How to Calculate the Diameter of a Circle

Three Methods:Calculation HelpCalculating the Diameter of a Circle Using the Radius, Circumference, or AreaCalculating the Diameter of a Circle from a Drawing of a Circle

Calculating a circle's diameter is easy if you know any of the other dimensions of the circle: the radius, the circumference, or the area. It's also possible if you don't know any of the above dimensions but you do have a drawing of the circle. If you want to know how to calculate the diameter of a circle, just follow these steps.

Calculation Help

Diameter of a Circle Cheat Sheet

Method 1
Calculating the Diameter of a Circle Using the Radius, Circumference, or Area

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    If you know the radius of the circle, double it to get the diameter. The radius is the distance from the center of the circle to its edge. For example, if the radius of the circle is 4 cm, then the diameter of the circle is 4 cm x 2, or 8 cm.
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    If you know the circumference of the circle, divide it by π to get the diameter. π is equal to approximately 3.14 but you should use your calculator to get the most accurate results. For example, if the circumference of the circle is 10 cm, then the diameter is 10 cm/π, or 3.18 cm.
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    If you know the area of the circle, divide the result by π and find its square root to get the radius; then multiply by 2 to get the diameter. This goes back to manipulating the formula for finding the area of a circle, A = πr2, to get the diameter. You can transform this into r = √(A/π) cm. For example, if the area of the circle is 25 cm2, divide that by π and find the square root. This equals cm 2.82cm, so the diameter of the circle is 2.82 x 2 = 5.64cm.

Method 2
Calculating the Diameter of a Circle from a Drawing of a Circle

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    Draw a horizontal line inside the circle from one edge to the other. Use a ruler or a straight edge to do this. It can be at the top, near the bottom, or anywhere in between.
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    Label the points where the line crosses the circle points "A" and "B."
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    Draw two overlapping circles, one using A as the center and the other using B as the center. Be sure the two circles overlap like a Venn diagram.
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    Draw a vertical line through the two points at which the circles intersect. This line marks the diameter of the circle.
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    Measure the diameter. Measure it using a ruler, or for greater accuracy, a pair of digital calipers. You're done!

Tips

  • Familiarize yourself with the use of a compass (the drawing tool, not the direction-finder). This is a very useful instrument in many applications, including drawing a circle's diameter, as outlined above. A divider (an instrument similar to a compass) can sometimes be used in such cases.
  • Using geometrical formulas and equations gets easier with practice. Ask for help from someone who has worked with circles or any other geometrical figures. You're likely to find that questions of geometry will seem less challenging with a little experience.

Things You'll Need

  • Calculator
  • Pencil with an eraser
  • Compass
  • Ruler
  • Digital calipers(optional)

Article Info

Categories: Mathematics