Semicircle Area Calculator: Formula and Example

A semicircle area calculator finds the area of half a circle from its radius or diameter. Enter either measurement in the same unit, and it returns the area in square units, along with the full circle’s area as a check.

Formula

The area of a semicircle is half the area of a circle:

A = πr² / 2

• A is the semicircle’s area, in square units.
• r is the radius, the distance from the circle’s center to its curved edge, in units such as centimeters, inches, or meters.
• π (pi) is approximately 3.14159.

If you know the diameter d instead, the radius is half of it: r = d / 2. Substituting that into the area formula gives A = πd² / 8. The calculator above takes a radius as its input, so halve a diameter before entering it.

Worked Example

Using the calculator’s default radius of 5 units:

1. Square the radius: 5² = 25.
2. Multiply by pi: π × 25 ≈ 78.5398.
3. Take half: 78.5398 / 2 ≈ 39.27 square units.

The full circle’s area is π × 5² ≈ 78.54 square units. The semicircle is exactly half of that before rounding, as the calculator’s second result shows.

How to Use the Calculator

Measure the radius from the center of the circle to its curved boundary. Enter that value in the Radius field; the default is 5 units. The displayed output uses generic units because the numerical formula is the same whether your measurements are in millimeters, inches, feet, centimeters, or meters.

If you have a diameter, measure straight across the circle through its center, then divide by two. For example, a diameter of 12 inches means a radius of 6 inches. Enter 6, and interpret the result as square inches. Do not enter 12 as the radius: doing so would make the calculated area four times too large.

Area is two-dimensional, so its units are squared. A radius in centimeters produces square centimeters (cm²); a radius in feet produces square feet (ft²). To convert an answer, convert the length unit and square the conversion factor. For example, 1 foot equals 12 inches, so 1 square foot equals 144 square inches—not 12 square inches. Metric conversions work the same way: 1 meter equals 100 centimeters, while 1 square meter equals 10,000 square centimeters.

What the Result Represents

A semicircle is one half of a circle, divided by a straight line through its center, called the diameter. Its area includes the curved half-disk, not just the curved outline and straight edge. The calculator reports the area of that filled-in region. It does not calculate the length of the boundary.

For a radius of 5 units, the semicircle covers about 39.27 square units. The result is not 5π or 2.5π: area depends on the square of the radius, so doubling the radius quadruples the area. That squared relationship is why a small measurement error can noticeably affect the result.

Common Mistakes and Limits

• Confusing radius and diameter: The radius is half the diameter. Check which measurement you have before entering it.
• Forgetting to halve the circle’s area: πr² gives the whole circle. A semicircle uses πr² / 2.
• Mixing measurement units: Keep the input in one length unit and label the answer in its square unit. Convert before calculating if measurements come from different systems.
• Rounding too early: Keep the full calculator result for intermediate steps and round the final area to a sensible number of decimal places for your measurement.
• Entering an approximate radius as exact: The output is only as precise as the measurement. More displayed decimal places do not make an imprecise measurement more accurate.

The formula assumes a true semicircle with a known radius. It does not account for irregular edges, thickness, material loss, or a shape that is only approximately circular. For a physical object with an uneven boundary, this result is an idealized estimate rather than a measurement of its exact area.

Area Compared with Perimeter

Area and perimeter answer different questions. Area measures the region inside the shape; perimeter measures the distance around its boundary. The perimeter of a semicircle includes both the half-circle arc and the straight diameter:

P = πr + 2r

Here, P is the perimeter in length units and r is the radius. For the default radius of 5 units, the perimeter is about 25.71 units, while the area is about 39.27 square units. Do not label a perimeter in square units or an area in ordinary length units.

Frequently Asked Questions

How do you calculate the area of a semicircle?
Square the radius, multiply by pi, and divide by two: A = πr² / 2. If you know the diameter, halve it to get the radius first.

What is the area of a semicircle with a diameter of 10?
The radius is 5. The area is π × 5² / 2, which is about 39.27 square units. The unit depends on whether the diameter was measured in inches, centimeters, or another length unit.

Can I calculate semicircle area from the diameter?
Yes. Use A = πd² / 8, where d is the diameter. This is equivalent to first dividing the diameter by two and then using the radius formula.

Is a semicircle’s area exactly half of a circle’s area?
Yes, when the semicircle and circle have the same radius. The semicircle occupies one of the two equal halves created by a diameter.

Why is the answer in square units?
Area measures two-dimensional space. Since the formula squares the radius, a measurement in inches produces square inches, and a measurement in meters produces square meters.

Does the straight edge count toward semicircle area?
No. The straight diameter is part of the boundary, not part of the area calculation. It does count when finding the semicircle’s perimeter.

Related

• Molarity × Volume: Formula and Solution Examples
• Kane Formula IOL Calculator: How It Works
• Minutes and Seconds Time Right Now?

in r | Radius | units | 5 | 0
out area | Semicircle area | square units | pi * r ^ 2 / 2 | 2
out circle | Full circle area | square units | pi * r ^ 2 | 2