Area of a Semicircle Calculator
Enter radius, diameter, or area — get all semicircle properties instantly with step-by-step working.
💡 Enter any one value — the others update instantly.
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Radius
Diameter
Area
Perimeter
✎ Step-by-Step Solution
Semicircle Area Formulas
From Radius
A = π × r² / 2
Square the radius, multiply by π, then divide by 2.
From Diameter
A = π × (d/2)² / 2
Halve the diameter to get radius, then apply A = πr²/2.
Perimeter
P = r × (π + 2)
Arc length (πr) plus the flat diameter (2r).
From Area
r = √(2A / π)
Rearrange A = πr²/2 to solve for the radius.
What Is a Semicircle?
A semicircle is exactly half of a circle, formed by cutting a circle along its diameter. It has one curved edge (the arc, which is half the circumference) and one straight edge (the diameter). The area of a semicircle is therefore half the area of the full circle with the same radius: A = πr²/2.
Unlike a full circle, the perimeter of a semicircle is not simply half the circumference — it includes the straight diameter as well: P = πr + 2r = r(π + 2). This distinction is important in engineering and architecture when calculating material lengths for arched structures.
How to Calculate the Area of a Semicircle
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1
Identify your known value
Do you know the radius, diameter, or area? Each leads to all other properties via a simple formula path.
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2
Convert to radius if needed
From diameter: r = d ÷ 2. From area: r = √(2A ÷ π).
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3
Apply the area formula
A = π × r² ÷ 2. Square r, multiply by π (3.14159…), then divide by 2.
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4
Calculate the perimeter
P = r × (π + 2) = πr + 2r. Remember: perimeter includes the flat diameter, not just the arc.
Worked Example — Swimming pool cross-section with radius 3.5 m
Real-World Applications
Architecture
Arch doorways, Romanesque windows, and vaulted ceilings all use semicircular geometry for structural integrity and aesthetic appeal.
Sports
The D-zone in basketball courts and semicircular swimming pool ends require precise area calculations for construction and regulation compliance.
Engineering
Tunnel cross-sections and pipe half-fills often take semicircular shapes. Knowing the area determines flow capacity and material volume.
Science
Protractors, semicircular lens elements, and spectrometer components all rely on semicircle geometry for accurate measurement and optics.
Design
Logo design, decorative arch elements, and UI components frequently use semicircles. Area knowledge ensures correct proportions and material estimates.
Food
Half pizzas, semicircular cake portions, and pastry cutting all involve semicircle area calculations for fair portioning and serving size estimates.
Common Semicircle Measurements
| Object | Radius | Diameter | Area | Perimeter |
|---|---|---|---|---|
| 📐 Protractor | 10 cm | 20 cm | 157.08 cm² | 51.42 cm |
| 🪟 Semicircular window | 30 cm | 60 cm | 1413.72 cm² | 124.25 cm |
| 🍕 Half pizza (12") | 15.24 cm | 30.48 cm | 365.3 cm² | 78.4 cm |
| 🚪 Arch doorway | 0.5 m | 1 m | 0.393 m² | 2.571 m |
| 🏟️ Stadium end zone | 15 m | 30 m | 353.4 m² | 77.1 m |
| 🌊 Half moon pool | 2 m | 4 m | 6.28 m² | 10.28 m |