Surface Area of a Hemisphere Calculator
Calculate total, curved, and base surface areas of a hemisphere with multiple input methods
Calculate Hemisphere Surface Area
Hemisphere Surface Area Results
Calculation Details
Formula used: A = 3πr²
Calculated radius: r = 0.0000 cm
Base area: π × r² = 0.0000 cm²
Cap area: 2π × r² = 0.0000 cm²
Total area: 3π × r² = 0.0000 cm²
Example Calculation
Example: Hemisphere with radius 15 cm
Given: Radius r = 15 cm
Base area calculation: Ab = π × r² = π × 15² = 706.86 cm²
Cap area calculation: Ac = 2π × r² = 2π × 15² = 1413.72 cm²
Total surface area: A = Ab + Ac = 3π × r² = 2120.58 cm²
Key Formulas
Base Area: Ab = π × r²
Cap Area: Ac = 2π × r²
Total Area: A = 3π × r²
Volume: V = (2/3)π × r³
Diameter: d = 2r
Surface/Volume: A/V = 9/(2r)
Hemisphere Properties
Two Surfaces
Base (flat circle) and cap (curved surface)
Half of a Sphere
Created by cutting a sphere through its center
More Surface Area
Two hemispheres have more area than one sphere
Available Input Methods
Radius (r)
Direct measurement from center to edge
Diameter (d)
Distance across the hemisphere through center
Volume (V)
Amount of space inside the hemisphere
Base/Cap Area
Area of flat base or curved cap surface
Applications
Architecture (domes, planetariums)
Geography (Earth's hemispheres)
Engineering (pressure vessels)
Material calculations
Understanding Hemisphere Surface Area
What is a Hemisphere?
A hemisphere is exactly half of a sphere, created by cutting a sphere through its center. Unlike a complete sphere, a hemisphere has two distinct surface areas: the curved cap surface and the flat circular base.
Surface Area Components
- •Base Area: The flat circular surface (π × r²)
- •Cap Area: The curved surface (2π × r²)
- •Total Area: Base + Cap = 3π × r²
Key Formulas
Total Surface Area: A = 3πr²
Base Area: Ab = πr²
Cap Area: Ac = 2πr²
Volume: V = (2/3)πr³
Surface-to-Volume Ratio: A/V = 9/(2r)
Important: The total surface area of two hemispheres is greater than the surface area of one complete sphere because of the additional base areas.