# Confusion about Mass and Weight Units

by Ron Kurtus (14 September 2016)

There seems to be some confusion concerning the uses of the units for mass and weight.

For example, everyday use of kilograms for weight in the metric or SI system and the use of the English or American system pounds for mass are incorrect and can cause confusion in scientific calculations.

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

Questions you may have include:

• What is the confusion with kilograms?
• What is the confusion with pounds?
• What is the weight/mass relationship?

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

## Confusion with kilograms

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

The official metric unit of weight is the newton (N). 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 or kilogram-weight, which is 9.8 times the kilogram-mass.

### Weight-mass relationship

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

W = mg or m = W/g

where

• W is weight in newtons (N), kilograms-force, or kilograms-weight
• m is the mass in kilograms
• g is the acceleration due to gravity in m/s2

On the Earth, g = 9.8 m/s2.

Thus, if an object has a mass of 50 kg, its weight is 540 N or 540 kg-force.

## Confusion with pounds

The pound is the standard unit of weight in the English or America system of measurements. The slug is the standard unit for mass in this system. However, many people use the word pounds to denote mass, instead of slugs. This can result in confusion when making calculations.

Calling the mass pound-mass could alleviate that confusion.

## Weight-mass relationship

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

W = mg or m = W/g

### Metric system

In the metric system:

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

Thus, if an object has a mass of 50 kg, its weight is 540 N or 540 kg-force.

### English/American system

In the English/American system:

• W is weight in pounds (lbs)
• m is the mass in slugs or pounds-mass
• g is the acceleration due to gravity in m/s2; On the Earth, g = 32 ft/s2.

Thus, if an object weighs 64 lbs, its mass is 2 slugs or 2 pounds-mass.

## 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 weight is the pound. Mass is stated as slugs or pounds-mass, not simply pounds.

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

Use exact words

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