Unit Converter: Length, Area, Volume and Weight

What This Unit Converter Does

This unit converter is designed to provide conversion estimates based on the definition of the units. It can calculate four measurement categories: length, area, volume, and weight. It provides a unit conversion equation between the chosen units and the steps to calculate the result. Most of the units available are taken from one of the following measurement systems:

How to Convert Units

Different measurement systems require a certain bridge to convert between each other accurately. It is easy to convert kilograms into grams and pounds into ounces, but it is not as simple to convert grams and ounces because the units are taken from different measurement systems. It requires a certain understanding of definitions of different units for the most precise conversion. The current practice for converting units from one system to another is through metrication.

Metrication refers to the practice of converting units to a metric or International System of Units. An International System of Units has been growing in its popularity due to its objectivity and simplicity when it comes to conversion between different units. While other popular systems such as Imperial and US Customary are tied to subjective metrics that may change over time, the International System of Units is tied to the speed of light traveling in the vacuum. A significant characteristic of the speed of light is that it is constant when traveling in a vacuum. Because of this characteristic, the SI measurement system is said to be objective.

The easiest way to understand how different measurement categories and systems are related to each other is to start with units of length.

Units of Length

Length is a measurement of distance. It is the most basic measurement because it quantifies a one-dimensional extent in space. It is useful to understand how to convert between different length units because it might be required in certain projects such as calculating stair dimensions. Unlike length, other measurements such as area and volume are defined by units of length. Because other measurements are defined by length, it is important to understand how different units of length are related to each other.

International System of Units (SI)

The International System of Units, also known as the metric system, contains units such as a meter, a kilometer, a millimeter, etc. The root word of each metric used in SI is meter, and it is considered a base unit of the system.

The rest of the units presented in SI are derived from the base unit - Meter. In fact, the prefixes of different units in SI refer to the factor by which a meter must be scaled to get the result. For example, a kilometer has the prefix kilo, which is derived from the Greek language and means Thousand. A kilometer means a thousand meters, and it is equal to 1,000 meters. The following table shows how different units of measurement are derived in the International System of Units.

As shown in the table above, different scales of a meter follow a similar structure. Every scale represents a certain exponent of 10 by which a meter is multiplied. Knowing what prefix refers to what exponent provides a simple and versatile way to convert between the units.

A meter is defined as an objective measure that is constant at all times. Using a definition of a meter, we can look at other systems of measurement and find a precise definition for each unit.

Imperial System

The Imperial system was first defined in 1824 by the British Weights and Measures Act. The most commonly used measures of the imperial system are inch (in.), foot (ft.), yard (yd.) and mile (mi.). Every measurement in the system had a clear relation to each other. For example, 1 foot was defined as 12 inches, and 1 yard was equal to 3 feet. The problem was that it did not have a clear conversion between imperial and metric systems. Because of that, the International Yard and Pound Agreement of 1959 defined 1 Yard = 0.9144 Meters.

It is important to note that there is an Imperial and a US Customary systems of measurement. Both systems have similar units, but they have slightly different definitions for units of area and volume. On the other hand, their length units are defined in the same way, which is reflected by the Imperial System.

Using the definition of a yard, it is possible to convert between Imperial and SI units of measurement precisely. The following table provides the definition of each Imperial unit of length and its conversion to SI units.

Units of Area

Units of area are widely used in various fields, and people deal with area units all the time. It can be used to calculate the square footage of a property, or even estimate how much roofing material you need to buy.

After understanding how length is being measured and what units measure length, we can start talking about the measurement units of area. Area is a two-dimensional measure that refers to the amount of space within the perimeter. It is important to note that measurement units of area refer to square shaped units. Area is measured using two lengths that are multiplied between each other. For example, a rectangle with a length of 2 meters and a width of 3 meters has an area of 2m × 3m = 6m². In this case, the length and width are both measures of length while the multiplication result is the measure of area. Unlike measures of length, measures of area are represented by square units such as square meters (m²) and square inches (in²). They are represented as square units because each measurement of area is simply two measurements of length multiplied by each other.

The fact that an area is simply a multiplication of two lengths provides an insight into how to find a relationship between different measurement systems based on the definitions of length. We know that 1 Yard = 0.9144 Meters. This means that a square with a side length of 1 Yard is equal to . Since 1 Yard = 0.9144 Meters, we can substitute the length in yards to length in meters and find how many meters is 1 Square Yard:

Using the definition of an area and the definition of length for different units, we can derive precise formulas for conversion between different units and different systems.

International System of Units (SI)

It is very easy to convert different units of area within the International System of Units. Using the definition of an area and the way it is calculated, we can easily calculate the area of each SI unit in meters. The following table provides the measures of area in square meters for each SI unit.

Note that the Area in Meters for each unit is simply the Length in Meters squared for each respective unit.

There are a few additional metric units that appear only in the relation to areas. This means that they are derived using SI units, but they are not generally accepted. These units are shown in the following table.

Imperial System

The approach for converting imperial units of area is the same as the approach for SI units. Since every area unit is simply a square of the length of the respective unit, we can compile a table to define the area of each imperial unit.

In addition to the area measures derived from the units of length, there are some measures in the Imperial System that are defined specifically as an area measurement. This means that there is no length measurement associated with these units. Instead, the definition of these measurements rely on a combination of different length measurements.

Area measurements are widely used in almost every field, and because of that, there are certain units that exist that do not fall under SI and Imperial measurement systems. These units are referred to as Non-SI Units, and even though they are not as popular, it is still worth mentioning them.

Non-SI Units of Area

The units of measurement that are either obsolete or have very specific use cases, may be classified as Non-SI Units. Some of the units have a clear definition that allows us to convert them, but others may not have a clear definition because it simply did not survive long enough. The following list provides a few of the most popular as well as obsolete Non-SI units of measurement. This list is not exhaustive as there are many other measurements that have been used by different nations and in different fields over time.

After understanding how area measurements are derived from different length measurements and how conversion between length and area are related, we can talk about volume measurements.

Units of Volume

Understanding how to convert volume is also an important skill for some projects. Certain construction projects require volume calculations. For example, building a house may require you to calculate how much concrete you need, which has to be done using volume.

Volume conversion follows the same logic as area, but unlike area, volume attributes to 3-dimensional shapes. This means that the shapes that have volume, also have 3 lengths. These 3 lengths are usually multiplied to find the volume, but some volume metrics, such as a barrel, are not defined by a cubic shape. Because of the inconsistency in definitions, some volume metrics are more difficult to calculate than the others.

An example of a volume metric and how it can be converted into another metric is a cube with a side length of 1 Yard. Using the logic that the volume can be calculated by multiplying three lengths and the fact that 1 Yard = 0.9144 Meters, we can perform the following calculations to find the conversion between a cubic meter and a cubic yard:

These calculations provide an example of how other units can be found using the definitions of length units and volume. Just as with length and area, the best way to start is with SI units and gradually move to other measurement systems.

International System of Units (SI)

Conversion between volume SI units is very similar to conversion between area SI units because the process follows the same logic. The only difference is that volume measures have to be cubed instead of squared. The following table provides the measures of volume in cubic meters for each SI unit.

Additionally, there are certain metric units that are often used in day-to-day life. These units have different names, but they still follow the same logic as the International System of Units. The base unit of a metric system is called a Liter, and it is defined as follows: 1L = 1000cm³. The following table provides metric values of volume.

In the example above, we have calculated the exact conversion between cubic yards and cubic meters, so now it is possible to find the conversion values for each unit presented in the Imperial System of Measurement.

Imperial System

Imperial system is the measurement system that has been used in Britain for a long time. It is important to note that there is a US Customary system of units, and it has similar units as the Imperial System, but they have different values. Because of that, it is important to have a clear distinction between the two systems and their units. Additionally, the volume metrics used in a day-to-day life are different from the metrics used to calculate length and area. For example, widely used volume metrics in imperial system are fluid ounce (fl. oz.), pint (pt.) and gallon (gal.). The Weights and Measures Act defined 1 gallon = 4.54609 liters, which allows us to convert between imperial and SI units precisely. The following table provides the names and definitions of the most used imperial volume units.

Even though the table above provides imperial volume units that are used in day-to-day life, the other units such as cubic inch and cubic yard still exist and are used in certain fields. They are calculated the same way SI volume units are calculated, and given that 1 Yard = 0.9144 Meters, it is possible to calculate them precisely too.

The US has a different system that has similar units to the imperial system, but they are measured differently.

US Customary System

The US Customary system is widely used in the United States for production and manufacturing purposes. Even though other fields use a metric system, it is important to talk about US Customary units because households face it every day.

The US Customary system is consistent with the imperial system for length and area units. Even volume units that are derived from length units such as cubic inch (in³) and cubic foot (ft³), are consistent with the imperial system. The difference between the units occurs in other volume metrics that are used in day-to-day life. Specifically, 1 US gallon = 231 Cubic Inches. Using this information, we can convert precisely each of the following units into a metric system.

This table makes it clear that the same units from US customary and imperial systems may have a different definition. Because of the differences in their definitions, the US gallon is equal to 3.79 liters while the imperial gallon is equal to 4.55 liters. Before calculating the volume, it is important to understand what measurement units need to be used.

Units of Weight

The last type of units this calculator can process is the units for weight. Just as with all the units discussed previously, the easiest way to understand how different units are related is to start with an international system of units.

International System of Units (SI)

This system takes a gram as the base measure and derives all the other units based on the measure of the gram. Before we get into deriving all the other units, we should look at the definition of a gram.

A gram is defined as “the absolute weight of a volume of pure water equal to the cubic centimeter at the temperature of melting ice.”

All the other units are derived from the gram in a similar way as different SI units of length are derived. The prefix of each unit is associated with a certain multiple, which represents the number of grams in a respective unit. The following table contains SI units of volume.

US Customary System

This system mostly uses ounces (oz.), pounds (lb.) and US tons. There is an agreement between the US, UK and other english-speaking countries to make 1 lb = 453.59237 g. This allows us to convert between the US Customary units and SI units precisely.

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