornerstone of classical mechanics, establishing the quantitative relationship between force, mass, and acceleration: $$F = ma$$. This law tells us that the net force acting on an object equals its mass multiplied by its acceleration. Rearranging this equation lets us solve for any one of the three variables when the other two are known: $$a = \frac{F}{m}$$ and $$m = \frac{F}{a}$$.
Published in Isaac Newton's Principia Mathematica (1687), this law transformed our understanding of motion from qualitative description to precise mathematical prediction. It applies to everything from subatomic particles to spacecraft, provided speeds remain well below the speed of light. Engineers use it to design bridges, physicists use it to model collisions, and biomechanists use it to analyze human movement.
This calculator provides a three-mode solver: choose which variable to find, enter the other two, and get an instant result. This flexibility makes it ideal for homework, engineering checks, and quick what-if analyses across any discipline that involves forces and motion.
The calculator rearranges Newton's Second Law based on your selection:
Solve for Force: $$F = m \times a$$
Solve for Acceleration: $$a = \frac{F}{m}$$
Solve for Mass: $$m = \frac{F}{a}$$
All inputs use SI units: force in newtons (N), mass in kilograms (kg), and acceleration in meters per second squared (m/s²). The law assumes a constant net force and non-relativistic speeds. For objects subject to multiple forces, $$F$$ represents the net (resultant) force — the vector sum of all individual forces.
When solving for force, a larger result means more push or pull is needed. When solving for acceleration, a larger force-to-mass ratio yields faster speed change. When solving for mass, the result tells you the inertia of the object that would produce the observed acceleration under the given force. Always ensure $$F$$ is the net force, not just one of several forces acting on the body.
Inputs
Results
F = 50 × 3 = 150 N. A moderate force, roughly the weight of a 15 kg object.
Inputs
Results
a = 8000 / 2000 = 4 m/s². The car gains 4 m/s of speed every second.
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass: $$\vec{F}_{net} = m\vec{a}$$. In words, more force means more acceleration, and more mass means less acceleration for the same force.
Applied force is a single force you exert on an object. Net force is the vector sum of all forces acting on it — gravity, friction, normal force, applied force, air resistance, etc. Newton's Second Law uses the net force. If forces cancel out, net force is zero and acceleration is zero (equilibrium).
Yes. Newton's Second Law works everywhere in the universe at non-relativistic speeds. In space, with negligible friction and air resistance, even tiny forces produce measurable acceleration. This is how ion thrusters work — they apply small forces over long periods to achieve high velocities.
When mass approaches zero, even a small force produces enormous acceleration ($$a = F/m$$). In practice, every real object has nonzero mass. At the subatomic scale, quantum mechanics supersedes classical mechanics, and the concept of force is replaced by quantum field interactions.
Yes. Negative acceleration (deceleration) simply means the object is slowing down relative to the chosen positive direction. The force causing this deceleration acts opposite to the direction of motion, such as braking friction on a car.
Newton's First Law (inertia) states that an object remains at rest or in uniform motion unless acted upon by a net force. The Second Law quantifies what happens when there is a net force: it produces acceleration proportional to the force and inversely proportional to the mass. The First Law is actually a special case of the Second Law where $$F_{net} = 0$$.
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