Arc Length of a Half Circle Calculator

This calculator finds the arc length of a semicircle (half circle) from its radius or diameter. Enter the radius (or diameter) and the tool returns the curved distance around the half circle, using the formula π × r. The result is given in the same unit you used for the input, so if you enter meters, you get meters.

Formula

The arc length L of a semicircle is exactly half the circumference of a full circle. Since the circumference of a full circle is C = 2Ï€r, half of that is:

L = π × r

where:

• L = arc length (same unit as the radius, e.g., meters, feet, inches)
• r = radius (distance from center to the edge)
• Ï€ ≈ 3.14159

If you only know the diameter d, the formula becomes L = π × d / 2 because the radius is half the diameter.

Worked Example

Using the calculator’s default radius of 5 meters:

1. Start with the formula: L = π × r
2. Plug in r = 5 m: L = π × 5
3. Multiply: L ≈ 3.14159 × 5 = 15.70795 m
4. Rounded to two decimal places: 15.71 m

This matches the calculator’s output exactly. The diameter shown (10 m) is just the radius doubled.

When to Use This Calculation

Semicircle arc length appears in many practical situations:

• Finding the length of a curved garden path or driveway that forms a half circle.
• Estimating the amount of trim, edging, or molding needed for a half-round window or arch.
• Computing the length of a curved wall in architecture or interior design.
• Determining the distance around a semicircular track or running path.
• Calculating the length of a curved piece of material in metalworking or woodworking.

In each case, you measure the radius (or diameter) and the formula gives the curved distance—not the straight-line distance across the diameter.

How to Read the Result

The output is the length of the curved portion only. It does not include the straight diameter segment that closes the semicircle. If you need the total perimeter of a half-circle shape (the curved part plus the straight base), you must add the diameter:

Perimeter of semicircle = π × r + 2r = r(π + 2)

For example, with r = 5 m, the arc length is 15.71 m, but the total perimeter is 15.71 + 10 = 25.71 m. Many people confuse these two, so check what your project actually requires.

Common Mistakes and How to Avoid Them

• Using diameter instead of radius: The formula needs the radius. If you have the diameter, divide it by 2 first, or use the form L = Ï€d/2. Forgetting this doubles your answer.
• Forgetting Ï€ is a ratio: Ï€ is approximately 3.14159, not 3.14 unless you accept a small error. For most DIY work, 3.14 is fine, but for precise engineering use more digits.
• Mixing units: If you measure the radius in feet, the arc length is in feet. Do not mix inches and feet without converting.
• Rounding too early: If you round Ï€ to 3.14 and then round the result, you may lose accuracy. Keep extra digits until the final step.
• Confusing arc length with perimeter: As noted, the arc is only the curved part. If you need the full outline, add the diameter.

Limits and Extensions

This formula works only for a perfect half circle—exactly 180 degrees. If your shape is a different fraction of a circle, use the general arc length formula:

L = (θ/360) × 2πr (for degrees) or L = θ × r (for radians, where θ is the central angle).

For a semicircle, θ = 180°, so the general formula gives (180/360) × 2πr = πr, which matches. The calculation also assumes a flat, two-dimensional curve; it does not account for terrain elevation or material stretching.

Frequently Asked Questions

How do I find the arc length of a half circle if I only know the diameter?

Divide the diameter by 2 to get the radius, then use L = π × r. Alternatively, use L = π × d / 2 directly. For example, a semicircle with a diameter of 10 m has an arc length of π × 10 / 2 ≈ 15.71 m.

Is the arc length of a semicircle the same as its perimeter?

No. The arc length is only the curved portion. The perimeter includes the straight diameter as well. For a semicircle, perimeter = πr + 2r. So for r = 5 m, arc length is 15.71 m, but perimeter is 25.71 m.

What if my shape is not exactly a half circle?

If the arc is not 180 degrees, you need the central angle. Use the general formula L = (θ/360) × 2πr for degrees. For example, a 90-degree arc with r = 5 m has length (90/360) × 2π × 5 ≈ 7.85 m.

Why is π in the formula?

π is the ratio of a circle’s circumference to its diameter, approximately 3.14159. Since a semicircle is half a circle, its arc length is half the full circumference, which is π times the radius.

Can I use this for a half-circle track?

Yes, if the track is a perfect semicircle. Measure the radius from the center to the inside or outside edge, depending on which lane you want. The arc length gives the curved distance; add the two straight sections if the track has them.

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in r | Radius | m | 5 | 0
out arc | Arc length | m | pi * r | 2
out diameter | Diameter | m | 2 * r | 2