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# 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/s^{2}or 32 ft/s^{2}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/s^{2}. *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/s^{2}, 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/s^{2}) = 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/s^{2}.

Since **W = mg**,

W = (1 lb)*(32 ft/s^{2}) = 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.

(See Confusion about Mass and Weight Units for more information.)

## 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.

W_{M}= mg_{M}

where

**W**is the weight on the Moon_{M}**m**is the mass of the object**g**is the acceleration due to the Moon's gravity (1.6 m/s_{M}^{2}or 5.3 ft/s^{2})

Since **g _{M} = g/6**, then:

W_{M}= 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.

(See Gravity on Earth versus on Moon for more information)

## 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

### Websites

**System of measurement** - Wikipedia

### Books

(Notice: The *School for Champions* may earn commissions from book purchases)

**Top-rated books on Simple Gravity Science**

**Top-rated books on Advanced Gravity Physics**

## Students and researchers

The Web address of this page is:

**www.school-for-champions.com/science/
gravity_mass_weight.htm**

Please include it as a link on your website or as a reference in your report, document, or thesis.

## Where are you now?

## Mass, Weight and Gravity