The circumference of a circle is the distance around its edges. If a circle has a circumference of 3.2 kilometers, you will have to walk 3.2 kilometers around the circle before you finally return to where you started. However, when you do math problems, you don't have to leave your seat. Read the questions carefully to see if the questions tell you fingers (r), diameter (d), or large (L) circle, then look for the part that corresponds to your problem. There are also instructions for finding the actual circumference of the circular object you want to measure.
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Method 1 of 4: Finding the Circumference If You Know the Fingers
Step 1. Draw the radius on the circle
Draw a line from the center of the circle to the edge of any circle. This line is the radius of the circle, which is often simply written r in math problems.
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Notes:
If your math problem doesn't tell you the length of the radius, you're probably looking at the wrong part. Check if the section for Diameter or Area is more appropriate for your problem.
Step 2. Draw the diameter across the circle
Continue the line you just drew so that it reaches the edge of the circle on the opposite side. You have just drawn the second radius. The two connected radii, having a length of 2 x the radii, are written as 2r. The length of this line is the diameter of the circle, which is often written d.
Step 3. Understand (pi)
Symbol ️, also written as pi, is not a magic number that happens to be used for this type of problem. In fact, the number is originally obtained by measuring a circle: if you measure the circumference of any circle (eg with a tape measure), and then divide by its diameter, you will always get the same number. This number is unusual because it cannot be written as a simple fraction or decimal. However, we can round it to the nearest number like 3, 14.
Even the button on the calculator doesn't have an exact value for, even though the values are very close
Step 4. Write down the definition of as an algebra problem
As explained above, stands for the number you get if you divide the circumference by the diameter. In the form of a mathematical equation: = K / d. Since we know that the diameter is equal to 2 x the radius, we can also write it as = K / 2r.
K is a shortened way to write circumference
Step 5. Change the problem so that you find K, the perimeter
We want to know the length of the circumference, which is K in a math problem. If you multiply both sides by 2r, You get x 2r = (K/2r) x 2r, which is equal to 2πr = K.
- You may write 2r on his left, which is also true. People like to move numbers in front of symbols so the equations are easier to read, and this doesn't change the result of the equation.
- In a math equation, you can always multiply the left side and the right side by the same amount and still have the correct equation.
Step 6. Enter the numbers to complete K
Now, we know that 2πr = K. Look back at the original math equation to see the value of r (fingers). Then, replace with 3, 14, or use the calculator's keys for a more accurate answer. Multiply 2πr using these numbers. The answer you get is the circumference.
- For example, if the length of the radius is 2 units, then 2πr = 2 x (3, 14) x (2 units) = 12, 56 units = circumference.
- In the same example, but using the calculator's keys for higher accuracy, you'd get 2 x x 2 units = 12, 56637… units, but unless your teacher asks you to, you can round the number to 12.57 units.
Method 2 of 4: Finding the Perimeter If You Know the Diameter
Step 1. Understand the meaning of diameter
Place your pencil on the edge of the circle. Draw a line through the center of the circle and across the opposite edge. This line is the diameter of the circle, which is often written d in math problems.
- The line passes through the center of the circle, not just anywhere inside the circle.
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Notes:
If the problem doesn't tell you the diameter, then use another method.
Step 2. Learn the meaning of d = 2r
The radius of a circle, also written as r, is half the distance through the circle. Since the diameter spans the length of the circle, the diameter is equal to two radii. A simple way to write it is d = 2r. This means that you can always replace d with 2r in mathematics, or vice versa.
We will use d, no 2r, because your math problem tells you the value of d. However, it's important to understand this step, so you don't get confused if your math teacher or textbook uses 2r when you expect d.
Step 3. Understand (pi)
Symbol ️, also written as pi, is not a magic number that happens to be used in a math problem like this. In fact, the number is originally obtained by measuring a circle: if you measure the circumference of any circle (eg with a tape measure), and then divide by its diameter, you will always get the same number. This number is unusual because it cannot be written as a simple fraction or decimal. However, we can round it to the nearest number like 3, 14.
Even the button on the calculator doesn't have an exact value for, even though the values are very close
Step 4. Write down the definition of as an algebra problem
As explained above, stands for the number you get if you divide the circumference by the diameter. In the form of a mathematical equation: = K / d.
Step 5. Change the problem so that you find K, the perimeter
We want to know the length of the circumference, so we need to move K alone on one side. Do this by multiplying each side of the equation by d:
- x d = (K / d) x d
- d = K
Step 6. Enter the numbers and find K
Go back to the original math problem to see the value of the diameter, and replace the d in this equation with that number. Replace with a rounding like 3, 14, or use the button on your calculator for more accurate results. Multiply the values for and d, and you get K, the circumference.
- For example, if the length of the diameter is 6 units, you will get (3, 14) x (6 units) = 18.84 units.
- In the same example, but using the calculator's buttons for higher accuracy, you'll get x 6 units = 18, 84956… but if you don't ask, you can round the number to 18.85 units.
Method 3 of 4: Finding the Perimeter If You Know the Area
Step 1. Understand how to calculate the area of a circle
Often, people don't measure the area of a circle (L) directly. However, they measure the radius of the circle (r), then calculate the area using the formula L = r2. The reason this formula can be used is a bit tricky, but you can learn more here if you're interested and want to work on more difficult algebra.
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Notes:
If the math problem doesn't tell you the area of a circle, you may want to use another method on this page.
Step 2. Learn the formula for calculating the circumference
Around (K) is the distance around the circle. Usually, you will find it with the formula K=2πr, but since we don't know the radius (r), we have to find the value of r before we can finish it.
Step 3. Use the area formula to move r on one side
Because L = r2, we can rearrange this formula to find r. If the steps below are too difficult for you to follow, you may want to start with the easier algebra problems or try other techniques for understanding algebra.
- L = r2
- L / = r2 / = r2
- (L/π) = (r2) = r
- r = (L/π)
Step 4. Change the perimeter formula using the formula you got
Whenever you have something in common, like r = (L/π), you can replace one side of the equation with the other. Let's use this technique to change the circumference formula above, K=2πr. For this problem, we don't know the value of r, but we know the value of L. Let's change it like this to make the problem solvable:
- K = 2πr
- K = 2π(√(L/π))
Step 5. Enter the numbers to find the perimeter
Use the area given to find the perimeter. For example, if the area of a circle (L) is 15 squared units, enter 2π(√(15/π)) to your calculator. Remember to include the brackets.
The answer for this example is 13, 72937… but if it's not asked you can round it to 13, 73.
Method 4 of 4: Finding the Real Circumference of a Circle
Step 1. Use this method to measure real circular objects
You can measure the circumference of the circle you find in the real world, not just in story problems. Try it on a bicycle wheel, pizza, or coin.
Step 2. Find a piece of thread and a ruler
The thread should be long enough to wrap around the hoop, and flexible so that it can be wrapped tightly. You will need something to measure the thread later, such as a ruler or measuring tape. The thread will be easier to measure if the ruler is longer than the thread.
Step 3. Wrap the yarn around the circle
Start by placing one end of the yarn over the edge of the hoop. Wrap the yarn around the hoop and pull it tight. If you're measuring a coin or other thin object, you may not be able to pull the string tightly around it. Lay the circle object flat and arrange the yarn around it, as tightly as you can.
Be careful not to wind it more than once. The ends of your yarn should form a complete loop, so that there is no part of the loop where the two yarns are next to each other
Step 4. Mark or cut the thread
Find the section of yarn that completes a full loop, touching the end of your starting yarn. Mark this area with a permanent marker or use scissors to cut it out at this point.
Step 5. Unravel the thread and measure it with a ruler
Use a full circle of yarn and measure it on a ruler. If you're using a marker, only measure from the end of the thread to the color mark. This is the part of the thread that goes around the circle, and since the circumference of the circle is just the distance around the circle, you've got the answer! The length of this thread is equal to the circumference of the circle.
