Calcylator
Newton's Second Law

Force equals mass
times acceleration (F = ma)

Calculate force in newtons from mass and acceleration, understand weight as a force, and see why a lift feels heavier when it speeds up.

Calcylator Editorial Team

Updated · 5 min read

Force from mass and acceleration

Force equals mass times acceleration, F = m × a. A 1,200 kg car accelerating at 2.5 m/s² needs a net force of 1,200 × 2.5 = 3,000 newtons.

Newton's second law =F = m × a
F:
net force in newtons (N)
m:
mass in kilograms
a:
acceleration in metres per second squared (m/s²)
One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².

  • Mass

    1,200 kg

  • Acceleration

    2.5 m/s²

  • Calculation

    1,200 × 2.5

Net force

3,000 N

This is the net force, after friction and other opposing forces are counted.

The Calcylator tool takes mass in kg and acceleration in m/s² and returns the force in newtons. A negative acceleration, such as braking, gives a negative force, meaning it acts opposite to the direction you called positive.

Net force, not just one push

The F in this law is the net force: the total of all forces on the object. If an engine pushes a car forward with 3,800 N while friction and air resistance pull back with 800 N, the net force is 3,000 N, and that is what accelerates it.

To go the other way, divide: acceleration = force ÷ mass, and mass = force ÷ acceleration. A 600 N net force on a 1,200 kg car gives only 0.5 m/s², a gentle acceleration.

Net force on a 1,200 kg car
Acceleration (m/s²)Net force (N)
11,200
22,400
56,000
1012,000

The table shows the straight-line relationship: twice the acceleration needs twice the force for the same mass.

Weight is a force too

Weight is the force of gravity on a mass, found with F = m × g. Using g of about 9.81 m/s², a 70 kg person weighs 70 × 9.81 = 686.7 N, and a 60 kg person weighs 588.6 N. Mass in kg stays the same everywhere, but weight in newtons changes with gravity.

A lift gives a second worked example. When it accelerates upwards at 1.5 m/s², the floor must push on a 70 kg person with 70 × (9.81 + 1.5) = 791.7 N, which feels heavier. When it accelerates downwards at 1.5 m/s², the push drops to 70 × (9.81 − 1.5) = 581.7 N, which feels lighter.

Where the formula is used

  • Vehicle design: estimating the force needed to reach a target acceleration.
  • Lifts and cranes: finding the cable tension when a load speeds up or slows down.
  • Sport: a 0.145 kg ball stopped by a glove from 40 m/s over 5 ms is decelerating at 8,000 m/s², a force of about 1,160 N.
  • Lab work: finding mass from a measured force and acceleration, for example on a trolley.

Engineers also use the formula backwards. If a 900 kg trolley is pushed with a net force of 450 N, it accelerates at 450 ÷ 900 = 0.5 m/s², so after 10 seconds from rest it moves at 5 m/s.

Notice that the ball example uses a very short time, which makes the acceleration, and therefore the force, large.

Common mistakes

  • Using grams instead of kilograms. 500 g is 0.5 kg.
  • Confusing mass with weight. Mass is in kg, weight is a force in newtons.
  • Using total push instead of net force, forgetting friction.
  • Entering acceleration in km/h per second without converting to m/s².
  • Forgetting the sign. A negative acceleration means slowing down in the chosen direction.

Common questions

How do I calculate force from mass and acceleration?

Multiply mass in kilograms by acceleration in metres per second squared. A 75 kg object accelerating at 3 m/s² needs 75 × 3 = 225 newtons. The Calcylator tool does this from your two inputs and gives the answer in newtons.

What is the unit of force?

The newton, written N. One newton is the force needed to accelerate a 1 kilogram mass at 1 metre per second squared. Bigger forces use kilonewtons, where 1 kN is 1,000 N, so 3,000 N is 3 kN.

How do I find the weight of an object in newtons?

Multiply its mass in kg by gravity, about 9.81 m/s² on Earth. A 70 kg person weighs 70 × 9.81 = 686.7 N. This is the same F = m × a formula, with gravitational acceleration as the acceleration.

Is force the same as net force?

The formula F = m × a gives the net force, which is the sum of all forces on the object. If an engine pushes with 3,800 N and friction pulls back with 800 N, the net force is 3,000 N and that sets the acceleration.

Can acceleration be negative in the calculator?

Yes. A negative acceleration means slowing down in the direction you chose as positive, and it gives a negative force. A 1,200 kg car braking at −4 m/s² has a net force of −4,800 N, acting against its motion.

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