# Relationship Between Mass, Weight and Gravity

by Ron Kurtus (updated 29 May 2023)

The gravity equation shows the relationship between mass, weight and acceleration due to gravity.

The mass of an object is the amount of matter it contains, regardless of its volume or any forces acting on it. Gravity is a force that attracts objects toward the Earth. The weight of the object is defined as the force caused by gravity on a mass.

Weight can vary slightly at different places on the Earth, due to differences in the force from gravity at the various locations. The weight of an object is much different on various planets and moons.

Questions you may have include:

• What is the gravity equation?
• What are the units of measurement?
• What is weight on the Moon?

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

## Gravity equation

The gravity equation defines the relationship between weight, mass, and gravity:

W = mg

where

• W is the weight on Earth in newtons (N) or pound-force (lb-f)
• m is the mass in kilograms (kg) or pounds (lb)
• g is the acceleration due to the force of gravity (g = 9.8 meters/s2 or 32 ft/s2 on Earth)

The gravity equation defines weight as the force applied on an object due to gravity.

## Units of measurement

The major systems for the units of measurement for mass, weight, and force of gravity are the:

• International System of Units (SI) or metric system
• British Imperial and United States system of measurements.

### SI system

#### Mass

The kilogram (kg) is the SI unit of mass and it is the almost universally used standard mass unit.

#### Force

The official metric unit of force is the newton (N), which is the force required to accelerate a mass of 1 kg to 1 meter/s2. Kilogram-force (kg-f) is also used to designate force.

#### Gravity and weight

Since the acceleration due to the force of gravity (g) equals aproximately 9.8 meters/s2, the weight of an object with a mass of 1 kilogram is 9.8 newtons under standard conditions on the Earth's surface.

Since W = mg,

W = (1 kilogram)*(9.8 meters/s2) = 9.8 newtons

### British or US system

#### Mass

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

#### Gravity and weight

The unit of weight is a pound-force (lb-f), which is equal to the force of gravity exerted on a mass of one avoirdupois pound at the surface of Earth.

The acceleration due to the force of gravity (g) equals aproximately 32 feet/s2.

Since W = mg,

W = (1 lb)*(32 ft/s2) = 32 lb-f

### Confusion between units of weight and mass

Many people (and even textbooks) mix up mass and weight. They will say that an object weighs 25 kg and another object as a mass of 2 pounds. Both expressions are scientifically incorrect.

## Weight on the Moon

The mass of an object—or the amount of matter it contains—is the same on the Moon as it is on the Earth. However, the weight of the object is a function of the acceleration due to gravity. Since gravity on the Moon is about 1/6 of that on Earth, an object will weigh 1/6 as much on the Moon.

WM = mgM

where

• WM is the weight on the Moon
• m is the mass of the object
• gM is the acceleration due to the Moon's gravity (1.6 m/s2 or 5.3 ft/s2)

Since gM = g/6, then:

WM = W/6

Thus, if you weigh 60 N or 132 pound-force on the Earth, you would weigh only 10 N (22 lb-f) on the Moon.

## Summary

The units of measurement for mass, weight, and force of gravity are the International System of Units (SI) or the British Imperial and United States system of measurements.

The gravity equation shows the relationship between mass, weight and acceleration due to gravity.

The mass of an object is the same on the Moon as it is on Earth, but its weight is 1/6 as much on the Moon as on the Earth.

Gravity is a heavy subject

## Resources and references

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### Websites

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System of measurement - Wikipedia

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