🌐 Surface Area of a Hemisphere Calculator
Calculate the surface area of a hemisphere quickly and accurately
How to Use This Calculator
Enter the Radius
Input the radius of the hemisphere in the input field. Make sure the radius is a positive number.
Click Calculate
Press the "Calculate Surface Area" button to compute the total surface area, curved surface area, and base area.
Review Results
View the calculated total surface area, curved surface area, and base area. The result shows all three measurements with the formula used.
Formula
Total Surface Area = 3πr²
Where: Curved Surface Area = 2πr² and Base Area = πr²
Where:
- r = radius of the hemisphere
- π ≈ 3.14159
- Curved Surface Area = 2πr² (the dome part)
- Base Area = πr² (the circular base)
Example 1: Find the surface area of a hemisphere with radius 5 units
Total Surface Area = 3πr²
Total Surface Area = 3 × π × 5²
Total Surface Area = 3 × π × 25
Total Surface Area = 75π ≈ 235.62 units²
Example 2: Find the surface area of a hemisphere with radius 7 cm
Total Surface Area = 3πr²
Total Surface Area = 3 × π × 7²
Total Surface Area = 3 × π × 49
Total Surface Area = 147π ≈ 461.81 cm²
About Surface Area of a Hemisphere Calculator
A hemisphere is half of a sphere, consisting of a curved dome surface and a flat circular base. The Surface Area of a Hemisphere Calculator helps you quickly calculate the total surface area by combining the curved surface area (2πr²) and the base area (πr²), resulting in a total of 3πr².
When to Use This Calculator
- Architecture: Calculate surface area for dome structures, half-sphere roofs, or hemispherical buildings
- Engineering: Determine material requirements for hemispherical containers, tanks, or covers
- Physics: Calculate surface area for heat transfer calculations or fluid dynamics
- Mathematics Education: Teach students about 3D geometry and surface area calculations
- Design: Plan surface coverage for hemispherical objects in product design
- Packaging: Calculate surface area for hemispherical packaging materials
Why Use Our Calculator?
- ✅ Instant Results: Get accurate surface area calculations immediately
- ✅ Multiple Metrics: Shows total surface area, curved surface area, and base area separately
- ✅ Step-by-Step Display: See the calculation formula and process
- ✅ 100% Accurate: Uses precise mathematical formulas
- ✅ Educational: Helps understand hemisphere geometry
- ✅ Completely Free: No registration required
Understanding Hemisphere Surface Area
A hemisphere has two distinct surface areas that combine to form the total:
- Curved Surface Area: The dome-shaped surface (2πr²) - this is half the surface area of a full sphere
- Base Area: The flat circular base (πr²) - equal to the area of a circle with the same radius
- Total Surface Area: Sum of both = 3πr²
Real-World Applications
Architecture: Calculate the surface area of a hemispherical dome with a 20-meter radius. Total surface area = 3π(20)² = 1200π ≈ 3,769.91 m². This helps estimate paint, tiles, or insulation materials needed.
Engineering: A hemispherical tank with radius 3 feet needs surface area coating. Total surface area = 3π(3)² = 27π ≈ 84.82 ft². This determines the amount of protective coating required.
Physics: For heat transfer calculations, a hemisphere with radius 0.5 meters has a total surface area of 3π(0.5)² = 0.75π ≈ 2.36 m², important for thermal analysis.
Frequently Asked Questions
What is a hemisphere?
A hemisphere is half of a sphere, created by cutting a sphere through its center. It consists of a curved dome surface and a flat circular base.
Why is the formula 3πr² instead of 2πr²?
The total surface area includes both the curved surface (2πr²) and the flat base (πr²). Adding them gives 2πr² + πr² = 3πr². If you only need the curved surface (no base), use 2πr².
What's the difference between surface area and volume?
Surface area measures the total area covering the outside of the hemisphere (in square units). Volume measures the space inside the hemisphere (in cubic units). For a hemisphere, volume = (2/3)πr³.
Can I calculate just the curved surface area?
Yes! The curved surface area of a hemisphere is 2πr² (half of a sphere's surface area). The calculator shows this separately in addition to the total surface area.
What units should I use?
Use any consistent units (meters, centimeters, inches, feet, etc.). The result will be in square units of whatever you input. For example, if radius is in meters, surface area will be in square meters.
How is this different from a sphere's surface area?
A full sphere has surface area 4πr² (no base). A hemisphere has 3πr² because it includes both the curved dome (2πr²) and the circular base (πr²).