What is a semicircle?

A semicircle is exactly half of a circle, created by cutting a circle along its diameter. It consists of a curved arc and a straight diameter edge.

Area formula

The area of a semicircle is half the area of a full circle:

A = \frac{\pi r^2}{2}

Where:

$A$ = area
$r$ = radius
$\pi$ ≈ 3.14159

Using diameter

If you know the diameter instead of the radius:

A = \frac{\pi d^2}{8}

Since $r = \frac{d}{2}$ , substituting gives us this equivalent formula.

Perimeter formula

The perimeter (total boundary) of a semicircle consists of two parts:

Arc length (the curved part): $\pi r$
Diameter (the straight edge): $2r$

P = \pi r + 2r = r(\pi + 2)

Or approximately:

P \approx 5.14r

Arc length

The arc length is the curved portion only:

\text{Arc} = \pi r = \frac{\pi d}{2}

This is exactly half the circumference of a full circle.

Relationship to full circle

Property	Full circle	Semicircle
Area	$\pi r^2$	$\frac{\pi r^2}{2}$
Circumference/Arc	$2\pi r$	$\pi r$
Central angle	360°	180°

Example calculation

For a semicircle with radius 5 units:

Area:

A = \frac{\pi \times 5^2}{2} = \frac{25\pi}{2} \approx 39.27 \text{ sq units}

Arc length:

\text{Arc} = \pi \times 5 \approx 15.71 \text{ units}

Perimeter:

P = \pi \times 5 + 10 \approx 25.71 \text{ units}

Real-world applications

Architecture

Arched windows and doorways
Dome cross-sections
Tunnel entrances

Engineering

Bridge arch calculations
Pipe flow areas
Structural beam profiles

Design

Logo and graphic design
Landscaping (semicircular patios, garden beds)
Furniture (half-round tables)

Related shapes

Quarter circle

A quarter circle has one-fourth the area of a full circle:

A = \frac{\pi r^2}{4}

Sector

A sector is a "pizza slice" of a circle with any central angle θ:

A = \frac{\theta}{360°} \times \pi r^2

A semicircle is a special case where θ = 180°.

Segment

A circular segment is the region between a chord and its arc. It differs from a semicircle unless the chord is the diameter.

Converting between units

When converting area between units, remember to square the conversion factor:

1 m² = 10,000 cm²
1 ft² = 144 in²
1 m² ≈ 10.764 ft²

For the perimeter (linear measurement), use the standard conversion factor without squaring.

Area of a Semicircle Calculator