Area of a circle formula Understand the circle formulas with derivation, examples, and FAQs. A circle is a 2-dimensional closed shape that has a curved side whose ends meet to form a round shape. In this math lesson, you'll master the area of a circle formula and learn how to find the area of a circl If you're wondering how to calculate the diameter of a circle, this diameter of a circle calculator is a perfect choice. Learn more about its types, formula, facts, and example. May 23, 2021 · Get interesting circle facts. 14 by the squared radius, the distance from the center to any point in the circle. 💡 The diameter is the line that crosses the center of the figure and touches both of its margins. Mar 7, 2024 · Some of the most common shapes you'll need to measure for area are rectangles, triangles and circles. The area of the circle is the space in a two-dimensional plane covered by a circle. 14159 x 36 = 113. Perimeter of the circle is the enclosing boundary of the circle. Discover how to calculate the surface area of a circle, whether by radius or diameter. The radius is the straight line from the center of a circle to the circumference of a circle. Fast, accurate, and completely free. Find solved examples and practice problems to improve your understanding of this important concept. Circumference (variable: C) is the perimeter of the circle. Area of a circular segment and a formula to calculate it given the radius of the circle and the height of the segment. The line from one side of the circle to the other is called the diameter. The area of a circle is proportional to the radius of the circle. Dec 15, 2024 · You can find the perimeter or area of composite shapes, including shapes that contain circular sections, by applying the circumference and area formulas where appropriate. Solution: Given: C Apr 29, 2025 · Learn how to calculate the area of a circle with step-by-step examples. Enter any single value and the other three will be calculated. Learn the formula and method to calculate the area of semicircle using solved examples. Area of Circles - Formula for area of circle, Find area, Find radius, diameter and circumference when given area, Word problems with area and circumference of circle, Proof for the formula of a circle, in video lessons with examples and step-by-step solutions. 14 * (64 Aug 3, 2023 · Formulas The formula to find the area of the segment of a circle can either be expressed in terms of degree or in terms of radians. Example: find the area of a circle Task 1: Given the radius of a circle, find its area. This calculator computes the values of typical circle parameters such as radius, diameter, circumference, and area, using various common units of measurement. Calculate the area of a circle using our Area Calculator, or try calculating it yourself with the formulas provided. Includes formulas, derivation, practical applications, and practice problems The circle formula calculator allows you to make circle calculations easily. Discover its applications in architecture, engineering & more! The area of a quarter circle is 1/4 of the total area of a circle. r: radius d: diameter A: Area The area of a circle is given by: A = Π ∙ r2 or A = Π ∙ (d/2)2 Π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3. 96 m2 Question 2. So, you can always draw a square around a circle, calculate the area of the square, and then the area of the circle is 78. This circle calculator finds c (circumference), d (diameter), a (area), and r (radius) of a circle. How to calculate the area of a circle? Area of a circle formula So, let's see how to find the area of a circle. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. Calculate circle area using radius or diameter. Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3. Additionally, we'll work through some examples related to circle area. Some of the plane shapes are rectangle, square, rhombus, pentagon, etc. 14 is often used. Area is the size of a surface Learn more about Area, or try the Area Calculator. Explore and learn more about the area of a sector with concepts, definition, formulas, examples, and solutions along with free worksheets Jan 25, 2023 · Learn the definition of the area of a circle. Circles are present in many places. The formula to find the area of the circle is; A = πr2 Where r is the radius of the circle, this formula is applicable to all the circles with different radii. See an example problem and a proof based on breaking the circle into sectors and forming a parallelogram. The area of a part of a circle is the amount of space enclosed in a segment of a circle, which is a region bounded by an arc of the circle and a chord connecting its endpoints. On this page, you can calculate area of a Circle. 141592653… The r stands for radius. Area is measured in square units of length while circumference is measured units of length. 14159. Learn how to find the area of a circle using different formulas and methods. Calculate the area of a circle based on its radius or diameter. Microsoft Excel is a very powerful data analysis tool that can be used for mathematical calculations, such as finding the area of circle. It is determined using the formula: πr^2 where r is radius of circle. Jul 23, 2025 · Area and Perimeter Formulas The table below provides a list of area and perimeter formulas to find values of area and perimeter of various 2D shapes. See solved examples and derivation of the formulas using geometry and trigonometry. In this circle area calculator we will consider 4 different ways to answer the question: How to calculate area of circle? What you need to do is just enter the necessary parameters, and our OwlCalculator will immediately give you an answer with formulas, solutions and definitions. A circle has the maximum possible area for a given perimeter and the minimum possible perimeter for a given area. Sep 2, 2025 · Calculate the area of a circle with ease. This guide explains how to calculate a circle's area, the formulas used, and walks you through using our free online circle area calculator to solve geometry problems quickly and accurately. For example: enter the radius and press 'Calculate'. Okay, let's do a formula. Learn the definition, formulas, facts with solved examples and more! Area of a circle is the region occupied by the circle in a two-dimensional plane. Explore more about chords of a circle with concepts, definitions, formulas, theorem, proof and examples. You can calculate the area using either the radius (distance from the center to the edge) or the diameter (distance across the circle through the center). Area of a circle is the region occupied by the circle in a two-dimensional plane. To find the area of a circle, multiply the pi which is approximately 3. The area May 8, 2024 · Are you ready to learn how to find the area of a circle? This free step-by-step guide will teach you how to find the area of a circle with diameter or radius given. Area formulas of common shapes The exact area of many common shapes can be calculated using well-defined formulas. Aug 19, 2025 · The area of a circle is one of the most fundamental concepts in geometry. What are some practical applications of this formula? This formula is used in many fields, including engineering, architecture, physics, and even cooking!. Area of a circle - derivation This page describes how to derive the formula for the area of a circle. Aug 3, 2023 · What is a circle with diagram - find out its definition, parts, and properties along with calculation of radius, diameter, area, and circumference using formulas Jul 23, 2025 · The area of the sector and the area of the segment of the circle are easily calculated using the above formula. Easily calculate the area with these step-by-step examples. Good question! Remember how the area formula needs radius? You can use the circumference to get the radius of the circle, and then get area from there. These formulae can help you solve a variety of circle-related difficulties. Our Area of a Circle Calculator simplifies the process—simply input the radius, diameter, or circumference of the circle, and let the tool compute the area for you. Apr 9, 2025 · Calculate a circle's area using A = πr². Parameters like area, circumference, the radius of a circle can be calculated using all circle formulas. 5% of that. We explain how to find the area of a circle and provide a quick calculator to work it out for you, step-by-step. Learn how to calculate the area of a circle using the formula A = πr2 or A = C2 / 4π. It can be further There’s no theoretical limit to the area of a circle. Learn this formula in terms of diameter, circumference, and area as well. Just enter its radius, diameter or circumference. Review the area and circumference of circles with Khan Academy's interactive lessons and practice problems. The area of a circle is the plane region bounded by the circle's circumference. Jan 21, 2020 · Easily find the Area of a Circle with 12 step-by-step examples designed to walk you through those tricky homework problems. This would make option “A” the only possible answer option. So, what is the area formula for a rectangle, a triangle and a circle? The area of a circle is the space occupied by the circle in a two-dimensional plane. Area of a Circle Calculator Our online tools will provide quick answers to your calculation and conversion needs. Learn about circles with concepts, properties, and examples. We will learn about its formulas and apply them to solve some practice problems. In geometry, the area of a circle is the amount of space occupied by the circle. The formula A = πr2 represents the area of a circle, which is the region contained by its circumference. Jul 23, 2025 · In this article, we'll delve into five methods for calculating the area of a circle: using the radius, diameter, circumference, sector, and segment. Apply the second equation to get π x (12 / 2) 2 = 3. Let's get started! The area of a circle refers to a measure of the region (in the 2-dimensional plane) enclosed within the circle. Area of a Circle (variable: A) is the area within the circle. Note that radius is half the diameter of a circle. Math, I was just wondering Easy way to Find the area of a circle with radius. Learn how the radius and pi work together in this simple step-by-step guide to circle geometry. Practical application Jul 23, 2025 · The formula for calculating a circle's circumference, or perimeter, is C = πd or C = 2πr, where "d" is the diameter and "r" is the radius. Nov 21, 2023 · Master the formula for finding the area of a circle using diameter in 5 minutes! Watch now to explore examples and test your knowledge with an optional quiz. Circle formula A circle is defined as the set of all points equidistant from a fixed point on a plane. Finding the area involves working with different measurements, whether using the radius, diameter, or circumference. Area of Circle – Explanation & Examples To recall, the area is the region that occupied the shape in a two-dimensional plane. What formulas do we use then? Area of a Circle Formula Area of any circle is the region enclosed by the circle itself or the space covered by the circle. It is measured in square units. We can, however, visualize the creation of the circle area formula, and examine Archimedes' investigation based upon geometry. Semicircle Formulas Half a portion of any circle is known as a semicircle and is formed by cutting a whole circle along the diameter. Area of a Circle Formula The area of a circle represents the space enclosed within its boundary. In this article, we will learn about the perimeter and area of a circle in detail. The two formulas for calculating circle’s segment are given below. There are several ways to achieve it. The perimeter of a circle can be calculated using the formula C = 2πr and the area can be calculated using the formula A = πr², where r is the radius of the circle. You can choose a way to calculate circle area that suits you: radius, diameter or circumference. Now that we have a set definition for a circle, let's quickly define the variables involved in the formulas of a circle. 54 sq in. Method 1: Visualization: How to find the area of a circle with the diameter. A plane shape is a two-dimensional shape that does not consist of thickness as a dimension. Just type into the box and hit the calculate button. Nov 18, 2022 · Because the coordinates provided in this question for the center of the circle are (0,4), the equation for the circle is (x-0) 2 + (y-4) 2 = r 2 Using this formula and the distance formula given the endpoint (4/3, 5), you will end up with r 2 = 25/9. Free area of circle calculator with step-by-step solutions. Coins, pizzas, and vinyl disks are examples of circular objects, and the area is an essential aspect of them. Oct 25, 2023 · Learn how to calculate the area of a circle using radius, diameter, or circumference. In this article, we will explore the areas of sector and segment in detail and also learn the basics of sector and segment of a circle. What is the smallest possible area of a circle? The smallest possible area is 0, which would be a circle with a radius of 0. Formulas for the Understand that you can easily determine the area of a circle using the formula Area = π × r^2, where π is approximately 3. This can be found using either the radius or the diameter, which we will cover in the examples below. Use this free circumference calculator to find the area, circumference and diameter of a circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Nov 21, 2023 · Discover how to find the area and circumference of a circle. its formula, derivation and different methods of finding the area with examples here at Embibe. You will also learn how to find area of half circle using the area of a half circle formula. 14159 x 25 = 78. Jun 9, 2025 · Learn how to find the area of a circle with clear formulas, step-by-step examples, and visual explanations—perfect for students and math learners of all levels. Jun 18, 2018 · Why is Area of a Circle Equal to Pi * (Radius Squared)? Deriving the formula using regular polygons My favorite derivation comes by way of a formula that applies to any regular polygon, and also answers the question, How can you find the area of a circle without using pi? Why Pi? Dr. Circle The area of a circle with radius r is: A = πr 2 Triangle The area of a triangle with base, b, and height, h, is: Nov 26, 2024 · The area of a circle is determined by the formula A = π r 2 A = πr2, where “r” represents the radius, and π π is a constant. By the end of this article Our Circle Area Calculator is designed to simplify these calculations, saving you time and effort. Given any 1 known variable of a circle, calculate the other 3 unknowns. The formula to find a circle's area $$ \pi $$ (radius) 2 usually expressed as $$ \pi \cdot r^2 $$ where r is the radius of a circle. Find A, C, r and d of a circle. Solution: Given: r = 8 m Since area of a circle = πr2 A = π (8)2 = 64π = 200. You will need either the radius, the circumference, or the area of a given circle for the calculations. It also gives formulas to calculate its parameters with reference to Oct 21, 2017 · Terminology related to circles in math: Properties of circle : Circle Formulas in Math : Area and circumference of a circle: Arc and sector of a circle: Segment of circle and perimeter of segment: Area of the circular ring: Formula for intersecting chords in circle: Formula for length of the tangents of circles: Geometry Math Number System. It is given by πr2/2. How To calculate the area of a circle? The area of a circle can be calculated using its radius, diameter, or circumference, depending on the given data. Includes the calculation formula and practical examples. Learn the area of a circle formula, step-by-step calculation methods, and solved examples for exams. But sometimes we need to work with just a portion of a circle's revolution, or with many revolutions of the circle. The area of a circle is calculated using the formula A = pr , where A is the area, p is the ratio of a circle's circumference to its diameter, and r is the radius of the circle. A line segment that joins two points on the circumference of the circle is defined to be the chord of a circle. 8π = 2πr, so r = 8π Circle Area The length `C` of the circumference (perimeter) of a circle is calculated using the formula: `C = 2pir`, where `r` is the radius of the circle. We'll also go through some examples to understand it better. Thus, the diameter of a circle is twice as long as the radius. For example, if the radius is 5 inches, then using the first area formula calculate π x 5 2 = 3. It is mostly calculated by the size of the circle's radius which is the distance from the center of the circle to any point on its edge. How the circumference and area of a Jan 16, 2023 · Learn how to find the area of a circle using the formula for radius, diameter, and circumference. So: 1. Find the area of a circle given its circumference is 12 cm. Learn Area of a Circle at Bytelearn. It supports different units such as meters, feet, and inches. There is also a separate calculator which will find the radius and diameter of a circle, if you already know the area. Students will first learn about circle math in the geometry standards in middle school and build upon that knowledge as they progress into a geometry course in Jul 23, 2025 · Area formulas are essential tools used in mathematics to calculate the amount of space enclosed by different two-dimensional shapes. Circumference -> Radius -> Area Let's try with this example, circumference of 8π. Read on if you're interested in: How to find the area and circumference of a circle. 1 cm 2 (square centimeters). Calculate the Circumference of circle. This circle calculator finds the area, circumference or radius of circles by considering a given variable that should be provided (area or diameter or circumference). Free area and circumference of a circle math topic guide, including step-by-step examples, free practice questions, teaching tips and more! In geometry, the area enclosed by a circle of radius r is πr2. Here, we can calculate the area of a circle using a diameter or using a radius. The area of the semicircle is half of the area of a circle. What is the formula for calculating the circumference of a circle? What is the formula for the area of a circle? How to calculate the area of a circle? Area of circle calculator online ¡Circular surfaces! We explain area of a circle formula = π × radius², and more. In other words, radius bridges the gap between circumference and area. Learn how to calculate the area of a circle using the formula A = πr2, where r is the radius and π is approximately 3. Learn the area of a circle formula, the circumference of a circle formula, how to The formula to find a circle's area $$ \pi $$ (radius) 2 usually expressed as $$ \pi \cdot r^2 $$ where r is the radius of a circle. Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference. Along the way, we'll cover the fundamentals of circles and their formulas for area. Therefore Our circle area calculator is used to find the area of a circle. The area, diameter and circumference will be calculated. In this blog, we explore its derivation, practical uses such as pizzas, fabrics and step-by-step Use the calculator above to calculate the properties of a circle. Welcome to our Area of a Circle Calculator page. Simple steps for accurate results. As you begin calculating areas, you may notice that you need some of the same components that perimeter formulas call for, such as length and width. Find area using radius, diameter, or circumference easily. A circle is easy to make: Draw a curve that is radius away from a central point. Area Calculator Use this area calculator to easily calculate the area of common bodies like a square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, regular octagon, and sector of a circle. See how to find the area, circumference, diameter, and radius of a circle in geometry. By finding the area of the polygon we derive the equation for the area of a circle. Know the definitions, see the examples, and practice problems of Area of a Circle. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. 14 * 82 A = 3. Jan 24, 2021 · To calculate the area of a circle, you can use the PI function together with the exponent operator (^). 14, and r represents the radius of the circle. Includes formulas, examples, and practical applications for geometry and real-world problems. Jul 23, 2025 · Answer : Area of circle (A) is calculate by using formula , Area = π × (radius)2 Geometry is a discipline that includes the study of plane shapes or flat shapes. The space occupied within the boundary/circumference of a circle is called the area of the circle. There are many circle formulas, such as the area of a circle formula, circumference formula, and diameter formula, all of which are discussed below along with the equations for a circle. In this mathematics article, we'll explore the area of a circle formula. The diameter of a circle divides the circle into two equal semicircles. π × 𝒓 × 𝒓, π × 𝒓² and 𝒓² × π. It is calculated using the formula A = πr^2, where 'r' is the radius of the circle. These are the formulas give us the area and arc-length (that is, the length of the "arc", or curved line) for the entire circle. Area formula The area of a two dimensional shape or geometric figure is the space contained within its perimeter. What is the lateral area? Solution: A = Pi * r2 Radius = d/2 = 16/2 = 8 A = 3. Dec 5, 2024 · Explore the area of a circle formula (A=πr²)’s derivation using triangles & integration. Derivation of the Area Formula: As was the case with circumference, the "formal" derivation (proof) of the area formula also involves calculus integration, which is beyond the scope of this course. Area of a Circle is the region enclosed by a circle in a two-dimensional plane. Learn the process of finding the area of a segment of a circle along with a few solved examples and practice questions. You will learn how to use the area of a circle formula. we start with a regular polygon and show that as the number of sides gets very large, the figure becomes a circle. Complete examples using arc length, central angle, and sector radians. Includes a calculator May 24, 2024 · Learn how to calculate the surface area, volume, and perimeter for shapes, including cylinders, cones, pyramids, polygons, circles, and more. Circle area calculator helps how to find the area of a circle. The area of a semicircle is defined as the space enclosed inside a half circle. Circle formulas and geometric shape of a circle. The area of a quarter circle of radius r is pi*r^2/4. In the example shown, the formula in C5, copied down, is: =PI()*B5^2 which calculates the area of a circle with the radius given in column B. You can use various units of measure. Each method uses specific formulas This calculator will calculate the area of a circle given its diameter, using the famous formula area = pi times (d/2) squared. Perfect for students and enthusiasts! A segment of a circle is the region that is bounded by an arc and a chord of the circle. Various parameters related to a semi-circle like a diameter, area, the perimeter can be calculated using semicircle formulas. Formulas and explanations on finding the area of any shape are below. It's given by the formula Calculating the Area of a Circle The formula for area of a circle is: A r e a = π (r) 2 The symbol π represents pi, or the number 3. See examples, comparisons, and applications with real-world problems. The area of a circle is the space enclosed within the boundary of a circle. The area of a circle is a fundamental concept in mathematics with applications in various fields. Keep reading to learn things like: The formula to calculate the diameter of a circle given its radius, or vice versa. Parts of a circle The figure below shows the key parts of a circle that we need to know to be able to work The area of a circle is the total 2D space bounded within the boundary of a circle. The r 2 means radius squared; whatever it is attached to must be doubled. Jul 23, 2025 · The area of a Circle is the measure of the two-dimensional space enclosed within its boundaries. If you're wondering how to calculate the diameter of a circle, this diameter of a circle calculator is a perfect choice. Jul 23, 2025 · A = πr2 where r is the radius of the given circle. The length of the side of the square is also d 2. In this article, we will walk you through a step-by-step guide on how to calculate the area of circle in Excel using a simple formula. It is usually abreviated as d. Learn the formula, derivation, examples, and more. Your one-stop solution for instant study helps. Understanding the area of a circle is important in many fields, including mathematics, engineering, and physics. The formula for calculating the area of a circle is πr² or π (d/2)². Task 2: Find the area of a circle given its diameter is 12 cm. Here’s another sample question: Jan 11, 2023 · Learn how to find the area of a sector of a circle using the area of a sector formulas. Take a look at the picture above the calculator to visualize each element. The radius may also be expressed using the diameter so that `2r = d`: `C=pid` The area `A` left inside the circle is calculated using the formula: `A=pir^2`, where `r` is the radius of the circle or correspondingly: `A=pi/4d^2`, where `d The area enclosed by two radii and the corresponding arc in a circle is called a sector of a circle. Try this In the figure A circle is, a set of points equal distrance (radius) from a fixed point (center point) on a plane. The Area of a Segment is the area of a sector minus the triangular piece shaded blue below: There is a lengthy reason, but the result is a slight modification of the Sector formula: Learn about the area of a circle, its formula, and its applications. It is given by πr2/4 . Understanding how to calculate the area of a circle empowers us to solve problems ranging from basic geometry to complex real-life scenarios. And also find the area of circles using triangle, rectangle. Key Points about Area of a Circle The area of a circle is the amount of space enclosed within the circumference of a circle. The area of a circle is pi times the radius squared (A = π r²). The area of a circle is the number of square units inside that circle. These formulas can be used to find the area of geometric figures such as squares, rectangles, circles, triangles, trapezoids, and ellipses. Circle math Here you will learn about the different parts of a circle including how to identify the key parts of a circle, properties of circles, circle formulas such as circumference and area, and how to solve various circle problems. In this article, you will learn the area of a circle and the formulas for calculating the area of a circle. Given below is the different area formulas chart for various 2d shapes. Free area of a circle math topic guide, including step-by-step examples, free practice questions, teaching tips and more! Aug 8, 2023 · Learn about the area of a circle, its definition, essential formulas, and explore real-life examples from this article Aug 26, 2025 · Area of a Circle: A Complete Guide The Knowledge Academy 26 August 2025 The Area of a Circle is the space enclosed within its boundary, calculated using the formula A = πr², where r is the radius. The formula for the area of a circle is used by multiplying π by the square of the radius. It finds the area, radius & diameter of a circle with the formula of area of a circle calculator. And so: All points are the same distance from the center. Feb 12, 2023 · A circle is one of the most universal geometric shapes, but exploring the mathematical concepts of diameter and area can sometimes feel tricky. Feb 11, 2025 · Master the circle area formula! Explore its derivation, practical applications, and cultural significance in this comprehensive guide. 1) Turn this into radius, using the circumference formula C = 2πr. "r" is the radius. Whether you are measuring the size of a round rug you need to purchase or determining the space you need to construct a circular garden or patio, knowing how to calculate the area of a circle from its diameter is a valuable skill. Are you interested in calculating the area and circumference of a circle and the formula behind it? This is the perfect tool. Jun 11, 2025 · Learn how to calculate the area of a circle using the formula A = πr², where r is the radius. The area of a circle is the space enclosed by a closed curve. Find the area of a circle given its radius is 8 m. Aug 1, 2025 · Calculate the area, circumference, radius and diameter of circles. A sector of a circle is a portion or part of a circle that is composed of an arc and its two radii. or A = C2/4π where C is the circumference of the given circle. Oct 21, 2017 · Terminology related to circles in math: Properties of circle : Circle Formulas in Math : Area and circumference of a circle: Arc and sector of a circle: Segment of circle and perimeter of segment: Area of the circular ring: Formula for intersecting chords in circle: Formula for length of the tangents of circles: Geometry Math Number System. Learn definitions, formulas, facts, examples, practice problems, and more. Whether you’re working with circular objects in real life or dealing with mathematical problems in school or work, understanding how to calculate the area of a circle is essential. In this guide, we’ll explore 5 ways to calculate the area of a circle using different formulas and approaches. Circle worksheets, videos, tutorials and formulas involving arcs, chords, area, angles, secants and more. Perimeter of Semi-Circle The semi-circle is formed when we divide the circle into two equal parts. The following are the formulas for calculating the area of a circle, along with detailed explanations and examples for each. Learn how to use this formula to find the area of a circle when given the diameter. Example 1: The diameter of a circle is 16 inches. 141593, however the value 3. It is measured in square units, such as cm or m . The unit of area is the square unit, such as m2, cm2, etc. Circle The area of a circle with radius r is: A = πr 2 Triangle The area of a triangle with base, b, and height, h, is: Calculate circle area instantly! Enter radius, diameter, or circumference - get precise area in any units. This fundamental geometric concept is essential in mathematics and real-world applications. If area is how many unit squares fit within a shape, how The area of a circle can be thought of as the number of square units of space the circle occupies. Examples using Area of Circle Formula Question 1. This can be entered on a calculator in different ways.