Semicircle area calculator

What is a semicircle area calculator?

A semicircle area calculator finds the surface enclosed by half of a circle — the region bounded by a diameter and the arc that connects the two ends of that diameter. Because a semicircle is exactly half of a full circle, its area is half the area of the circle that contains it.

This calculator takes a single input — the radius — and returns the area. You can enter the radius in any common length unit (millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles) and read the result in any compatible squared unit. The math is identical regardless of the unit; only the conversion changes.

Key concepts

• Radius (r) — the distance from the center of the original circle to a point on its boundary. In a semicircle, this is the perpendicular distance from the middle of the straight edge to the curved edge.
• Diameter (d) — twice the radius. The diameter forms the flat side of the semicircle.
• Area (A) — the two-dimensional region enclosed by the diameter and the arc.
• Pi (π) — the constant ratio of a circle’s circumference to its diameter, approximately 3.14159.

How does the calculator work?

The area of a full circle is $\pi r^2$. A semicircle is half of that circle, so its area is exactly half. The calculator squares the radius, multiplies by π, and divides the result by two. It performs the calculation internally in square meters and then converts the answer to whichever unit you have selected for the output.

Formula

Equivalently, using the diameter:

Worked examples

Example 1: radius of 10 cm

A semicircle has a radius of 10 cm.

Example 2: radius of 5 cm

For a smaller semicircle with a radius of 5 cm:

Example 3: unit radius

A semicircle of radius 1:

Example 4: unit conversion

A semicircle has a radius of 2 m. The area in square meters is:

Practical uses

• Architecture and design — calculating the surface area of arched windows, doorways, or decorative half-circle elements.
• Civil engineering — sizing half-pipe drainage channels, tunnels with semicircular cross sections, or curved retaining walls.
• Sports and landscaping — laying out the semicircular keys on basketball courts, throwing circles, or garden bed edges.
• Manufacturing — estimating material for half-disk components such as protractors, gauges, or rounded brackets.
• Geometry homework — confirming answers when working with composite shapes that combine a semicircle with a rectangle or triangle (see the circle area calculator for the full disk).

Notes

• The radius must be a positive number; a radius of zero gives an area of zero.
• The semicircle area is always exactly half of the corresponding circle area.
• If you need the curved perimeter of the same shape, use the semicircle perimeter calculator — note that the perimeter includes the diameter, not just the arc.
• The result is unitless when the radius is unitless; otherwise the area carries the squared unit of the radius.