Semicircle Calculator
Area and perimeter of a half circle from its diameter — and the perimeter is the part people get wrong, because it includes the straight edge.
With diameter — the straight edge 8 ft, semicircle comes to 25.133 sq ft — area. It is reached in 6 steps, the last of which is full_area / 2, and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.
Formula and sources checked · How we check
Diameter — the straight edge 8 ft
25.133 sq ft
Area for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Radius
diameter / 24 ft- Area of the whole circle
pi * pow(radius, 2)50.265 sq ft- Area of the semicircle
full_area / 225.133 sq ft- Curved edge
pi * radius12.566 ft- Perimeter, including the straight edge
curved_edge + diameter20.566 ft- Centre of area, from the straight edge
4 * radius / (3 * pi)1.698 ft
Worked example
An 8 ft semicircle covers 25.133 sq ft. Its perimeter is 20.566 ft — the 12.566 ft curve plus the 8 ft straight edge. Halving the circumference alone gives 12.566 and leaves out the side the arch actually sits on.
How to work it out yourself
- 1.Measure the straight edge: that is the diameter.
- 2.Halve it for the radius, then take π times the radius squared and halve that for the area.
- 3.For the curved edge alone, multiply π by the radius.
- 4.For the full perimeter, add the diameter back — the straight edge is part of the boundary.
The formula
- Radius
diameter / 2 - Area of the whole circle
pi * pow(radius, 2) - Area of the semicircle
full_area / 2 - Curved edge
pi * radius - Perimeter, including the straight edge
curved_edge + diameter - Centre of area, from the straight edge
4 * radius / (3 * pi)
Source: Wolfram MathWorld — semicircle, NIST Digital Library of Mathematical Functions
Questions people actually ask
- Is the perimeter just half the circumference?
- No, and this is the usual mistake. Half the circumference is only the curve. The perimeter of the shape also includes the straight edge, so it is π × radius plus the diameter.
- Where is the centre of a semicircle?
- Not at the middle of the straight edge. The centre of area sits 4r/3π from it — about 0.42 of the radius — which matters when balancing or supporting an arched piece.
Related
- Circle CalculatorArea, circumference and radius of a circle from its diameter — in square feet and square inches.
- Circumference CalculatorCircumference of a circle from its diameter or the other way round, with the radius, the area and the arc of one degree shown alongside.
- Arc Length and Sector Area CalculatorArc length, sector area, chord and sector perimeter from a radius and an angle, with the fraction of the full circle shown as its own step.
- Diagonal & Rafter Length CalculatorHypotenuse of a right triangle in feet and inches — brace lengths, rafter runs, and squaring a layout.
- Tank & Cylinder Volume CalculatorVolume of a cylinder in cubic feet, US gallons and litres — round tanks, pools, culverts and post holes.
- Slope & Grade CalculatorGrade percentage, angle in degrees, ratio and roof pitch from a rise and a run.
Put this calculator on your site
Free, no attribution required beyond the link.
<iframe src="https://rulecalculators.com/embed/semicircle-area" width="100%" height="420" style="border:1px solid #e7e4de;border-radius:12px" title="Semicircle Calculator"></iframe>