# Confusion about Units of Mass and Weight

by Ron Kurtus (revised 18 June 2020)

There can be confusion about the units of mass and weight used in scientific measurements, as well as everyday life. For example, it is common to refer to both kilograms and pounds as weight. However, in technical terms they are both actually units of mass.

The SI or metric system definitions state that the kilogram is a unit of mass and the newton as the unit of force or weight. Also, in the British or American standards, the avoirdupois pound is the unit of mass, while pound can also be used as weight.

As a student of science, you need to be make sure you understand the definitions used for mass and weight, especially when converting between the systems.

Questions you may have include:

• What is the confusion with kilograms?
• What is the confusion with pounds?
• What about converting between systems?

This lesson will answer those questions. Useful tool: Units Conversion

## Confusion concerning kilograms

A kilogram is defined as the SI or metric unit of mass. Unfortunately, many people—and even some textbooks—state weight in terms of kilograms. This can cause confusion when trying to make scientific calculations.

The official metric unit of force is the newton (N), which is the force required to accelerate 1 kg-mass to 1 meter/second-squared. Weight is then the resulting force when a mass is accelerated by gravity, as stated in newtons.

However, most people do not use newtons for weight in everyday measurements. When they say "an object weighs a kilogram", they really mean kilogram-force (kg-f), which is about 9.8 times the kilogram-mass.

Although it is inconvenient, in scientific work you should refer to an object as kilogram-mass (kg) and kilogram-weight (kg-f) as the safest approach.

Note that designating kilogram-mass as kg-m could result in confusion with kg-meters.

### Weight-mass relationship

The relationship between the weight of an object and its mass in the metric system is:

W = mg

where

• W is weight in newtons (N) or kilograms-force (kg-f)
• m is the mass in kilograms (kg)
• g is the acceleration due to gravity; on the Earth, g = 9.8 m/s2

Thus, if an object has a mass of 50 kg, its weight is 490 N or 490 kg-force:

W = mg

490 kg-f = (50 kg)*(9.8 meters/s2)

## Confusion concerning pounds

The avoirdupois pound (lb) is legally defined as a measure of mass in the British Imperial measurement system, as well as the United States system of units.

However, in common use, people often state weight in terms of pounds. Also, some Physics textbooks say that a pound is a unit of weight or force, as in foot-pounds for torque.

This can result in confusion when making calculations. Calling the mass of the object a pound-mass could alleviate that confusion.

### Weight-mass relationship

The relationship between the weight of an object and its mass in the English/American system is:

W = mg

where

• W is weight in pounds-force (lb-f)
• m is the mass in pounds-mass (lb)
• g is the acceleration due to gravity; on the Earth, g = 32 ft/s2.

Thus, if an object weighs 64 lbs, its mass is 2 pounds-mass:

W = mg

64 lb-f = (2 lb)*(32 ft/s2)

## Conversion between systems

When you convert between the British/American system and the metric system, you need to be careful which definitions of weight and mass are used for the conversion.

• One kilogram-force is approximately 2.2 pound-force
• The international avoirdupois pound is defined as about 0.45 kilogram-mass

Conversion tables:

Kilograms to Pounds

Pounds to Kilograms

## Summary

It is important to state units of mass and weight in a manner that will not cause confusion in calculations.

In the metric system, the unit of mass is the kilogram. Weight is stated as newtons, kilograms-force, or kilograms-weight, not simply kilograms.

In the American system, the unit of mass is the pound-mass. Pounds as weight is commonly used, but it really refers to pound-force.

As a student of science, you need to be careful in what you call things.

Use exact words in scientific work

## Resources and references

Ron Kurtus' Credentials

### Websites

United States customary units - Wikipedia

Mass and Weight - Engineering Toolbox

Pound (mass) - Wikipedia

Pound (force) - Wikipedia

Slug (unit) - Wikipedia

Gravity Resources

### Books

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