Area of a Circle Calculator
Use this calculator to easily calculate the area of a circle, given its radius in any metric: mm, cm, meters, km, inches, feet, yards, miles, etc.
- Area of a circle formula
- How to calculate the area of a circle?
- Example: find the area of a circle
- Practical application
Area of a circle formula
The formula for the area of a circle is π x radius2, but the diameter of the circle is d = 2 x r2, so another way to write it is π x (diameter / 2)2. Visual on the figure below:
π is, of course, the famous mathematical constant, equal to about 3.14159, which was originally defined as the ratio of a circle's circumference to its diameter. The formula above is the one used in our area of a circle calculator.
How to calculate the area of a circle?
Calculation is easy once you have measured the circle's radius or diameter, or if you know it from plans and schematics: just plug the numbers into the formulas above use our area of a circle calculator above. If you are measuring it by hand, remember that the diameter is the largest measurement you can get from a circle.
Example: find the area of a circle
Task 1: Given the radius of a cricle, find its area. For example, if the radius is 5 inches, then using the first area formula calculate π x 52 = 3.14159 x 25 = 78.54 sq in.
Task 2: Find the area of a circle given its diameter is 12 cm. Apply the second equation to get π x (12 / 2)2 = 3.14159 x 36 = 113.1 cm2 (square centimeters).
Circle geometry has a wide array of practical uses. Circles are used when planning athletic tracks, recreational areas, buildings, and roundabouts, so knowing their area is important in construction, landscaping, etc. The famous Ferris-wheel attraction is a circle, as are the wheels on your car or bike. Circle-like parts, e.g. cylinders, tubes, gears, and others are used by engineers in clocks, bikes, cars, trains, ships, planes, and even rockets. The invention of the wheel was one of the transforming events in early human history, as it dramatically reduced the energy expended in moving stuff around and made travelling easier. The number π has application in calculating statistical distributions like the normal distribution (gaussian distribution), which are used throughout the sciences.
Cite this calculator & page
If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:
Georgiev G.Z., "Area of a Circle Calculator", [online] Available at: https://www.gigacalculator.com/calculators/area-of-circle-calculator.php URL [Accessed Date: 27 Sep, 2021].