Half Circle Calculator: Area, Arc & More

This calculator computes the key measurements of a half circle (semicircle) from a single input: the radius, diameter, or arc length. You enter one known value, and it returns the area, perimeter (arc length plus the diameter), arc length, and the straight-line distance across. The formulas are standard geometry, so the results are exact for any semicircle.

Formula

The area of a full circle is πr², so the area of a half circle is exactly half of that:

Area = (π × r²) / 2

The arc length (the curved part) is half the circumference of a full circle (2Ï€r), so:

Arc length = π × r

The perimeter of a semicircle is the arc length plus the straight diameter:

Perimeter = π × r + 2r

Where:

• r = radius (distance from center to the curved edge), in meters (or any unit)
• Ï€ (pi) ≈ 3.14159
• Area is in square units (e.g., m²)
• Arc length and perimeter are in linear units (e.g., m)

Worked Example

Using the default radius of 5 meters:

1. Area = (π × 5²) / 2 = (3.14159 × 25) / 2 = 78.5398 / 2 = 39.27 m² (rounded to 2 decimals)
2. Arc length = π × 5 = 15.71 m
3. Perimeter = π × 5 + 2 × 5 = 15.71 + 10 = 25.71 m
4. Diameter = 2 × 5 = 10 m

These match the calculator output exactly.

When to Use a Half Circle Calculator

You need this whenever a project involves a semicircular shape. Common real-world cases include:

• Estimating the area of a half-round garden bed or patio
• Finding the amount of material for a semicircular arch or window
• Calculating the surface area of a dome’s flat cross-section
• Determining the length of trim or edging around a semicircular feature
• Checking the size of a half-circle table or rug

The calculator works for any unit – inches, feet, centimeters, meters – as long as you stay consistent. If you enter inches, the area comes out in square inches, and the arc length in inches.

How to Read the Results

The area is the amount of flat space enclosed by the semicircle. The arc length is the distance along the curved edge. The perimeter is the total length of the boundary: the curved part plus the straight diameter. The diameter is simply twice the radius, which is the straight-line width of the semicircle.

For example, if you are building a semicircular deck with radius 5 m, the deck surface area is 39.27 m², and the railing along the curved edge would need to be 15.71 m long. If you want to edge the whole shape, you need 25.71 m of edging.

Common Mistakes and How to Avoid Them

• Using diameter instead of radius: The formula requires the radius. If you have the diameter, divide it by 2 first. Confusing the two will give an area that is 4 times too large.
• Mixing units: If you measure the radius in feet, the area is in square feet, not square meters. Convert all measurements to the same unit before calculating.
• Forgetting the straight edge in perimeter: The perimeter of a semicircle is not just the arc length – you must add the diameter. Many people forget this when buying trim or fencing.
• Rounding too early: If you round Ï€ to 3.14, your result will be slightly off. Use the Ï€ button on your calculator for better accuracy.

Limitations of the Formula

These formulas apply only to a perfect mathematical semicircle – exactly half of a circle with a straight diameter. Real-world objects may have slight imperfections, but for most practical purposes, the difference is negligible. If the shape is not a true semicircle (for example, an arch that is flatter or taller than a half circle), these formulas will not be accurate, and you would need a different geometric calculation.

Frequently Asked Questions

How do I find the radius if I only know the diameter?

Divide the diameter by 2. For instance, if the diameter is 10 cm, the radius is 5 cm. Then use the calculator with that radius.

Can I use this for a half-cylinder volume?

No, this calculator only gives area and linear measurements. To find the volume of a half-cylinder, you would multiply the area of the semicircle by the length of the cylinder. For example, a half-pipe with radius 2 m and length 10 m has a volume of (π × 2² / 2) × 10 ≈ 62.83 m³.

What is the difference between arc length and perimeter?

Arc length is only the curved portion. Perimeter is the total boundary, which includes the curved part plus the straight diameter. For a semicircle with radius 5 m, the arc length is 15.71 m, but the perimeter is 25.71 m.

Can I enter the arc length instead of the radius?

This calculator requires the radius. However, you can reverse the formula: if you know the arc length (L), then the radius is L / π. For example, an arc length of 15.71 m corresponds to a radius of 5 m.

Does the calculator work for any unit?

Yes, as long as you use one unit consistently. The area will be in square units of that measurement (e.g., square inches, square feet, square meters) and the arc length and perimeter in the same linear unit.

Why is the area of a semicircle half the area of a circle?

Because a semicircle is exactly half of a full circle. The area of a full circle is πr², so half of that is (πr²)/2. This is a direct geometric fact, not an approximation.

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in r | Radius | m | 5 | 0
out area | Area | m² | (pi * r^2) / 2 | 2
out arc | Arc length | m | pi * r | 2
out perim | Perimeter (arc + diameter) | m | pi * r + 2 * r | 2
out diam | Diameter | m | 2 * r | 2