What is Newton's second law?

Newton's second law states that the net force on an object equals its mass multiplied by its acceleration: F = ma. It is the bridge between forces and motion — tell it what forces act on something and it tells you how the motion changes. The law also explains why the same push has such different effects on different objects: acceleration is force divided by mass, so a heavy object responds far less to the same force.

What is a newton, and how big is one?

A newton is defined as exactly the force required to accelerate a mass of one kilogram at one metre per second squared, so 1 N = 1 kg·m/s². In everyday terms it is close to the weight of a small apple resting in your hand — about 100 grams under Earth's gravity weighs 0.98 N. A one-kilogram bag of sugar weighs about 9.8 N, and an average adult weighs somewhere around 700 to 800 N.

What is the difference between mass and weight?

Mass is how much matter an object contains and never changes, no matter where the object is. Weight is a force — specifically the force gravity exerts on that mass — and it changes with local gravity, following W = mg. A 70 kg person is 70 kg everywhere, but weighs about 687 N on Earth, 113 N on the Moon and 1,735 N on Jupiter. Confusion arises because bathroom scales are labelled in kilograms while actually measuring force.

How do I calculate force from mass and acceleration?

Multiply them, having first converted both into SI units. A 1,500 kg car accelerating at 3 m/s² needs 1,500 × 3 = 4,500 N, which is 4.5 kN or about 1,012 pounds-force. The commonest mistake is mixing units — using grams instead of kilograms understates the force by a factor of a thousand, and using g-force instead of m/s² overstates it by nearly ten. This calculator converts everything for you before multiplying.

What does 'net force' mean, and why does it matter?

F = ma applies to the net force — the vector sum of every force acting on the object, not just the one you are applying. Push a crate with 200 N while friction resists with 150 N and the net force is only 50 N, so that is what determines the acceleration. This is also why an object can have huge forces acting on it and not accelerate at all: a book resting on a table has gravity pulling down and the table pushing up, and because they cancel, the net force is zero.

What is g-force, and how does it relate to acceleration?

G-force expresses acceleration as a multiple of standard gravity, which is exactly 9.80665 m/s². So 1 g is 9.81 m/s², 2 g is 19.6 m/s² and so on. It is popular in aviation, motorsport and aerospace because it describes what a body actually feels. A sharp car corner might reach 1 g, a roller coaster 4 to 5 g, and fighter pilots train to withstand around 9 g. Enter a value in g-force in this calculator and it converts automatically.

What is the difference between pounds and pounds-force?

A pound (lb) is a unit of mass equal to exactly 0.45359237 kg. A pound-force (lbf) is a unit of force, defined as the weight of one pound of mass under standard gravity, which works out to exactly 4.4482216152605 N. The two are numerically equal at Earth's surface, which is precisely why they get confused — a 10 lb mass weighs 10 lbf here, but on the Moon it would still be 10 lb of mass while weighing only about 1.7 lbf.

Why does the same force move a light object faster than a heavy one?

Because acceleration is force divided by mass, so mass sits in the denominator. Apply 100 N to a 10 kg object and it accelerates at 10 m/s²; apply the same 100 N to a 100 kg object and it manages only 1 m/s². Mass is effectively a measure of resistance to being accelerated — physicists call this inertia. It is why an empty shopping trolley darts forward at a touch while a full one needs a determined shove.

Does F = ma always work?

It works superbly for everyday objects at everyday speeds, which covers nearly every practical problem. It breaks down in two regimes. At speeds approaching light, relativity takes over and effective inertia grows without limit, so the more general form F = Δp/Δt is required. At atomic scale, quantum mechanics replaces it entirely. It also needs care when mass itself changes during the motion, as with a rocket burning fuel, where the momentum form is again the correct tool.

Force Calculator (F = ma)

Calculate force, mass or acceleration from Newton's second law, F = m × a — the single equation that connects a push to the motion it produces. Enter any two of the three quantities and this calculator returns the third, converts it into every unit you are likely to need, and animates the result so ...

F = m × a

SOLVE FOR

MASS

ACCELERATION

EVERYDAY EXAMPLES

FORCE REQUIRED

4,500.00 N

KILONEWTONS

4.500

POUNDS-FORCE

1,011.64

KILOGRAMS-FORCE

458.87

Mass

1,500.000 kg

Acceleration

3.000 m/s²

Force

4,500.000 N

As g-force

0.306 g

Weight on Earth

14,715.00 N

Force ÷ weight

0.306 ×

STEPS

Convert to SI: mass = 1,500.0000 kg, acceleration = 3.0000 m/s²

Apply Newton's second law: F = m × a

F = 1,500.0000 × 3.0000 = 4,500.0000 N

FORCE IN ACTION

TIME

0.00 s

DISTANCE

0.00 m

SPEED

0.00 m/s

Acceleration is inversely proportional to mass. Halve the mass and the same push produces twice the acceleration; double it and the object crawls.

HOW BIG IS THIS FORCE?

WHAT THIS MASS WEIGHS ELSEWHERE

Earth

14,715.0 N

Moon

2,430.0 N

Mars

5,580.0 N

Venus

13,305.0 N

Jupiter

37,185.0 N

Mass never changes — weight does, because weight is just the force gravity applies: W = m × g.

Live simulation · updates as you type

Created with❤️byeaglecalculator.com

HOW TO USE

1
Choose what you want to find using the SOLVE FOR buttons: Force, Mass or Acceleration. The input fields change to ask for whichever two quantities the calculation needs.
2
Enter your values and pick the units beside each field. Mass can be in kilograms, grams, tonnes or pounds; acceleration in m/s², g-force or ft/s²; force in newtons, kilonewtons, pounds-force or kilograms-force. Everything is converted to SI before the maths runs.
3
Read the result in the black box, with the three most useful alternative units underneath. The key-facts grid below restates all three quantities in SI, plus the object's weight on Earth and how your force compares to that weight.
4
Study the simulation on the right: the block is sized by mass and the gold arrow by force. Watch the three-lane race to see how the same force moves different masses, then check the logarithmic scale to see how your force compares with everyday and extreme examples.

THE FORMULAS

Newton's second lawF = m × a

Solve for massm = F ÷ a

Solve for accelerationa = F ÷ m

Weight (force of gravity)W = m × g

One newton1 N = 1 kg·m/s²

Pound-force1 lbf = 4.448222 N

Kilogram-force1 kgf = 9.80665 N

Momentum formF = Δp ÷ Δt

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Last updated: July 28, 2026 · Formula verified · Eagle-eyed accuracy for every calculation.