Circumference of the Earth

Circumference is a term used to describe the length of the boundary of a circle. The Earth is considered to be spherical in shape and so it has a radius, a diameter, and a circumference. The circumference of the Earth is measured in kilometers or miles. It is measured around the Equator and around the poles which give different values. Let us discuss how they are calculated individually.

The circumference of the Earth is the length or distance measured around it. For example, if you stand at a point on the earth and move around the earth in a straight path, and reach the same point again, then the distance covered by you is the circumference of the earth. The circumference of the Earth depends on how it is measured. When it is measured around the equator, it is 40,075 km (approximately, 24,901 miles), whereas, if it measured from the north pole to the south pole it is 40,008 km (approximately, 24,860 miles).

A sphere does not have a circumference but the circular cross-section of a sphere has a circumference. Knowing the location of the cross-section is important because the length of the radius changes as we move away from the center of the sphere. For that, we need to find out the biggest circle (the great circle) of the sphere. Observe the following figure which shows the great circle of a sphere.

Now, the circumference of the great circle or the circular cross-section is the distance around it and can be referred to as the circumference of the sphere. Mathematically, it can be calculated by the formula:
Circumference = 2πR or πD, where 'R' is the radius of the sphere and 'D' is the diameter of the sphere (if the circular cross-section is taken at the exact center of the sphere).

Example

Consider a tennis ball whose great circle has a diameter of 10 inches.

Now, the circumference (C) of the tennis ball will be:

C = πD
    = 3.14 × 10 
    = 31.4 inches

Therefore, circumference = 31.4 inches.

The circumference of the Earth can be found by two methods.

Method 1: Earth's circumference can be found out by using the geometric formula that was used over 2,000 years ago. Eratosthenes, the head librarian in Alexandria, Egypt, in 200 B.C. estimated the earth's circumference using the following method. He knew the following things and based his calculations on them accordingly:

• On the longest day of the year, the sun would be directly above Syene, Egypt, which means that the angle of the sun rays would be 0°.
• The distance of the city of Alexandria from Syene, Egypt, was 5000 stadia. ('Stadia' is the plural form of 'Stadion', a unit of length, which refers to a distance of around 185 to 192 meters, or 607 feet)

He calculated the angle of rays in the city of Alexandria, which was measured as 7.2°.

He then used the following relation:

"Ratio of the angle of the arc to the complete angle = Ratio of the length of the arc to the circumference", which can be written as, 7.2°/360° = 5000/C. On simplifying, He arrived at the estimated value of 2,50,000 stadia, which is approximately equal to 28,738 miles. This estimated value is close to the actual value of 24,901 miles.

Method 2: We can also find out the circumference of the earth by using the direct formula for the circumference. Circumference = 2 πR or π D; where R is the radius of the sphere and D is the diameter of the sphere. Since Earth is not a perfect sphere but an oblate spheroid, i.e., it has an equatorial diameter greater than the polar diameter (the equatorial diameter of the earth is 7,926 miles and the polar diameter of the earth is 7,900 miles). Hence, the circumference of the earth will be different for both the cases mentioned above. 

Therefore, the Circumference of the earth around the equator is:

\(C_{E}\) = π × 7926 (where \(C_{E}\) is the circumference of Earth around the Equator)
         = 24,887.64 miles (which is close to 24,901 miles)

And the Circumference of the earth around the poles is:

\(C_{P}\) = π × 7900 (where \(C_{P}\) is the circumference of Earth around the Poles)
          = 24,806 miles

Topics Related to Circumference of the Earth

Check out some interesting topics related to the circumference of Earth.

• Circumference
• Circumference to Diameter
• Sphere
• Circles
• Radius
• Diameter
• Radius of Circle Calculator
• Area of a Circle

Important Notes

• The location of the cross-section on the sphere is important because the length of the radius changes as we move away from the center of the sphere.
• Eratosthenes assumed that Syene was precisely on the Tropic of Cancer and Syene and Alexandria are on the same meridian.

What is Circumference?

Circumference is defined as the length of the boundary of a circle. It can also be described as the arc length around a circle.

What is the Radius and Diameter of a Circle?

Radius is defined as the distance between the center of the circle to the circumference of the circle. Diameter is the line segment that passes through the center of a circle, and two of its endpoints lie on the circumference of the circle.

What is the Circumference of the Earth?

The circumference of the Earth is the distance measured around it. It is measured around the Equator and around the poles which give different values. The circumference of the Earth measured around the Equator is approximtely 24,887.64 miles, whereas, if it is measured around the poles, it is approximately 24,806 miles.

How to Calculate the Circumference of the Earth?

The circumference of the Earth can be calculated using the formula, Circumference = 2 πR or π D, where R is the radius of Earth and D is the diameter. By knowing the Equatorial diameter or the polar diameter of the Earth, the circumference can be found. The circumference of the Earth (around the equator) is approximately 24,887 miles.

Where is the Earth's Circumference the Greatest?

As the shape of the earth is an oblate spheroid, the diameter is different at the equator and at the poles. Since the diameter at the equator is greater than the diameter at the poles, hence, the circumference of the great circle at the equator is the greatest.