How to Calculate the Circumference of a Circle

Whether you're doing craft work, putting fencing around your hot tub, or just solving a math problem for school, knowing how to find the circumference of a circle will come in handy in a variety of circle-related problems.

Method 1 of 2: Using the Diameter

1. 
   1
   Write down the formula for finding the circumference of a circle using the diameter. The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14.

2. 
   2
   Plug the given diameter into the equation and solve. Let's say you're solving this problem: you have a hot tub with a diameter of 8 feet, and you want to build a white fence that creates a 6-foot wide space around the tub. To find the circumference of the fence that has to be created, you should first find the diameter of the tub and the fence which will be 8 feet + 6 feet + 6 feet, which will account for the entire diameter of the tub and fence. The diameter is 8 + 6 + 6, or 20 feet. Now plug it into the formula, plug π into your calculator for its numerical value, and solve for the circumference:
   

   • C = πd
   • C = π x 20
   • C = 62.8 feet

   
   

3. Method 2 of 2: Using the Radius

   1. 
      1
      Write down the formula for finding the circumference of a circle using the radius. The radius is half as long as the diameter, so the diameter can be thought of as 2r. Keeping this in mind, you can write down the formula for finding the circumference of a circle given the radius: C = 2πr. In this formula, "r" represents the radius of the circle. Again, you can plug π into your calculator to get its numeral value, which is a closer approximation of 3.14.
   2. 
      2
      Plug the given radius into the equation and solve. For this example, let's say you're cutting out a decorative strip of paper to wrap around the edge of a pie you've just made. The radius of the pie is 5 inches (12.7 cm). To find the circumference that you need, just plug the radius into the equation:
      

      • C = 2πr
      • C = 2π x 5
      • C = 10π
      • C = 31.4 inches (79.8 cm).