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Circumference Formula

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Understanding Circumference and Perimeter of Circles

Comprehensive Definition, Description, Examples & Rules 

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Introduction to Circumference and Perimeter

While the­ circumference and pe­rimeter share similarities, there’s a fundamental distinction between these two terms. The perime­ter refers to the­ length of the outline of a shape­ with straight sides, while the circumfe­rence specifically pe­rtains to the length of a circle’s outline­. The concept of circumfere­nce relates to the­ complete distance around the­ curved geometric shape.

Importance in Geometry

The importance of circumference and perimeter in geometry is:

  • It helps to identify the length of the outline and determine the surrounding length, which helps to calculate geometrical calculations. 
  • The circumference and perimeter will also help you quantify a physical shape and provide a foundation for advanced trigonometry, algebra, and calculus mathematics. 

Importance in Real-life Application

The significance of circumference and perimeter in real-life application is:

  • Calculating the circumference of your waist is something you are doing in the form of the shape of a circle, not an exact circle, but the principle calculation is similar.
  • Civil engineers are the primary users of both the perimeter and the circumference formula in real life, as building and construction require this calculation to a great extent.

How to Find the Circumference of a Circle?

The circumference of a circle is the measurement of the circle’s boundary, defined as the region occupied by the outside line. If you open the circle and make it in the form of a straight line, the length of the line will be the circumference of the circle, which is measured in single units — cm, m, inch. 

The Step-by-Step guide to follow is:

  • First, you must use the circle’s radius to calculate the shape’s exact circumference. 
  • If the circle’s radius is not provided, then you have to use the circle’s diameter to calculate the radius.
  • Then, use the formula and the value of Pi. 

The formula is:

  • C = 2πr

Here, c is denoted as the circle’s circumference, while r is the circle’s radius. 

The value of pi can be used as 22/7 or 3.14159. 

Or

  • C = 2√πA

It is the formula you use when you do not have the radius or diameter, but the area of the circle is provided. 

Visual Representation

Circumference of a Circle

Circumference Formula Explained

Suppose you break down the components of the circumference formula. In that case, you have to denote that you are multiplying the value of pi with the circle’s radius and then multiplying the exact value by two, which will help you calculate the circle’s circumference. 

The significance of π (pi) in the formula is very high as it is a Greek letter of the mathematical term discovered as a constant equal ratio of the circumference of a circle to its diameter, so the number is calculated in decimal points. It’s of higher clarity in the circle circumference formula. 

Example:

If the diameter of the circle is 20 cm, find the circumference of the circle

Solution:

The radius of the circle is exactly half of the diameter.

So, 

radius = diameter/ 2

= 20/2

= 10 cm

So,

Circumference = 2πr

= 2×22/7×10

= 62.86

So, the circumference of the circle is 62.86 cm

Finding the Perimeter of a Circle

The perimeter in the context of a circle is similar to that of the circumference. Still, the perimeter is a word used for single-line shapes, especially rectangles, squares, or triangles. The circumference is commonly used for circular shapes that do not have a side. The perimeter is commonly used for shapes that consist of a side. 

The formula to calculate the perimeter of the circle is similar to the circumference of the circle itself, which is:

  • 2πr

The circle’s perimeter and circumference are similar because both have similar formulas and meanings. Just as the circle is a shape without any sides, it does not offer the use of the word perimeter.

Circle Circumference Formula In Action

Real-world practical visual examples for calculating the circumference of the circle

calculating the circumference of the circle

Calculate the circumference of the circle with a diameter of 30 cm

Solution:

The radius of the circle is exactly half of the diameter.

So, 

radius = diameter/ 2

= 30/2

= 15 cm

So,

Circumference = 2πr

= 2×22/7×15

= 94.29

So, the circumference of the circle is 94.29 cm

Comparing Circumstance and Area

The length of the outline of a particular shape is the perimeter or the circumference of the circle, but the area is the total amount of space consumed inside the outline shape of the circle. The perimeter is the outside region, while the area is the inside region.

The uses of the circumference and the area are different in various situations, such as when calculating the outline border of a particular region, you use the circumference formula, while when calculating the area inside a particular shape, you have to use the area of the circle formula. 

Perimeter of Circle vs. Perimeter of Other Shapes

The circle’s perimeter is known as the circumference of the circle, as you use the word perimeter when the shape has a particular side. The circle is not a plane figure, and the boundary of a plane figure, such as a triangle or a square, is the perimeter, while the circle is a circumference calculation.

The formula to calculate the circumference or perimeter of the circle differs from the formula you have to use to calculate the perimeter of the other shapes. If you add all the sides of the other shapes, you will get their perimeter, but you have to use a different formula for the circle. 

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Key Takeaways

  1. The Perimeter or the circumference is a similar thing. 

  2. The perimeter is calculated for shapes like triangles, rectangles, and squares, while the circumference is calculated for circles. 

  3. The radius of the circle is half of its diameter. 

  4. You can also calculate the circumference of the circle by using its area and without the presence of the radius of the circle.

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Frequently Asked Questions

The circumfe­rence of a circle is simply the­ distance around its outer border. If you were to straighten out the curve­d line that makes up the circle­, the length of that line would be referred to as the­ circumference. The formula that you have to use to calculate the circumference of the circle is:

  • C = 2πr

There is no direct difference between the circumference and perimeter of a circle as the word circumference is used for circles while the word perimeter is used for the straight line length shapes that consist of a side. For the other shapes, you add up the sides and you calculate the perimeter, but for the circle unit, use a formula for which it is known as the circumference.

The value of PI is the ratio of the circle’s circumference to its diameter, and the value is an approximate value by which you can divide the circumference and get the exact value of your circumstance. It plays a very important role in your calculation, and to find the most of the circle’s values, you have to use the π (pi) for accurate calculation.

The circle’s circumference has a direct relationship with its area, as you can find the area of a circle by taking the product of half of the circumference and the radius of the circle. There is also a formula that you can use to calculate the circumference of the circle using the area when the radius is not provided in the formula:

  • C = 2√πA

Yes, It is possible to find the circumference of a circle without knowing its radius. If the area of the circle is provided, then you can use that formula to calculate its circumference as:

  • C = 2√πA
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2D Shapes2cosacosb Formula30-60-90 Formulas3D ShapesAbsolute Value FormulaAcute AngleAcute Angle triangleAdditionAlgebra FormulasAlgebra of MatricesAlgebraic EquationsAlgebraic ExpressionsAngle FormulaAnnulusAnova FormulaAnti-derivative FormulaAntiderivative FormulaApplication of DerivativesApplications of IntegrationArc Length FormulaArccot FormulaArctan FormulaArea Formula for QuadrilateralsArea FormulasArea Of A Sector Of A Circle FormulaArea Of An Octagon FormulaArea Of Isosceles TriangleArea Of ShapesArea Under the Curve FormulaArea of RectangleArea of Regular Polygon FormulaArea of TriangleArea of a Circle FormulaArea of a Pentagon FormulaArea of a Square FormulaArea of a Trapezoid FormulaArithmetic Mean FormulaArithmetic ProgressionsArithmetic and Geometric ProgressionAssociative Property FormulaAsymptote FormulaAverage Deviation FormulaAverage Rate of Change FormulaAveragesAxioms Of ProbabilityAxis of Symmetry FormulaBasic Math FormulasBasics Of AlgebraBinary FormulaBinomial Probability FormulaBinomial distributionBodmas RuleBoolean AlgebraBusiness MathematicsCalculusCelsius FormulaCentral Angle of a Circle FormulaCentral Limit Theorem FormulaCentroid of a Trapezoid FormulaChain RuleChain Rule FormulaChange of Base FormulaChi Square FormulaCirclesCircumference FormulaCoefficient of Determination FormulaCoefficient of Variation FormulaCofactor FormulaCompound Interest FormulaConditional Probability FormulaConeConfidence Interval FormulaCongruence of TrianglesCorrelation Coefficient FormulaCos Double Angle FormulaCos Square theta FormulaCos Theta FormulaCosec Cot FormulaCosecant FormulaCosine FormulaCovariance FormulaCubeCylinderDiscover the world of MathsEllipseEquilateral triangleEuler’s formulaHeptagonIntegrationIntegration by partsLinesLocusNatural numbersNumber lineParallelogramPerimeterPolygonPrismProbabilityPyramidSetsSphereSquareStandard deviation formulaSubtractionSymmetryTimeVector
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