## Introduction

In Physics, every physical entity can be measured in different ways. Every unit can be related to one another by performing unit conversions without violating the laws of physics and laws of nature.

Newton is the SI unit of force and kg is the unit of mass. According to Newton’s Second law of motion, force is directly proportional to the mass of the object on which force has been exerted. Thus we can say Newton and Kg are also directly proportional to each other, thus if we encounter any change in the unit of force in Newton it will result in a change in the unit of mass in Kg keeping the acceleration constant.

To arrive at a mathematical description for the relation between Kg and Newton, let us discuss the definition of Kg and Newton respectively. In this article, we try to explain to students the concept with great simplicity and clarity making the students grasp the knowledge with ease.

### Table of Content -

Introduction

Meaning of KG

Meaning of Newton

Derivation

Examples

Learning from the topic

Benefits of referring the notes

Frequently asked questions

### What is Kg?

There are seven fundamental units in physics, Kg is one of them. (Fundamental units are the units that are independent quantities, all other units are derived from them). The Abbreviation of Kilogram is Kg.

1 Kilogram is nearly equal to 1000grams. The kilogram is one of the basic units of metric systems.

### What is Newton?

Newton is the SI unit of Force. It is defined as the force required to accelerate an object of the mass of 1 kilogram (1kg) by 1m/s^{2} in the direction of applied force. In the CGS system, 1N is equal to 10^{5} Dyne. Dyne is the unit of Force in the CGS system.

### Derivation

Mathematically we can describe one Newton by using Newton’s second law of motion,

I.e.,

⇒ F = ma

⇒ 1 Newton = 1Kg x 1m/s^{2}

From the above expression, Newton is directly proportional to Kg. Therefore,

If the object under consideration is having negligible mass or considerably less mass then the force required in Newton will also be very less.

If the object an action-heavy, then the force required will also be more.

### 1N is Equal to How Many Kg?

We can not convert Kg to Newton, because Newton is a unit of Force whereas Kg is the unit of mass respectively. Conversion of units can be done for two identical scales but not for two different physical scales. So, we can give a relation for the two units, saying conversion of them will be the wrong term.

When an object is dropped from a certain height above the ground level, it will experience a force purely due to the acceleration due to gravity. While free fall the object will experience a force and the force experienced is known as Weight of the body/object and mathematically is given by:

W = mg ……..(1)

Now we can give a relation between newton and kg by analyzing how many Kg in one Newton. Let us assume that a 1Kg mass is dropped from a height above ground level with an initial velocity zero then the force experienced by the object is,

W = 1Kg x 9.81 m/s^{2} = 9.81 N

From the discussion of the relation between Kg and Newton, we have concluded that they are directly proportional to each other. Therefore, we write:

1Kg=9.81N

Therefore, 1 newton is equal to how much Kg or 1 kg how many newtons? The answer is 9.81N.

Similarly, If the question demands for 1 kg wt is equal to how many newtons? (Which is in terms of gravitational force) Then also the answer is either 9.8N or 9.81N or 10N because the value of acceleration due to gravity is considered depending upon the convenience.

### Example

1. The mass in Kg of an object that Weighs about 40N.

Ans: Given that weight of the object is 40N.

We are asked to find the mass of the object.

From the relation between Kg and Newton we have,

⇒ 1Kg = 9.81N

⇒ 1N = 0.102Kg

Thus,

⇒ 40 N = 40 x 0.102Kg = 4.077Kg

Therefore, the mass in kg of an object that weighs about 40N is 4.077.

An alternative method for calculating the mass of an object whose weight is given is as follows:

We know that,

⇒ 1N = 1Kgm/s^{2}

Therefore,

⇒40N = 40Kgm/s^{2}

We want to convert 40N into Kg, to do that divide the above expression by acceleration due to gravity, i.e., divide by 9.81 m/s^{2}

⇒ 40N = 40Kgms−2/9.81 ms^{−2}

⇒ 40N = 4.077kg

This is the required answer.

2. How many Newtons is 5Kg?

Ans: We know that 1kg = 9.81N, then:

⇒ 5Kg = 5 x 9.81 N = 49.05N

therefore,49.05N is 5Kg.

### Learning From the Topic -

Every object has a unit of measurement, which measure in different ways and forms

Kg and Newton are also forms of units of measurement

Kg is the unit of a mass where kg equals 1000 grams of mass of an object

Newton is the unit to measure the force required to accelerate an object of 1kg of mass.

Newton’s second law of motion is used to derive one newton. The second law says the rate of change of linear momentum of a body is directly proportional to the external force applied to the body in the direction of applied force.

Therefore, 1 Newton = 1Kg x 1m/s

^{2}

Read the full article to understand more about the concepts and try to solve a few practical questions to evaluate your level of understanding of the topic.

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## FAQs on Relation Between KG and Newton

**1. 1n(newton meter) is equal to how much Kg?**

We know that 1Kg is 9.81N therefore,

1N=0.102Kg.

**2. What is the kg-wt (kilogram weight) of an object?**

Kg-wt is the gravitational force experienced by an object. The relation between 1kg-wt and Newton is given by 1kg-wt =9.81N.

**3. What is the difference between mass and weight? are mass and weight the same?**

No. Mass and Weight are two different physical quantities. The mass of an object is its amount of matter, Weight of an object is the force exerted on the body due to gravity.

**4. How can we mathematically write the relation between newton and kg? **

The relation between newton and kg can be mathematically expressed as -

1N=Kg×ms^{2}

Here, N is the force of the newton

Kg denotes the mass of an object

m signifies the distance travelled in meters

And, s denotes the time duration in seconds.

From this, we understand that 1N is equal to the force needed to accelerate 1 kg of mass at the rate of 1 m/s^{2}