Semicircle Area Calculator
Find the area, curved arc length and full perimeter of a semicircle from its measured radius.
How the result changes
Only radius changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Semicircle Area Calculator: Find the area, curved arc length and full perimeter of a semicircle from its measured radius. Enter radius; the reported quantities are semicircle area (m²), curved arc length (m), total perimeter (m). The equations and examples below show how those inputs lead to the result and where the model's assumptions matter.
Formula
area = πr²/2; curved arc = πr
Worked example
With Radius: 5 m, semicircle area is 39.269908 m².
Method and inputs
A semicircle is exactly half of a disk. Compute full-circle area pi times radius squared, then divide by two. Half the circumference is pi times radius; add the straight diameter, twice the radius, if total perimeter is wanted.
Worked example
At radius 5 meters, the area is 12.5pi, about 39.27 square meters. The curved arc is 5pi, about 15.71 meters, and the complete perimeter is 5pi plus 10, about 25.71 meters.
A radius of 10 meters is twice the example radius, so area becomes four times as large, about 157.08 square meters. Arc and perimeter only double. This different growth rate is useful for checking scaling estimates in landscape design or sheet cutting.
How to read the result
Area, curved arc and perimeter answer different questions. Area is a two-dimensional region in square units; the other two are lengths. The total perimeter includes the flat edge, while curved arc length does not.
A painted semicircular region uses area, while edging around it uses total perimeter. If the straight diameter lies against an existing wall, edging material may cover only the curved arc. Select the output that matches the physical work rather than assuming one boundary measure fits all jobs.
Assumptions and checks
The shape must be a true half circle, bounded by a diameter. A circular segment cut by an off-center chord has a different area. Radius cannot be negative and should be measured from the center to the arc.
A frequent perimeter error is reporting only half the circumference and omitting the diameter. Another is entering diameter as radius, which quadruples the area. If only diameter is known, divide it by two before entry.
Common questions
What does the semicircle area calculator calculate?
It returns the region area, the curved boundary length and the entire boundary length of a perfect semicircle.
When should I recalculate or check another method?
Recalculate if the shape is a smaller circular segment or if a drawing specifies diameter rather than radius. For material estimates, allow separately for cutting waste and construction tolerances.
Inputs
- Radius (m)