What Is a Semicircle Calculator?
A Semicircle Calculator is a geometry tool that
helps you calculate the important measurements
of a semicircle using its radius or diameter.
A semicircle is exactly half of a circle. It has
one curved half of the circular boundary and one
straight edge formed by the diameter.
This calculator can determine the area, radius,
diameter, curved arc length, and complete perimeter
of a semicircle.
The tool is useful for students, teachers,
engineers, designers, and anyone working with
geometric measurements.
How to Use the Semicircle Calculator
Enter either the radius or diameter of your
semicircle. The calculator automatically derives
the radius when the diameter is provided.
1
Enter a Measurement
Enter the radius or diameter of the
semicircle into the calculator.
2
Calculate
Click the calculate button to apply the
appropriate semicircle formulas.
3
View Results
Instantly view the area, perimeter, diameter,
radius, and curved length.
Semicircle Formulas
Area of a Semicircle
Since a semicircle is half of a circle, its area
is half of π multiplied by the square of its radius.
A = πr² / 2
Diameter
The diameter is twice the radius.
d = 2r
Curved Length
The curved portion of a semicircle is half of
the circumference of a complete circle.
L = πr
Perimeter
The total perimeter of a semicircle includes the
curved portion plus the straight diameter.
P = πr + 2r
P = r(π + 2)
Semicircle Calculation Example
Suppose a semicircle has a radius of
10 units.
Its area is:
A = π × 10² / 2
A = 50π
A ≈ 157.08 square units
Its diameter is:
d = 2 × 10
d = 20 units
The curved length is:
L = π × 10
L ≈ 31.42 units
The complete perimeter is:
P = π(10) + 2(10)
P ≈ 51.42 units
Therefore, a semicircle with a radius of
10 units has an area of approximately
157.08 square units and a
perimeter of approximately
51.42 units.
Semicircle Area vs. Perimeter
Area and perimeter describe different properties
of a semicircle. Area measures the amount of
two-dimensional space enclosed by the shape,
while perimeter measures the complete boundary.
For a semicircle, the perimeter includes two
different parts: the curved half of the circle
and the straight diameter.
Area = πr² / 2
Perimeter = πr + 2r
Remember that area is expressed in square units,
while perimeter and curved length are expressed
in linear units.
Frequently Asked Questions
What is a semicircle?
A semicircle is exactly half of a circle. It
contains a curved arc and a straight diameter.
What is the formula for the area of a semicircle?
The area is calculated using A = πr² / 2,
where r is the radius.
How do you calculate the perimeter of a semicircle?
Add the curved length πr to the diameter 2r.
Therefore, P = πr + 2r.
What is the curved length of a semicircle?
The curved length is half the circumference of
a full circle, so it equals πr.
How do I find the radius from the diameter?
Divide the diameter by two. The formula is
r = d / 2.
Does the semicircle perimeter include the diameter?
Yes. The perimeter of a semicircle includes both
the curved arc and the straight diameter.
Is a semicircle half the area of a circle?
Yes. A semicircle has exactly half the area of
a complete circle with the same radius.
Is the curved length the same as the perimeter?
No. The curved length includes only the curved
arc. The perimeter also includes the straight
diameter.
What units can I use for a semicircle?
You can use any consistent unit such as inches,
feet, meters, centimeters, or millimeters.
Can I enter the diameter instead of the radius?
Yes. Enter the diameter and the calculator will
automatically divide it by two to determine the
radius.