A measuring cup with milk

Overview

Units

Cubic Meters

Liters

Gill

Dram

Cooking

Teaspoon

Tablespoon

Cup

Quart and Gallon

Pint

Fluid Ounce

Calculating Volume

Fluid Displacement

Formulas for Calculating Volume

## Overview

Volume is the amount of space that is occupied by a substance or an object. It could also mean the space inside a container that is available for occupation. While area is a two-dimensional quantity, volume is a three-dimensional one. Therefore, the volume of one- and two-dimensional objects such as points and lines is zero.

## Units

### Cubic Meters

The base SI unit for volume is the cubic meter. It is defined as the volume of a cube that has edges of one meter in length. Derivatives of a cubic meter such as cubic centimeters are also used.

### Liters

A liter is also a common unit in the metric system. It is equal to the volume of a cube with edges 10 centimeters long, yielding:

1 liter = 10 cm × 10 cm × 10 cm = 1000 cubic centimeters

This is equal to 0.001 cubic meters. One liter of water at 4℃ is very close in mass to 1 kilogram. A milliliter is often used as well; it is 1/1000 of a liter or one cubic centimeter. It is often abbreviated as cc.

### Gill

A seafood restaurant in the city of Nara, Japan

Gills are currently used to measure alcoholic beverages, with one gill equal to five fluid ounces in the imperial system, and four fluid ounces in the US system. A US gill is a quarter of a pint or half of a cup. When serving alcohol in pubs, a standard measure in Ireland is ¼ of a gill or 35.5 milliliters. In Scotland, it was ⅕ of a gill or 28.4 milliliters, and in England, it was ⅙ of a gill or 23.7 milliliters, but now it is either 25 or 35 milliliters in both areas, and the bartender can decide which measure of the two to use.

### Dram

Dram or drachm is a unit of mass, volume, and also a coin. It was used in apothecary and equaled one teaspoon until the teaspoon volume was redefined. Today one US teaspoon is about 1 and 1/3 drams.

## Cooking

Liquids in recipes are usually measured by volume, in contrast to the use of mass for many of the dry ingredients in the metric system.

### Teaspoon

The volume for a teaspoon, commonly abbreviated as tsp, has several different values. Historically it was ¼ of a tablespoon, later increased to ⅓, a value in use today in the USA. It is about 4.93 milliliters. In nutrition in the US system, a teaspoon is exactly 5 milliliters. This is the same as 1 metric teaspoon. In the UK, a teaspoon is generally equal to about 5.9 milliliters, although some sources quote 5 milliliters. In general, measuring spoon sizes are standardized to a degree, but the volume of teaspoons used as cutlery is not.

Tablespoon with milk

### Tablespoon

The volume of a tablespoon, commonly abbreviated as tbsp, also varies by geographical region. US tablespoon is three teaspoons, ½ of an ounce, about 14.7 milliliters, or 1/16 of a US cup. Tablespoons in the UK, Canada, Japan, South Africa, and New Zealand are also defined as three teaspoons. Therefore, a metric tablespoon is 15 milliliters. A UK tablespoon is about 17.7 milliliters when the teaspoon is 5.9 milliliters, and 15 when the teaspoon is 5. Australian tablespoon is about ⅔ of an ounce, 4 teaspoons, and is standardized to be 20 milliliters.

### Cup

A cup is an informal measure of volume ranging from about 200 to 250 milliliters. A metric cup is 250 milliliters, while a US cup is smaller, about 236.6 milliliters. Nutrition labels in the US define a cup as 240 milliliters. A Japanese cup is even smaller, equal to 200 milliliters.

### Quart and Gallon

The value of a gallon also varies depending on the geographical region. The imperial gallon is about 4.55 liters, and the US liquid gallon is about 3.79 liters. Gallons are frequently used to measure the fuel. A quart is a quarter of a gallon. The US quart is about 1.1 liters, and an imperial quart — about 1.14 liters.

### Pint

A pint is commonly used to measure beer, even in countries that do not use pints for other measurements. It is also used to measure milk and cider in the UK. Pints are used in some other parts of Europe and throughout the Commonwealth countries. Because of the different definitions of a gallon, a pint represents different volumes in different regions. Both the imperial and the US pint are ⅛ of a gallon. This makes an imperial pint about 568.2 milliliters, while a US pint is about 473.2 milliliters.

An 8 fluid ounces tube of Oatmeal Daily Moisturizing Lotion

### Fluid Ounce

The volume for the US and the imperial fluid ounce is not equivalent, with one imperial fluid ounce equalling about 0.96 US fluid ounces. This makes an imperial fluid ounce about 28.4 milliliters, and the US one — about 29.6 milliliters. Six teaspoons, two tablespoons, or ⅛ of a US cup equal one US fluid ounce.

## Calculating Volume

### Fluid Displacement

The volume of an object can be calculated by measuring the fluid displacement that it produces. For example, if a measuring cup has 1 liter of water, and the water level rises to 1.5 liters once the object is placed in the cup and completely covered by water, then the object’s volume is 0.5 liters. This method will only work with materials that do not absorb water.

### Formulas for Calculating Volume

Volume is calculated in the following way for the geometrical shapes below:

**Prism:** product of the area of the base and its height.

**Rectangular prism:** product of length, width, and height.

**Cube: ** length of its side cubed.

**Ellipsoid: ** product of semi-axes, multiplied by 4/3*π*.

**Pyramid: ** product of the area of the base and its height, times ⅓.

**Rectangular cuboid: ** product of length, width, and height. If the height is unavailable, then it can be calculated using the third side and the angle between this side and the base. If we call them ** a** and

**respectively, and call length —**

*𝛂***, and width —**

*l***, then we can use the formula below to calculate the volume**

*w***:**

*V** V = l w a* cos(

*π*)

Other ways of calculating this volume can also be derived from the properties of right-angle triangles.

**Cone: ** radius squared, multiplied by height and by ⅓ *π*.

**Sphere: ** radius cubed, multiplied by 4/3 *π*.

**Cylinder:** product of the area of its base, *π*, and its height: *V* = *π r*² *h* where *r* is the radius of its base and *h* is its height.

Using algebra, one can derive the ratio for the volume of cylinder:sphere:cone, which is 3:2:1.

References

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