Semicircle Area Calculator

A semicircle is exactly half of a full circle, meaning its formulas derive directly from standard circular geometry. The primary calculation for area is derived by taking the area of a full circle (A = πr²) and dividing it by two: Area = (π × r²) / 2, where r represents the radius. If you are starting with the diameter, you can find the radius simply by dividing the diameter by two (r = d / 2). Finding the perimeter of a semicircle requires adding the curved arc length (half the circle circumference, or πr) to the straight bottom edge (the diameter, which equals 2r), giving the formula Perimeter = πr + 2r.

Let us walk through a practical example to see how these equations function in practice. Imagine you are building a semicircular garden bed with a radius of 10 inches. First, calculate the area by squaring the radius (10² = 100), multiplying by Pi (π ≈ 3.14159), which gives 314.159, and then dividing by 2. The resulting area is approximately 157.08 square inches. Next, to find the total boundary length or perimeter, calculate the curved arc length (π × 10 = 31.416 inches) and add the straight diameter edge (2 × 10 = 20 inches), yielding a total perimeter of 51.42 inches.

Always double-check whether your starting measurement is given as a radius or a diameter, as confusing the two is the most common source of geometry errors. Remember that the perimeter of a semicircle includes the flat baseline edge; do not just calculate half of a circle circumference unless you are measuring strictly the curved arch. When working on physical layout projects, keep your units consistent—never mix inches and feet within the same equation without converting them first.