Content

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• Advice

The radius of a circle is the distance from the center of a circle to any point on its circumference. The easiest way to calculate the radius of a circle is to divide its diameter in half. If you don't know the diameter of the circle but know other measures, such as the circumference () or the area () of the circle, you can still find the radius of the circle using formulas and separators Out .

Steps

Method 1 of 4: Calculate the radius knowing the circumference of a circle

1. 

   Write down the formula for the perimeter of the circle. This formula is, where is the perimeter, and is the radius.
   • The symbol ("pi") is a special number approximately 3.14. You can use this value (3.14) in a calculation or use a symbol on a calculator.

2. 

   
   
   Calculate r (radius). Use algebraic calculation to convert the circumference formula until only it remains r (radius) on one side of the equation:

   For example
   
   
   
   

3. 

   Plug the perimeter value into the formula. When threads indicate value C of the circumference of a circle, you can use this equation to find the radius r. I will change the value C of the circumference of the circle in the problem enter the equation:

   For example
   If the circumference is 15 cm, we will have the formula: cm

   
   

4. 

   Round to a decimal answer. Enter the result in the calculator with the button and round the number. If you don't have a calculator, you can do the math by hand, using 3.14 as the approximate value of the number.

   For example
   approximately equal to 2.39 cm

   
   
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Method 2 of 4: Calculate the radius knowing the area of ​​a circle

1. 

   Write down the formula for the area of ​​a circle. This formula is, where is the area of ​​the circle, and is the radius.

2. 

   Solve the equation to find the radius. Use algebra to give r on one side of the equation:

   For example
   Divide both sides by:
   
   
   Get the square root of both sides:
   
   

3. 

   Plug the area value into the formula. Use this formula to find the radius if the problem is for the area of ​​the circle. We will substitute the area value of the circle for the variable.

   For example
   If the area of ​​the circle is 21 square centimeters, this formula would be:

4. 

   Divide the area by the number. Start by simplifying the part below the square root (. Use a button calculator if you can. If you don't have a calculator, use 3.14 as the value of the number.

   For example
   If we use 3.14 instead of number, we have the calculation:
   
   
   If the calculator allows you to enter the entire formula in one row, you will get a more accurate answer.

5. 

   Calculate the square root. You may need to use a calculator to do this calculation, since this is a decimal number. The result will be the radius of the circle.

   For example
   . Thus, the radius of a circle with an area of ​​21 square centimeters is about 2.59 cm.
   Areas always use square units (like square centimeters), but the radius always uses units of length (like centimeters). If you look at the units in this problem, you will notice.

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Method 3 of 4: Calculate the radius knowing the diameter of a circle

1. 

   Find the diameter of the circle in the problem. The radius of a circle is easy to calculate if the problem is for diameter data. If you are working on a particular circle, you can measure the diameter by placing the ruler on the circle so that the ruler edge passes through the center of the circle, touching both opposite points on the circle.
   • If you are not sure where the center of the circle is, position the ruler across the circle as estimated. Keep the zero line on the ruler close to the circle, and slowly move the other end of the ruler around the circle. The largest measurement you will find will be the diameter measurement.
   • For example, your circle might be 4 cm in diameter.

2. 

   Split the diameter. The radius of a circle is always half the length of the diameter.
   • For example, if the diameter of a circle is 4 cm then its radius will be 4 cm ÷ 2 = 2 cm.
   • In a mathematical formula, the radius is denoted by r and the diameter is d. This formula in the textbook can be written as follows:.
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Method 4 of 4: Calculate the radius knowing the area and angle at the center of the fan shape

1. 

   Write down the formula for the area of ​​the fan. This formula is, where the fan-shaped area, is the angle at the center of the fan shape in degrees, and is the radius of the circle.

2. 

   Plug the area and center angle of the fan into the formula. Remember that this is the area of ​​the fan shape, not the area of ​​the circle. We will substitute the fan-shaped area values ​​for the variable and the central angle for the variable.

   For example
   If the fan-shaped area is 50 square centimeters, and the central angle is 120 degrees, you have the formula like this:
   .

3. 

   Divide the center angle by 360. So we will know how many parts of the circle the fan shape.

   For example
   , that is, a fan shape is made of a circle.
   We will have the following equation:

4. 

   Separate numbers. To do this step, divide both sides of the equation by the fraction or decimal we just calculated above.

   For example
   
   
   

5. 

   Divide both sides of the equation by the number. This step will separate the variable. For more accurate results, you can use a calculator. It is also possible to round the number to 3.14.

   For example
   
   
   

6. 

   Calculate the square root of both sides. The result of the calculation will be the radius of the circle.

   For example
   
   
   
   Thus, the radius of the circle will be about 6.91 cm.

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Advice

• The actual number is in the circle. If we measure the circumference C and diameter d of the circle exactly, then the calculation will result in a number.