Semicircle Area Calculator

Whether you're slicing fruit, sketching out a curved patio, or solving a geometry problem, semicircle area is one of those concepts that shows up more often than you'd expect. Though the shape seems simple, accurately measuring its area can make a huge difference, whether in home projects, design work, or academics. The best part? You just need a basic formula and a bit of reasoning to get it right.

Want to learn more about other shapes? Try our full collection of Area Calculators.

What Is Semi-Circle Area?

The area of a semicircle refers to the space within half of a circle. If you’ve ever halved a round cake and wondered how much frosting you need for just one side, you’ve already thought about the semicircle area, just without the math.

From curved garden borders to archways in architecture, semicircles are everywhere. Understanding how to calculate their area isn’t just a math trick — it’s a practical skill. Whether you're estimating materials, designing curved elements, or validating a measurement, this knowledge gives you better control over rounded spaces.

Try out Square Area Calculator

How to Calculate the Area of a Semicircle

Calculating the area of a semicircle starts with a formula you may already know:

Area of a full circle = π × r²
Area of a semi circle = (π × r²) ÷ 2

That’s all there is to it — take the regular area formula for a circle and cut it in half.

Here’s a breakdown:

• π (pi) is a constant, about 3.14159

• r is the radius — the distance from the center to the edge

• r² means the radius is squared

• Then divide by 2, since you're only calculating half the circle

Say you have a semi-circular driveway with a radius of 6 meters:

Area = (π × 6²) ÷ 2 = (π × 36) ÷ 2 = 113.1 square meters (rounded)

This gives you a precise surface area — great for estimating paving, landscaping, or sealing needs.

💡 Pro tip: Use our free Circle Area Calculator, then divide the result by two. It’s a quick way to double-check your math, especially with tricky decimals.

Semi-Circle vs. Circle: What’s the Real Difference?

At first glance, the difference between a semicircle and a full circle seems obvious—one is simply half of the other. But when you dive into the math behind area and perimeter, there are a few key distinctions worth knowing.

Area — Yes, It’s Half

When it comes to area, a semicircle truly is half of a full circle. The formula is straightforward:

Semi Circle Area = (π × r²) ÷ 2

So, if a full circle covers 78.5 square centimeters, its semi-circular counterpart will span exactly 39.25 square centimeters. That part’s easy to remember.

Perimeter — Not Half

Here’s where many people go wrong: the perimeter of a semicircle isn’t half the circumference.

Why? Because a semicircle’s perimeter includes:

• The curved edge (half the circumference), plus

• The flat edge (the diameter)

So the correct formula is:

Perimeter = (π × r) + 2r
or
Perimeter = (π × d ÷ 2) + d

That means if you're planning something like a semi-circular garden bed, building a curved fence, or laying pavers around an arc, don’t forget that flat base. It plays a crucial role in both your measurements and your material costs.

The Arch in Ancient Rome

The semicircle isn’t just a concept from geometry class—it’s a foundational element in some of the world’s most iconic architecture.

Walk through ancient Roman ruins—or even a modern city influenced by classical design—and you’ll spot one recurring shape: the arch. From the towering structures of aqueducts to the impressive entrances of coliseums and city gates, the semi-circular arch was a defining feature of Roman engineering.

But this wasn’t just for aesthetics. The Romans had a keen understanding of physics and geometry. They realized that the semi-circular shape naturally pushes weight outward and downward, creating incredible structural stability. This insight allowed them to construct larger and more durable buildings, all without the benefit of modern materials like steel or reinforced concrete.

They used wedge-shaped stones, known as voussoirs, carefully arranged into a semicircle. When fitted together, these stones formed an arch that could support immense weight. Thanks to this innovation, some Roman aqueducts—built more than 2,000 years ago—are still standing today, a testament to the strength and genius of semi-circular design.