Find the circumference and area of the circle calculator

Random converter

• Calculators
• Mathematics

Definitions and Formulas

In geometry, a circle is a set of all points in a plane that have the same distance to a point called the center of the circle. In other words, a circle is a locus of coplanar points equidistant from a certain point called the center. Coplanar points are points located in a plane. The distance from any point of the circle to its center is called the radius. We used to view a circle as a round line or figure. However, a circle looks round only in Euclidean geometry. In some metric spaces, for example in the taxicab or Chebyshev’s spaces the circles look rather square.

The diameter of a circle is the distance across the circle. In more exact words, it is the segment of a straight line that passes through the center of the circle and ends where it touches two points on the circle. The diameter equals twice the radius of the circle. Any diameter divides the circle (or rather the disk) into two equal halves.

To be more exact, a circle is a line or a closed curve and in strict language, the circle is only the line that encloses the figure called a disk in American English or disc in British English.

Circumference

The circumference C of a circle is the length of the perimeter of a circle, that is, the length of the circle or the distance around the circle. It is measured in linear units. If we divide the circumference of any circle by its diameter D, we get the number 3.14159265359… This number is the most important mathematical constant called π:

where R is the radius. Rearranging the above formula, we can solve it for the circumference and get the formula everyone remembers from school:

The mathematical constant π is widely used in many formulas in mathematics, engineering, science and architecture, and construction. Though this number is known from antiquity, it has been represented by the Greek letter π recently — since the mid-18 century. π is an irrational and transcendental number. This means it cannot be represented exactly by a common fraction and it is not the root of any polynomial with rational coefficients. There are common numbers that are irrational, but not transcendental. For example, √2 is irrational, but not transcendental because it is a root of the equation x² — 2 = 0. It is interesting to note that since the exact value of π cannot be calculated, it is impossible to find the exact circumference or area of a circle.

Circle Area

We will start by stating the interesting fact that in the English language the area of a disk is somewhat incorrectly called the area of a circle, which is actually the area of a line or a curve (yes, a circle is a curve!) and a line or a curve has no area!

A disk, which is a round portion of a plane with a circular outline has an area A defined as π R squared:

And this area of a disk is more often called the area of a circle. In many other languages, there is no such ambiguity. The area of a circle can be also described as the number of square units needed to cover the surface of a disk surrounded by a circle.

Circles in Architecture

A circle is a perfect shape because every part of the circle is the same distance from its center. Some consider it the most perfect of figures. Like other perfect shapes, a circle is often used in architecture. Many famous buildings have circles as part of their architecture. Round buildings are hard to build; they require great technology and are expensive. Therefore, there has to be a strong motivation to build them. Probably religion provides the strongest motivation. Circles and spheres can be found in almost every culture, religion, and belief system as a magical and symbolic sign. Many places of worship across different cultures were built across a circular footprint — some examples are the Buddhist stupas and the Stonehenge.

People lived under the canopy of the heavens for thousands of years and the early builders used the shape of the Sun or the Moon in construction to build shelters and settlements because it was easy to mark out on land a circle using primitive tools: two stakes and some string of leather or other material

Three stained-glass circular rose windows are among the most famous features of Notre-Dame de Paris. The picture shows the rose window on the west façade of Notre-Dame, Paris

North rose window, Notre-Dame, Paris

Architects consider the circle and sphere to be the most perfect of all forms. In architecture, domes that resemble the hollow upper part of a sphere come in many shapes and sizes. They can be hemispherical or pointed, with conical outer shells like Islamic domes. Or they can be spherical like Roman and Byzantine domes and have the onion form like domes in Russian traditional church and Indo-Islamic Mughal architecture.

The gilded dome of Saint Isaac’s Cathedral in Saint Petersburg, Russia is almost hemispherical

Taj Mahal in the Indian city of Agra is a famous example of Mughal architecture with five onion domes

Spherical domes are often used in Hindu temple architecture as can be seen in this white marble BAPS Shri Swaminarayan Mandir in Toronto, Canada

Semi-circular arches are known since the 2nd millennium BC and the ancient Romans started using them systematically. The Pont de la Tournelle arch bridge spanning the river Seine in Paris

Circles in Technology

It is hard to imagine engineering without wheels and other circular parts. Some of them are in very obvious places like cars and trucks, others are hidden from view in computers, washing machines, dishwashers, fridges, turbines, and other equipment.

Spherical radomes are often used to protect the rotational mechanisms and sensitive electronics of radars

Hatches in spacecraft like this hatch in the descent module of the Soyuz TMA-M spacecraft are often made circular because this design eliminates sharp corners and greatly reduce stresses on the structure; this design also makes it easier to provide sealing

The engine room of the Tower Bridge Museum in London with old working bridge mechanisms

How many wheels can be counted in this picture taken on the ground floor of the Science Museum in London?

Circles in Agriculture

While flying over arid deserts, we can often see the green circles. These are fields that have this form because the farmers use center pivot irrigation, which is an automated sprinkler system that pivots around a central point.

Circular fields using center pivot irrigation in the Mojave Desert, Nevada as seen from a plane on route from Toronto to San Francisco; the radius of a circle is typically ¼ mile (400 m), the circumference is 1.56 mi or 2.5 km and the area is 125.4 acres or 0.51 sq. km.

Mathematics

This online unit converter allows quick and accurate conversion between many units of measure, from one system to another. The Unit Conversion page provides a solution for engineers, translators, and for anyone whose activities require working with quantities measured in different units.

We work hard to ensure that the results presented by TranslatorsCafe.com converters and calculators are correct. However, we do not guarantee that our converters and calculators are free of errors. All of the content is provided “as is”, without warranty of any kind. Terms and Conditions.

If you have noticed an error in the text or calculations, or you need another converter, which you did not find here, please let us know!

TranslatorsCafe.com Unit Converter YouTube channel

How do you find the circumference and area of a circle?

How do I calculate the circumference of a circle?

What is 2πr in circle?

How do you find the area of a circle calculator?