Semicircle perimeter calculator

What is a semicircle perimeter calculator?

A semicircle perimeter calculator finds the total distance around half of a circle. The boundary of a semicircle has two distinct parts: the curved arc, which is half of the original circle’s circumference, and the straight edge, which is the diameter of that circle. Adding the two together gives the full perimeter.

This calculator takes a single input — the radius — and returns the perimeter. 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 length unit. The underlying math is the same regardless of which unit you choose; only the final 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, $d = 2r$. The diameter forms the flat side of the semicircle.
• Arc length — half the circumference of the original circle, $\pi r$.
• Perimeter (P) — the total length of the boundary: the curved arc plus the straight diameter.
• Pi (π) — the constant ratio of a circle’s circumference to its diameter, approximately 3.14159.

How does the calculator work?

The circumference of a full circle is $2\pi r$. Half of that is the arc that bounds the curved side of the semicircle, $\pi r$. The straight side is the diameter, $2r$. The calculator adds these two contributions and factors out the radius, then performs the calculation internally in meters and 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 perimeter in meters is:

Practical uses

• Architecture and design — measuring trim, weatherstripping, or moulding around arched windows, doorways, or half-round decorative panels.
• Civil engineering — calculating the bounding length of half-pipe drainage channels, semicircular tunnels, or curved retaining walls.
• Sports and landscaping — laying out the painted boundary of basketball keys, throwing circles, or garden bed edges that combine a curve with a straight back.
• Manufacturing — estimating the edge length for half-disk parts such as protractors, gauges, or rounded brackets that need a gasket or rubber lining.
• Geometry homework — checking composite-shape problems that combine a semicircle with a rectangle (see the circumference calculator for the full circle).

Notes

• The radius must be a positive number; a radius of zero gives a perimeter of zero.
• The semicircle perimeter is not half of the full circumference — that would only give the arc. You must also add the diameter.
• If you need the enclosed area of the same shape rather than the boundary length, use the semicircle area calculator.
• The unit of the perimeter matches the unit of the radius. Switching either unit selector reconverts the result automatically.