Mass vs. Weight
Mass vs. weight  the Gravity Force.
Mass and Weight are two often misused and misunderstood terms in mechanics and fluid mechanics.
The fundamental relation between mass and weight is defined by Newton's Second Law . Newton's Second Law can be expressed as
F = m a (1)
where
F = force (N, lb_{f} )
m = mass (kg, slugs )
a = acceleration (m/s^{2}, ft/s^{2})
Mass
Mass is a measure of the amount of material in an object, being directly related to the number and type of atoms present in the object. Mass does not change with a body's position, movement or alteration of its shape, unless material is added or removed.
 an object with mass 1 kg on earth would have the same mass of 1 kg on the moon
Mass is a fundamental property of an object, a numerical measure of its inertia and a fundamental measure of the amount of matter in the object.
 mass electron 9.1095 10 ^{ 31 } kg
 mass proton 1.67265 10 ^{ 27 } kg
 mass neutron 1.67495 10 ^{ 27 } kg
Weight
Weight is the gravitational force acting on a body mass. The generic expression of Newton's Second Law (1) can be transformed to express weight as a force by replacing the acceleration  a  with the acceleration of gravity  g  as
F_{g } = m a_{g } (2)
where
F_{g } = gravitational force  or weight (N, lb_{f} )
m = mass (kg, slugs (lb_{m} ))
a_{g } = acceleration of gravity on earth (9.81 m/s^{2}, 32.17405 ft/s^{2})
Example  The Weight of a Body on Earth vs. Moon
The acceleration of gravity on the moon is approximately 1/6 of the acceleration of gravity on the earth. The weight of a body with mass 1 kg on the earth can be calculated as
F_{g_ } _{earth } = (1 kg) (9.81 m/s^{2})
= 9.81 N
The weight of the same body on the moon can be calculated as
F_{g_ } <_{moon } = (1 kg) ( (9.81 m/s^{2}) / 6)
= 1.64 N
The handling of mass and weight depends on the systems of units used. The most common unit systems are
 the International System  SI
 the British Gravitational System  BG
 the English Engineering System  EE
One newton is
 ≈ the weight of one hundred grams  101.972 gf (g_{F } ) or 0.101972 kgf (kg_{F } or kilopond  kp (pondus is latin for weight))
 ≈ halfway between onefifth and onefourth of a pound  0.224809 lb or 3.59694 oz
The International System  SI
In the SI system the mass unit is the kg and since the weight is a force  the weight unit is the Newton ( N ). Equation (2) for a body with 1 kg mass can be expressed as:
F_{g } = (1 kg) (9.807 m/s^{2})
= 9.807 (N)
where
9.807 m/s^{2}= standard gravity close to earth in the SI system
As a result:
 a 9.807 N force acting on a body with 1 kg mass will give the body an acceleration of 9.807 m/s^{2}
 a body with mass of 1 kg weights 9.807 N
 More about the SI System  A tutorial introduction to the SIsystem.
The Imperial British Gravitational System  BG
The British Gravitational System (Imperial System) of units is used by engineers in the Englishspeaking world with the same relation to the foot  pound  second system as the meter  kilogram  force second system (SI) has to the meter  kilogram  second system. For engineers who deals with forces, instead of masses, it's convenient to use a system that has as its base units length, time, and force , instead of length, time and mass .
The three base units in the Imperial system are foot, second and poundforce .
In the BG system the mass unit is the slug and is defined from the Newton's Second Law (1) . The unit of mass, the slug , is derived from the poundforce by defining it as the mass that will accelerate with 1 foot per second per second when a 1 poundforce acts upon it:
1 lb_{f} = (1 slug) (1 ft/s^{2})
In other words, 1 lb_{f} (poundforce) acting on 1 slug of mass will give the mass an acceleration of 1 ft/s ^{2}.
The weight (force) of the mass can be calculated from equation (2) in BG units as
F_{g } (lb_{f} ) = m (slugs) a_{g } (ft/s^{2})
With standard gravity  a_{g } = 32.17405 ft/s^{2}  the weight (force) of 1 slug mass can be calculated as
F_{g } = (1 slug) ( 32.17405 ft/s^{2})
32.17405 lb_{f}
The English Engineering System  EE
In the English Engineering system of units the primary dimensions are are force, mass, length, time and temperature. The units for force and mass are defined independently
 the basic unit of mass is poundmass (lb_{m} )
 the unit of force is the pound (lb) alternatively poundforce (lb_{f} ).
In the EE system 1 lb_{f} of force will give a mass of 1 lb_{m} a standard acceleration of 32.17405 ft/s^{2}.
Since the EE system operates with these units of force and mass, the Newton's Second Law can be modified to
F = m a / g_{c } (3)
where
g_{c } = a proportionality constant
or transformed to weight (force)
F_{g } = m a_{g } / g_{c } (4)
The proportionality constant g_{c } makes it possible to define suitable units for force and mass. We can transform (4) to
1 lb_{f} = (1 lb_{m} ) (32.174 ft/s^{2}) / g_{c }
or
g_{c } = (1 lb_{m} ) (32.174 ft/s^{2}) / (1 lb_{f} )
Since 1 lb_{f} gives a mass of 1 lb_{m} an acceleration of 32.17405 ft/s^{2} and a mass of 1 slug an acceleration of 1 ft/s^{2}, then
1 slug = 32.17405 lb_{m}
Example  Weight versus Mass
The mass of a car is 1644 kg . The weight can be calculated:
F_{g } = (1644 kg) (9.807 m/s^{2})
= 16122.7 N
= 16.1 kN
 there is a force (weight) of 16.1 kN between the car and the earth.
 1 kg gravitation force = 9.81 N = 2.20462 lb_{f}
Weight Converter
Kg to lb Converter
Related Topics

Basics
Basic engineering data. SIsystem, unit converters, physical constants, drawing scales and more. 
Fluid Mechanics
The study of fluids  liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time. 
Mechanics
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more. 
Statics
Forces acting on bodies at rest under equilibrium conditions  loads, forces and torque, beams and columns.
Related Documents

Acceleration
Change in velocity vs. time used. 
Acceleration of Gravity and Newton's Second Law
Acceleration of gravity and Newton's Second Law  SI and Imperial units. 
Acceleration Units Converter
Converting between units of acceleration. 
Acetone  Density and Specific Weight
Online calculator, figures and tables showing density and specific weight of acetone at temperatures ranging from 95 to 275 °C (138 to 530 °F) at atmospheric and higher pressure  Imperial and SI Units. 
Air  Drying Force
The drying force of air depends on the air moisture holding capacity and the water surface to air evaporation capacity. 
Ammonia Gas  Density vs. Temperature and Pressure
Online calculator with figures and tables showing density and specific weight of ammonia for temperatures ranging 50 to 425 °C (50 to 800 °F) at atmospheric and higher pressure  Imperial and SI Units. 
Apothecaries' Weight System
Apothecaries' fluid and weight system with ounces, drachms, grains, scruples and more. 
Argon  Density and Specific Weight
Online calculator, figures and tables showing density and specific weight of argon, Ar, at varying temperature and pressure  Imperial and SI Units. 
Benzene  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and table showing density and specific weight of benzene, C_{6}H_{6}, at temperatures ranging from 5 to 325 °C (42 to 620 °F) at atmospheric and higher pressure  Imperial and SI Units. 
Beryllium  Specific Heat vs. Temperatures
Specific heat of beryllium related to temperature. 
Bodies Moving on Inclined Planes  Acting Forces
Required forces to move bodies up inclined planes. 
Bollard Forces
Friction, load and effort forces acting in ropes turned around bollards. 
Butane  Density and Specific Weight vs. Temperature and Pressure
Online calculators, figures and tables showing density and specific weight of liquid and gaseous butane, C_{4}H_{10}, at varying temperarure and pressure, SI and Imperial units. 
Center Mass
Calculate position of center mass. 
Center of Gravity
A body and the center of gravity. 
Density vs. Specific Weight and Specific Gravity
An introduction to density, specific weight and specific gravity. 
Ethane  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of ethane, C_{2}H_{6}, at varying temperature and pressure  Imperial and SI Units. 
Ethylene  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of ethylene, C_{2}H_{4}, at varying temperature and pressure  Imperial and SI Units. 
Floors  Live Loads
Floors and minimum uniformly distributed live loads. 
Force
Newton's third law  force vs. mass and acceleration. 
Forces acting on Body Moving on a Horizontal Plane
The forces acting on bodies moved in horizontal planes. 
Gallons vs. Pounds of Water Converter
 and vice versa. 
Gases  Densities
Densities and molecular weights of common gases like acetylene, air, methane, nitrogen, oxygen and others. 
Gears
Gears effort force vs. load force. 
Helium  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of helium, He, at varying temperature and pressure  Imperial and SI Units. 
Hot Air Balloons  Calculate the Lifting Force
Calculate hot air ballon lifting force. 
Human Body Composition
Composition of the human body. 
Levers
Use levers to magnify forces. 
Lifting Wheels
Loads and effort force with lifting wheels. 
Liquids  Densities
Densities of common liquids like acetone, beer, oil, water and more. 
Mass Moment of Inertia
The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation  the Radius of Gyration. 
Methane  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of methane, CH_{4}, at temperatures ranging from 160 to 725 °C (260 to 1300 °F) at atmospheric and higher pressure  Imperial and SI Units. 
Methanol  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of methanol,CH_{3}OH, at varying temperature and pressure  Imperial and SI Units. 
Nitrogen  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of nitrogen, N_{2}, at temperatures ranging from 175 to 1325 °C (280 to 2400 °F) at atmospheric and higher pressure  Imperial and SI Units. 
Ounces and Pounds vs. Grams
Converting ounces (ozs.) and pounds (lbs.) to grams (g). 
Oxygen  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of oxygen, O_{2}, at varying temperature and pressure  Imperial and SI Units. 
Propane  Density and Specific Weight vs. Temperature and Pressure
Online calculator, figures and tables showing density and specific weight of propane, C3H8, at temperatures ranging from 187 to 725 °C (305 to 1300 °F) at atmospheric and higher pressure  Imperial and SI Units. 
Pulleys
Pulleys, blocks and tackles. 
SI System
An introduction to the SI metric system. 
Solids  Densities
Densities of selected solids. 
Support Reactions  Equilibrium
Static equilibrium is achieved when the resultant force and resultant moment equals to zero. 
Threaded Rods  Proof Loads  Metric Units
Proof load capacities of metric threaded steel rods. 
Toluene  Density and Specific Weight vs. Teemperature and Pressure
Density and specific weight of liquid toluene. 
Troy Weight
Weight unit for preciuos metals like gold and silver. 
Universal Gravitational Law
Gravitational attraction between two objects vs. mass of the objects and the distance between them. 
Water  Density, Specific Weight and Thermal Expansion Coefficients
Definitions, online calculator and figures and tables with water properties like density, specific weight and thermal expansion coefficient of liquid water at temperatures ranging 0 to 360°C (32 to 680°F).