Circle (with diameter)- perimeter and area
Online calculator — enter the values and get the result instantly, with the formula and a worked example.
P - perimeter
A = area
d = diameter
r = radius
A circle is a two-dimensional shape made up of all the points in a plane that lie at the same fixed distance from a single central point. That distance is called the radius, and every radius drawn from the center to the edge has exactly the same length. A straight line that crosses the circle through its center is the diameter, and it is always twice the radius, splitting the circle into two equal halves. The boundary of the circle itself is called the circumference, and it encloses the flat region we measure as its area. One of the circle's most remarkable features is that the ratio of its circumference to its diameter is always the same number, the constant pi (about 3.14159), no matter how large or small the circle is. This perfect, uniform symmetry makes the circle one of the most efficient shapes in nature, enclosing the greatest area for a given boundary length. From wheels, gears, and pipes to lenses, clocks, orbits, and the ripples on water, circles appear everywhere in mathematics, engineering, design, and the natural world.
Area of the circle
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Circumference
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Radius r
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Diameter d
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Area
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Drag the edge of the circle Re-center
Worked example
Let's assume we have a circle with a diameter of d = 10 cm.
Calculation of the perimeter
The perimeter C is calculated using the formula:
C = π · d
Since π ≈ 3.14159, we can calculate the perimeter:
C = 3.14159 · 10
C = 31.4159 cm
Calculation of the area
The area A is calculated using the formula:
A = π · (d/2)^2
First, we calculate the radius r as half of the diameter:
r = d/2 = 10/2 = 5 cm
Now we can calculate the area:
A = 3.14159 · 5^2
A = 3.14159 · 25
A = 78.53975 cm²
Summary
Diameter of the circle: d = 10 cm
Circumference of the circle: C ≈ 31.4159 cm
Area of the circle: A ≈ 78.53975 cm²
