Units of Force

Team Physics - Examples.com
Created by: Team Physics - Examples.com, Last Updated: April 25, 2024

Units of Force

Units of force measure the intensity of a push or pull acting on an object, causing it to accelerate. The most commonly used unit is the Newton (N), defined as the force necessary to accelerate a one-kilogram mass by one meter per second squared. Other units include the dyne, used in the centimeter-gram-second (CGS) system, where one dyne is the force needed to accelerate a one-gram mass by one centimeter per second squared. Additionally, the pound-force (lbf) is used in the imperial system, equivalent to the force exerted by gravity on one pound of mass. Each of these units reflects the effect of force within different measurement systems.

Newton (N) is the standard unit of force in the International System of Units (SI). It is named after Sir Isaac Newton, in recognition of his work in classical mechanics. A Newton is defined as the force required to accelerate a one-kilogram mass at a rate of one meter per second squared (1 m/s²).

What is the Units of Force

Units of force measure the intensity of a push or pull acting on an object, causing it to accelerate. Force is a fundamental concept in physics, representing the interaction that causes an object to move, stop, or change direction. Understanding the units of force is crucial for students and educators alike, as it forms the basis for analyzing dynamics in mechanical systems. Here, we’ll explore the various units used to measure force, emphasizing their applications and conversions

SI Unit of Force

SI Unit : Newton (N)

The Newton (N) serves as the SI unit of force. It derives its name from Sir Isaac Newton, whose laws of motion laid the groundwork for classical mechanics. The definition of one Newton is quite specific: it is the force required to accelerate a one-kilogram mass at a rate of one meter per second squared.

1 Newton (N) = 1 kg×1 m/s²

Derivation of SI Unit of Force

Step-by-Step Derivation

Start by considering Newton’s Second Law of Motion, which asserts that the force acting on an object is a product of its mass and the acceleration it undergoes. This law is mathematically expressed as

F = m × a

Here, F represents force, m denotes mass, and a signifies acceleration.

  • Mass (m): The unit of mass in the International System of Units (SI) is the kilogram (kg).
  • Acceleration (a): Acceleration is measured as the rate of change in velocity, with its unit being meters per second squared (m/s²).

When you merge the units of mass and acceleration, the resulting unit of force emerges:

Unit of Force = kg × m/s²

This combination of kg·m/s² precisely defines one Newton (N). Thus, a Newton is the force necessary to accelerate a one-kilogram mass at a rate of one meter per second squared.

List of Force Units

Here’s a table listing various units of force, presented in the same format you requested:

Unit of ForceSymbol
Ton-force (metric)tf
Ton-force (short, US)tonf

Newton (N)

1N = 1kg⋅m/s²

The Newton is the SI unit of force named after Sir Isaac Newton. It measures the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared. This unit is universally used in science and engineering to quantify force.

Dyne (dyn)

1 dyn = 1g⋅cm/s² = 10^-5 N

A dyne is the unit of force in the centimeter-gram-second (CGS) system of units. It measures the force needed to accelerate a mass of one gram by one centimeter per second squared. It is primarily used in physics, particularly in contexts involving small forces.

Kilopond (kp)

1 kp = 9.80665 N

Also known as a kilogram-force (kgf), the kilopond measures force as the gravitational force exerted by a one-kilogram mass at Earth’s surface. It is used historically in engineering and still appears in some contexts, like rocketry and engine specifications.

Pound-force (lbf)

1 lbf = 4.44822 N

The pound-force is the unit of force in the imperial system, predominantly used in the United States. It measures the force exerted by gravity on one pound of mass. This unit is common in automotive and aerospace industries, as well as many fields of engineering and physics in the U.S.

Kip (kip)

1 kip = 1000 lbf = 4448.22 N

A kip is a unit of force used primarily in engineering to measure large forces, such as loads in building and bridge materials. It is equal to 1000 pounds-force and is common in architectural and engineering specifications, especially in the United States.

Ounce-force (ozf)

1 ozf = 1/16 lbf ≈ 0.278 N

The ounce-force is a smaller unit of force in the imperial system, used to measure smaller forces. It is often used in applications like measuring the force of springs and other light force applications.

Ton-force (metric) (tf)

1 metric tf = 1000 kgf = 9806.65 N

The metric ton-force is a unit of force based on the gravitational force exerted by a metric ton (1000 kilograms). It is occasionally used in engineering and industrial applications, particularly outside the United States.

Ton-force (short, US) (tonf)

1 short tonf = 2000 lbf = 8896.44 N

The short ton-force is used in the United States and is based on the gravitational force exerted by a short ton (2000 pounds). It’s applied in industries like shipping, construction, and other areas where large forces are measured.

Conversion of Force Units

Conversion of Force Units
Force UnitNewton (N)Dyne (dyn)Kilopond (kp)Pound-force (lbf)
Newton (N)1100,0000.101970.22481
Dyne (dyn)0.0000111.0197E-62.2481E-5
Kilopond (kp)9.80665980,66512.20462
Pound-force (lbf)4.44822444,8220.453591

Newton to Dyne

  • Conversion: 1 Newton = 100,000 dynes.
  • Example: To convert 2 Newtons to dynes, multiply by 100,000.2 N×100,000=200,000 dynes2N×100,000=200,000dynes.

Newton to Kilopond

  • Conversion: 1 Newton = 0.10197 kiloponds.
  • Example: To convert 5 Newtons to kiloponds, multiply by 0.10197.5 N×0.10197=0.50985 kp5N×0.10197=0.50985kp

Newton to Pound-force

  • Conversion: 1 Newton = 0.22481 pound-force.
  • Example: To convert 10 Newtons to pound-force, multiply by 0.22481.10 N×0.22481=2.2481 lbf10N×0.22481=2.2481lbf

Dyne to Newton

  • Conversion: 1 dyne = 0.00001 Newtons.
  • Example: To convert 500,000 dynes to Newtons, multiply by 0.00001.500,000 dyn×0.00001=5 N500,000dyn×0.00001=5N

Kilopond to Newton

  • Conversion: 1 kilopond = 9.80665 Newtons.
  • Example: To convert 3 kiloponds to Newtons, multiply by 9.80665.3 kp×9.80665=29.41995 N3kp×9.80665=29.41995N

Pound-force to Newton

  • Conversion: 1 pound-force = 4.44822 Newtons.
  • Example: To convert 4 pound-force to Newtons, multiply by 4.44822.4 lbf×4.44822=17.79288 N4lbf×4.44822=17.79288N

Effects of Force

Acceleration and Motion

Firstly, one of the primary effects of force is the acceleration of an object. According to Newton’s Second Law of Motion, a force applied to an object causes it to accelerate in the direction of the force. This relationship is expressed as F=m × a, where F is the force applied, m is the mass of the object, and a is the acceleration.

Change in Velocity

Additionally, force can change the velocity of an object. This change might involve an increase or decrease in the speed, or a change in direction, or both. For instance, when a car speeds up, slows down, or turns, it is experiencing different forces that alter its velocity.


Moreover, forces can cause deformation. When a force is applied to an object, it may change shape temporarily or permanently, depending on the material properties of the object and the magnitude of the force. Elastic deformation occurs when the object returns to its original shape after the force is removed, while plastic deformation results in permanent changes.

Change in State of Rest or Motion

Furthermore, force is instrumental in changing the state of rest or motion of an object. An object at rest will move if a force is applied, and a moving object will come to rest when a force opposes its motion. This effect is crucial in numerous mechanical systems and devices.

Balancing Forces and Equilibrium

In addition, forces play a key role in creating equilibrium conditions. When the net force acting on an object is zero, the object is said to be in a state of equilibrium, meaning it either remains at rest or moves with constant velocity. This principle is vital in statics and dynamics, fields concerned with analyzing forces in systems at rest and in motion, respectively.

Types of Forces 

Contact Forces

Contact forces are those that require physical contact between two interacting objects. They are predominant in everyday phenomena and mechanical operations. Key examples include:

  • Frictional Force: Acts tangentially across the surface of an object that moves or attempts to move across another. It opposes the direction of an object’s movement to prevent slipping.
  • Tension Force: Transmitted through a string, rope, cable, or wire when it is pulled tight by forces acting from opposite ends. It acts along the length of the wire and pulls equally on the objects attached to both ends.
  • Normal Force: Exerts perpendicularly from the surface of an object in contact with another surface. It supports the object and balances other forces acting upon it, such as gravity.
  • Air Resistance: A type of frictional force that acts against the motion of an object as it travels through the air, slowing it down.

Non-Contact Forces

Non-contact forces, also known as action-at-a-distance forces, occur even if the interacting objects are not physically touching. These forces can act over a distance through a field. The primary types include:

  • Gravitational Force: An attractive force that acts between all masses. The strength of this force is dependent on the mass of the objects and their distance from each other. It is why objects fall toward Earth and why planets orbit the sun.
  • Electromagnetic Force: Includes all forces caused by electric charges, both static and moving. It acts between charged particles and is responsible for practically all interactions that do not involve gravity. This force can be attractive or repulsive.
  • Strong Nuclear Force: The most powerful force, acting to bind protons and neutrons together in the nucleus of an atom. It operates at very short ranges and ensures the stability of the atomic nucleus.
  • Weak Nuclear Force: A force that causes nuclear decay processes. It is essential in particle physics, particularly in the disintegration of the neutron into a proton, an electron, and an anti-neutrino.


What are the units for impact of force?

Units for measuring the impact of force include the Newton (N) for direct force, Pascals (Pa) for pressure, and Joules (J) for energy transferred during the impact.

Is Joules a unit of force?

No, Joules is not a unit of force. It is the unit of energy, work, or amount of heat, measuring the impact of a force over distance.

Why is the unit of force called?

The unit of force is called the Newton (N), named after Sir Isaac Newton to honor his groundbreaking work in developing the laws of motion and gravity.

AI Generator

Text prompt

Add Tone

10 Examples of Public speaking

20 Examples of Gas lighting