What is the difference between mass and weight?

Mass is the amount of matter in an object (measured in kg) — it is constant regardless of location. Weight is the gravitational force on that mass: W = mg, where g = 9.81 m/s² on Earth's surface. On the Moon (g ≈ 1.62 m/s²), your weight is ~1/6 of Earth weight, but your mass stays the same.

What happens when net force is zero?

When net force = 0, acceleration = 0 (Newton's first law). This means the object either remains at rest or continues at constant velocity. This is called equilibrium. For example, a book on a table: gravity pulls down, normal force pushes up; net force = 0, acceleration = 0.

Newton's Second Law Calculator (F = ma)

Solve F = ma for force, mass, or acceleration with full unit conversion. Supports N, kN, lbf, kg, lb, m/s², ft/s², and g-units.

Solve for:

Presets:

Force (F)

Mass (m)

Acceleration (a)

Fill in two known values — the third is calculated automatically.

Newton's Three Laws of Motion

Law of Inertia

An object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted on by a net external force.

Law of Acceleration — F = ma

The net force acting on an object equals its mass multiplied by its acceleration. Direction of acceleration matches direction of net force.

Law of Action & Reaction

For every action force, there is an equal and opposite reaction force. Forces always occur in pairs acting on different objects.

Understanding F = ma

Solve for Force

F = m × a

Given mass and acceleration.

Solve for Mass

m = F / a

Given force and acceleration.

Solve for Acceleration

a = F / m

Given force and mass.

Isaac Newton published the second law in Principia Mathematica (1687). It tells us that acceleration and force are directly proportional, while mass and acceleration are inversely proportional. The SI unit of force, the newton (N), is defined as the force that gives a 1 kg mass an acceleration of 1 m/s².

Force vs Weight — The Key Difference

Mass is the amount of matter in an object (kg) — it never changes. Weight is the gravitational force on that mass: W = mg. On Earth g = 9.80665 m/s², on the Moon g ≈ 1.62 m/s², and in deep space g ≈ 0.

Object	Mass (kg)	Weight on Earth (N)	Weight on Moon (N)
Apple	0.1	0.98	0.16
Person (70 kg)	70	686.5	113.4
Car (1500 kg)	1,500	14,710	2,430
Elephant (5000 kg)	5,000	49,033	8,100

Worked Examples

Example 1 — Box push

m = 10 kg, a = 2 m/s²

F = 10 × 2

F = 20 N

Example 2 — Car 0–100 km/h in 8s

m = 1500 kg, a = 27.78/8 = 3.47 m/s²

F = 1500 × 3.47

F = 5,208 N ≈ 5.2 kN

Example 3 — Find mass

F = 1000 N, a = 5 m/s²

m = F / a = 1000 / 5

m = 200 kg

Example 4 — Find acceleration

F = 200 N, m = 50 kg

a = F / m = 200 / 50

a = 4 m/s²

Force Unit Conversion Table

Unit	Equivalent in Newtons	Notes
1 N (Newton)	1 N	SI unit; 1 kg·m/s²
1 kN (kilonewton)	1,000 N	Used in structural engineering
1 dyn (dyne)	0.00001 N	CGS unit; g·cm/s²
1 lbf (pound-force)	4.44822 N	Imperial unit of force
1 kgf (kilogram-force)	9.80665 N	Weight of 1 kg on Earth
1 ton-force (metric)	9,806.65 N	Used for large structures

Frequently Asked Questions

Newton's second law states that the net force acting on an object equals the product of its mass and acceleration: F = ma. The greater the net force, the greater the acceleration; the greater the mass, the smaller the acceleration for the same force.

Mass is the amount of matter in an object (measured in kg) — it is constant regardless of location. Weight is the gravitational force on that mass: W = mg. On the Moon (g ≈ 1.62 m/s²), your weight is about 1/6 of Earth weight, but your mass stays the same.

The SI unit of force is the newton (N), defined as 1 N = 1 kg·m/s². One newton is the force required to accelerate a 1 kg mass at 1 m/s². Other units include kN (1000 N), dyne (10⁻⁵ N), lbf (4.44822 N), and kgf (9.80665 N).

1 pound-force (lbf) = 4.44822 Newtons. To convert lbf to N, multiply by 4.44822. For example, 10 lbf = 44.48 N. To convert N to lbf, divide by 4.44822.

1 g = 9.80665 m/s² — the standard gravitational acceleration on Earth's surface. Fighter pilots experience up to 9g in tight turns; astronauts during launch experience about 3g.

Yes — Newton's second law applies everywhere in the universe (at non-relativistic speeds). In space there is no gravity anchor, so even tiny forces cause measurable acceleration. Spacecraft thrusters apply F = ma to change velocity.

F = ma is a special case of the impulse-momentum theorem. Since a = Δv/Δt and p = mv, we get F = Δp/Δt — force equals the rate of change of momentum. When mass is constant, this simplifies to F = ma.

When net force = 0, acceleration = 0 (Newton's first law). The object either remains at rest or continues at constant velocity — called equilibrium. Example: a book on a table has gravity pulling down and a normal force pushing up; net force = 0, acceleration = 0.

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