Enter either the radius or the diameter to calculate the area.
How to Calculate the Area of a Semicircle
A semicircle is exactly half of a full circle. Therefore, finding its area is a straightforward process: you calculate the area of a complete circle with the same radius and then divide the result by two.
The Semicircle Area Formula
The standard formula for the area of a circle is A = πr². To adapt this for a semicircle, we use:
Area = (π × r²) / 2
Where:
π (Pi): Approximately 3.14159
r: The radius (distance from the center to the edge)
Calculating with Diameter
If you only have the diameter (the full width of the flat side), you must first divide it by 2 to get the radius. The formula then becomes:
Area = (π × (d/2)²) / 2
Step-by-Step Example
Let's say you have a semicircular window with a radius of 4 meters.
Square the radius: 4 × 4 = 16
Multiply by Pi: 16 × 3.14159 = 50.265
Divide by 2: 50.265 / 2 = 25.1325
The area is 25.13 square meters.
Common Area Calculations Reference
Radius
Diameter
Total Area (Approx.)
5 cm
10 cm
39.27 cm²
10 m
20 m
157.08 m²
15 ft
30 ft
353.43 ft²
Real-World Applications
Understanding the area of a semicircle is vital in various fields:
Architecture: Designing arched windows, doorways, or tunnels.
Landscaping: Calculating the amount of sod or mulch needed for semicircular flower beds.
Engineering: Determining the cross-sectional area of pipes or structural supports.
Manufacturing: Measuring material requirements for curved components.
function calculateSemicircleArea() {
var radius = parseFloat(document.getElementById('radiusInput').value);
var resultBox = document.getElementById('result-box');
var areaOutput = document.getElementById('areaOutput');
var stepsOutput = document.getElementById('calculationSteps');
if (isNaN(radius) || radius <= 0) {
alert("Please enter a valid positive number for radius or diameter.");
resultBox.style.display = 'none';
return;
}
// Calculation: (PI * r^2) / 2
var pi = Math.PI;
var area = (pi * Math.pow(radius, 2)) / 2;
areaOutput.innerHTML = "Area: " + area.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
stepsOutput.innerHTML = "Calculated using Radius " + radius + ": (" + pi.toFixed(5) + " × " + radius + "²) / 2";
resultBox.style.display = 'block';
}