Calculate the area of a circle, with examples, formulas and calculator

This article will be about How to find the area of any circle, steps, formulas and examples, and a calculator to solve problems.

The area of a circle defines how much space is in the surface of a circle. To find the area of a circle it is necessary to know some parts of the circle like the radius, the diameter or the circumference. The general formula to find the area of a circle is: a = π * radius2, this formula works if we know the radius of the circle, and it would change if instead of knowing the radius we know the diameter or the circumference.

Know the area of a circle in real life situation is useful, even when is not that obvious, probably people is not measuring things constantly, but we can calculate the area of things just with the eyes, for example to know how big is a pizza that somebody is going to eat, so we can know if he is going to skip the diet, or the amount of paint we would need to paint a circle in a draw, sometimes we do not need to have the exact measures of the objects so the things explained in this article are useful.

The area of a circle can be expressed in miles, kilometers, meters or in centimeters (all squared like m2), because the measures of space are represented like this, if instead of using squared longitudes we use only longitudes, then the result would be wrong although the data would be wrong.

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Now we are going to define the parts of the circle that must be known to calculate the area of a circle, to calculate the area of a circle is only necessary to know one of the following parts, not all of them.

Radius

The radius of a circle is a straight line that goes from the center of the circle to the circumference of the circle in any direction, is the main part of the circle to be known to calculate the area. The radius of a circle is also half the length of the diameter.

Diameter

The diameter is a part of the circle that divides the circle in half, the line of the diameter goes from one edge to another, passing by the center of the circle, the diameter is twice the length of the radius, so knowing the diameter we can find the radius so then find the area of the circle.

Circumference

The circumference is the line that forms the circle, we can also calculate the area of the circle by knowing the circumference.

Fórmulas para calcular el área de un circulo

There are 3 formulas to calculate the area, one for each part of the circle mentioned before, the most common one is the one with the radius, but there are sometimes where we need to know the formula using the diameter and circumference.

r = radio | diámetro = d | circunferencia = c | 𝜋 = 3.1416

  • Formula with the radius
  • a = 𝜋 * r2
  • Formula with the diameter
  • a = (d/2)2 * 𝜋
  • Formula with the circumference
  • a = ( (c/𝜋) /2 )2 * 𝜋2

Examples of finding the area of a circle

Example 1: Calculate the area of a circle which radius is of 30cm

  • Resolution
  • a = 𝜋 * r2
  • a = 𝜋 * 30cm2
  • a = 2,827 cm2

Example 2: Calculate the area of a circle that has a diameter of 120cm

  • Resolution
  • a = (d/2)2 * 𝜋
  • a = (120/2)2 * 𝜋
  • a = 602 * 𝜋
  • a = 3600 * 𝜋
  • a = 11 309.76 cm2

Example 3: Calculate the are of a circle that has a circumference of 600 meters

  • Resolution
  • a = ( (c/𝜋 ) /2)2 * 𝜋
  • a = ( (600/𝜋 ) /2)2 * 𝜋
  • a = ( (190.99 ) /2)2 * 𝜋
  • a = ( 95.5)2 * 𝜋
  • a = ( 9120) * 𝜋
  • a = 28 652.11 m2

Example 4: The tire of a bicycle has a longitude of 1.5 meters, knowing this, which is the area covered by the tire?

  • Resolution
  • We write the most convenient formula
  • a = ( (c / 𝜋) /2 )2 * 𝜋
  • We replace the data
  • a = ( (1.5 / 𝜋) /2 )2 * 𝜋
  • And solve
  • a = (0.477 /2)2 * 𝜋
  • a = 0.2392 * 𝜋
  • a = 0.0569 * 𝜋
  • a = 0.18 m2

Example 5: 5 In a clock of a square the hand that marks the seconds of 1.25 meters long, if we know that the minute hand is 0.5 times bigger than the seconds hand, ¿Which is the area where the hand that marks the minutes move?

First we have to determine the length of the minute hand clock

  • Mh=Minute hand | Sh= Second hand
  • Mh = Ms + Ms/2
  • Mh = 1.25 + (1.25 * 0.5)
  • Mh = 1.875 m2

Now knowing the measure of the minute hand we know the radius of the circle, because it goes from the center to the extreme of the circle, so now we can calculate the area.

  • Write the formula
  • a = 𝜋 * r 2
  • Replace the data
  • a = 𝜋 * 1.875 2
  • Solve
  • a = 𝜋 * 3.52
  • a = 11.04 m2

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