Area of Semi Circle Calculator - Free Online Math Tool
How Semi-Circle Area Calculator Works
Enter Radius/Diameter
Input the radius or diameter of the semi-circle
Apply Formula
Area = (π × r²) / 2
Common Semi-Circle Examples
Area Of Semi Circle Calculator
What is a Semi Circle?
A semi circle is half of a complete circle. It has one curved edge and one straight edge. The straight edge is the diameter of the original circle.
Why Use This Calculator?
This tool helps you find the area and perimeter of semi circles quickly. It is perfect for homework, work projects, and learning geometry.
Real World Uses
Semi circles are used in building arches, designing gardens, making windows, and creating art. This calculator helps with all these projects.
How to Calculate Semi Circle Area
Find the radius of your semi circle. If you have the diameter, divide it by 2 to get the radius.
Use the formula: Area = (π × radius × radius) ÷ 2. This means you multiply pi by the radius squared, then divide by 2.
The result is your semi circle area in square units. For example, if your radius is 5 cm, the area is about 39.27 square cm.
Semi Circle Calculation Examples
| Radius | Calculation | Area | Perimeter |
|---|---|---|---|
| 1 unit | (π × 1²) ÷ 2 | 1.57 sq units | 5.14 units |
| 2 units | (π × 2²) ÷ 2 | 6.28 sq units | 10.28 units |
| 5 units | (π × 5²) ÷ 2 | 39.27 sq units | 25.71 units |
| 10 units | (π × 10²) ÷ 2 | 157.08 sq units | 51.42 units |
What is a Semi Circle?
A semi circle is exactly half of a complete circle. When you cut a circle in half along its diameter, you get two semi circles. Each semi circle has one curved edge and one straight edge. The straight edge is called the diameter.
Semi circles are very common in everyday life. You can see them in arches of buildings, rainbow shapes, half-moon cookies, and many architectural designs. They are also used in mathematics and engineering.
Key Facts About Semi Circles:
- A semi circle has 180 degrees (half of a full circle's 360 degrees)
- The area of a semi circle is half the area of a full circle
- The perimeter includes the curved part plus the straight diameter
- All points on the curved edge are the same distance from the center
Semi Circle Formulas Explained
Area Formula
π (pi) = 3.14159... (a special number in math)
r = radius (distance from center to edge)
r² = radius × radius (radius squared)
÷ 2 = divide by 2 (because it's half a circle)
Perimeter Formula
π × r = curved part (half of circle's circumference)
2r = straight part (the diameter)
Total = curved edge + straight edge
This gives you the distance around the entire semi circle
Step by Step Guide
Method 1: Using Radius
Measure or find the radius
The radius is the distance from the center of the semi circle to any point on the curved edge.
Square the radius
Multiply the radius by itself. For example: if radius = 5, then 5 × 5 = 25.
Multiply by π (pi)
Multiply your result by 3.14159. Using our example: 25 × 3.14159 = 78.54.
Divide by 2
Divide your result by 2 to get the semi circle area. Example: 78.54 ÷ 2 = 39.27 square units.
Method 2: Using Diameter
Measure the diameter
The diameter is the straight edge of the semi circle. It goes from one end to the other through the center.
Find the radius
Divide the diameter by 2 to get the radius. For example: if diameter = 10, then radius = 10 ÷ 2 = 5.
Follow the radius method
Now use the radius you found and follow steps 2-4 from Method 1 above.
Where Do We Use Semi Circles?
🏛️ Architecture
Arches in buildings, doorways, windows, and bridges use semi circle shapes. They are strong and look beautiful.
🎨 Art and Design
Artists use semi circles in paintings, logos, and decorations. They create pleasing and balanced designs.
🌈 Nature
Rainbows appear as semi circles in the sky. The sun and moon also look like semi circles when they rise or set.
🏗️ Construction
Tunnels, pipes, and curved roofs often use semi circle shapes. They help distribute weight evenly.
📚 Education
Students learn about semi circles in geometry class. This calculator helps with homework and tests.
🍕 Everyday Life
Pizza slices, half-moon cookies, and many food items have semi circle shapes that we see daily.
Frequently Asked Questions
What is a semi circle?
A semi circle is half of a complete circle. It has one curved edge and one straight edge. The straight edge is the diameter of the original circle.
How do I find the area of a semi circle?
Use this simple formula: Area = (π × radius × radius) ÷ 2. First find the radius, then multiply it by itself, then multiply by 3.14159, then divide by 2.
What is the difference between radius and diameter?
The radius goes from the center to the edge. The diameter goes all the way across through the center. Diameter is always twice as long as the radius.
How do I calculate the perimeter of a semi circle?
Add the curved part and the straight part together. The curved part is π × radius. The straight part is 2 × radius. So perimeter = π × radius + 2 × radius.
What units can I use with this calculator?
You can use any length unit like centimeters, meters, inches, or feet. The area will be in square units (like square cm or square inches).
Is this calculator good for school homework?
Yes! This calculator is perfect for geometry homework. It shows you the formula and gives you the right answer. You can also learn how the calculation works.
Where do we see semi circles in real life?
Semi circles are everywhere! You can see them in building arches, rainbows, pizza slices, half-moon cookies, tunnels, and many architectural designs.
What is pi (π) and why do we use it?
Pi is a special number that equals about 3.14159. We use it in circle calculations because it shows the relationship between a circle's diameter and its circumference.
Can I calculate area if I only know the diameter?
Yes! First divide the diameter by 2 to get the radius. Then use the radius in the area formula. This calculator can do both for you automatically.
Why is the area formula divided by 2?
Because a semi circle is exactly half of a full circle. The full circle area is π × r². Since we want half of that, we divide by 2 to get (π × r²) ÷ 2.
Tips and Tricks
💡 Quick Memory Trick
Remember: Semi circle area is just half of a full circle area. So take the circle area formula (π × r²) and divide by 2!
📏 Measuring Tips
If you can't measure the radius directly, measure the diameter (the straight edge) and divide by 2. This gives you the radius.
🔢 Easy Numbers
For quick estimates, use 3.14 instead of the full pi value. For example: radius 2 gives area ≈ (3.14 × 4) ÷ 2 = 6.28.
✅ Check Your Work
The area should always be less than the full circle area. If your semi circle area is bigger than π × r², check your calculation.
Practice Problems
Problem 1: Garden Design
Sarah wants to plant flowers in a semi circle garden. The radius is 6 meters. How much area does she need to cover?
Solution: Area = (π × 6²) ÷ 2 = (3.14159 × 36) ÷ 2 = 56.55 square meters
Problem 2: Pizza Slice
A pizza has a diameter of 16 inches. If you cut it in half, what is the area of each semi circle piece?
Solution: Radius = 16 ÷ 2 = 8 inches. Area = (π × 8²) ÷ 2 = (3.14159 × 64) ÷ 2 = 100.53 square inches
Problem 3: Window Arch
An architect designs a semi circle window with a radius of 4 feet. What is the area of the window?
Solution: Area = (π × 4²) ÷ 2 = (3.14159 × 16) ÷ 2 = 25.13 square feet
Common Mistakes to Avoid
Forgetting to divide by 2
Don't use the full circle formula π × r². Remember to divide by 2 because it's only half a circle.
Using diameter instead of radius
If you have the diameter, divide it by 2 first to get the radius. Then use the radius in the formula.
Wrong units in the answer
Area is always in square units. If your radius is in cm, the area is in square cm (cm²), not just cm.
Double-check your calculation
Always verify that your semi circle area is exactly half of what the full circle area would be.