Semicircle Area Calculator

Calculate the area of a semicircle with half of π times radius squared. Includes the formula, a worked example, and real-world uses for archways and windows.

Calculate area of semicircle

Formula

\\text{area} = \\\\frac{\\\\pi r^2}{2}

Where r is the radius of the semicircle.

Worked example

Calculate the area of a semicircle with radius 7 cm:

\\text{area} = \\\\frac{\\\\pi \\\\times 7^2}{2} = \\\\frac{\\\\pi \\\\times 49}{2} \\\\approx \\\\frac{3.1416 \\\\times 49}{2} = \\\\frac{153.94}{2} = 76.97 \\\\text{ cm}^2

Result: 76.97 cm²

How to use

Enter the radius of the semicircle
Click "Calculate" to see the area

Related formulas

Full circle area: $\\\\pi r^2$
Circumference of semicircle: $\\\\pi r + 2r$
Perimeter: Include the diameter plus the curved edge

Common use cases

Architectural semi-circular designs
Land parcel with curved boundaries
Manufacturing semi-circular parts
Graphics and design applications

FAQ

What if I only know the diameter? Divide by 2 to get the radius: $r = \\\\frac{d}{2}$

Can I calculate the perimeter? Yes, add the curved edge ( $\\\\pi r$ ) plus the diameter ( $2r$ ).

What units should I use? Any consistent unit. The area will be in square units.

How is this different from a sector? A semicircle is exactly half a circle (180°), while a sector can be any angle.

Other related tools

★ FeaturedArea CalculatorCalculate the area of common geometric shapes and the surface area and volume of 3D solids, right in your browser.internalcalculator