🌐 Volume of a Hemisphere Calculator
Calculate the volume of a hemisphere
How to Use This Calculator
Enter the Radius
Input the radius of the hemisphere in the input field. The radius is the distance from the center to any point on the curved surface. Make sure the radius is a positive number.
Click Calculate
Press the "Calculate Volume" button to compute the volume of the hemisphere using the formula V = (2/3)πr³.
Review Result
View the calculated volume displayed in cubic units. The result also shows the full sphere volume for comparison, demonstrating that a hemisphere has exactly half the volume of a sphere with the same radius.
Formula
Volume = (2/3)πr³
Where r is the radius of the hemisphere
Where:
- V = volume of the hemisphere
- r = radius of the hemisphere (same as the sphere it came from)
- π ≈ 3.14159
Relationship to Sphere:
A hemisphere is half of a sphere. The volume of a full sphere is (4/3)πr³, so:
Hemisphere Volume = (1/2) × Sphere Volume = (1/2) × (4/3)πr³ = (2/3)πr³
Example 1: Hemisphere with radius 5 units
Volume = (2/3) × π × 5³
Volume = (2/3) × π × 125
Volume = 250π/3 ≈ 261.80 units³
Compare: Full sphere volume = 500π/3 ≈ 523.60 units³ (exactly double)
Example 2: Hemisphere with radius 7 units
Volume = (2/3) × π × 7³
Volume = (2/3) × π × 343
Volume = 686π/3 ≈ 718.38 units³
Example 3: Hemisphere with radius 3 units
Volume = (2/3) × π × 3³
Volume = (2/3) × π × 27
Volume = 18π ≈ 56.55 units³
About Volume of a Hemisphere Calculator
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. This calculator finds the volume of a hemisphere using the formula V = (2/3)πr³, which is exactly half the volume of a full sphere with the same radius.
When to Use This Calculator
- Architecture: Calculate volumes for dome structures, half-sphere roofs, or hemispherical buildings
- Engineering: Determine material volumes for hemispherical containers, tanks, or covers
- Physics: Calculate volumes for hemispherical objects in fluid dynamics or mechanics
- Mathematics Education: Teach students about 3D geometry and sphere/hemisphere relationships
- Design: Plan volumes for hemispherical objects in product design
- Packaging: Calculate capacity of hemispherical containers
Why Use Our Calculator?
- ✅ Instant Results: Get accurate volume calculations immediately
- ✅ Simple Input: Just enter the radius
- ✅ Comparison Display: Shows full sphere volume for comparison
- ✅ Step-by-Step Display: See the formula applied with your value
- ✅ 100% Accurate: Uses precise mathematical formulas
- ✅ Educational: Helps understand hemisphere geometry
- ✅ Completely Free: No registration required
Understanding Hemisphere Volume
A hemisphere has unique volume properties:
- Half of a Sphere: Volume is exactly half the volume of a full sphere with the same radius
- Formula: V = (2/3)πr³, which equals (1/2) × (4/3)πr³ (full sphere volume)
- Radius: Same as the sphere it came from - distance from center to curved surface
- Shape: Consists of a curved dome (half sphere surface) and a flat circular base
- Volume Relationship: Hemisphere volume : Full sphere volume = 1 : 2
Real-World Applications
Architecture: A hemispherical dome with radius 10 m has volume = (2/3)π × 1000 ≈ 2,094.40 m³. This determines the airspace inside the dome. A full sphere would have 4,188.79 m³ (exactly double).
Engineering: A hemispherical tank with radius 3 m has volume = (2/3)π × 27 ≈ 56.55 m³ (storage capacity). This is useful for liquid or gas storage where a full sphere isn't needed.
Physics: For buoyancy calculations, a hemisphere with radius 0.5 m submerged in water displaces volume = (2/3)π × 0.125 ≈ 0.26 m³ of water, important for understanding floating forces.
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 (half the sphere's surface) and a flat circular base. The radius of a hemisphere is the same as the radius of the sphere it came from.
Why is the formula (2/3)πr³ instead of (1/2)πr³?
A hemisphere has exactly half the volume of a full sphere. Since a sphere's volume is (4/3)πr³, half of that is (1/2) × (4/3)πr³ = (4/6)πr³ = (2/3)πr³. The factor 2/3 comes from halving the 4/3 in the sphere formula.
How is hemisphere volume related to sphere volume?
Hemisphere volume is exactly half of sphere volume. If a sphere has volume (4/3)πr³, then hemisphere volume = (2/3)πr³ = (1/2) × sphere volume. This relationship is exact for any radius.
What's the difference between volume and surface area?
Volume measures the space inside the hemisphere (cubic units). Surface area measures the area covering the outside (square units). For a hemisphere with radius r, volume = (2/3)πr³ and total surface area = 3πr² (curved surface 2πr² + base πr²).
Can I calculate if I only know the diameter?
Yes! If you have the diameter (d), the radius is half: r = d/2. Then use the radius in the formula. For example, if diameter = 10, then radius = 5, and volume = (2/3)π × 5³.
How is this different from a cone?
A hemisphere has a curved dome surface and circular base, with volume (2/3)πr³. A cone has a triangular cross-section and volume (1/3)πr²h. For a cone with height = radius, volume = (1/3)πr³, which is less than hemisphere volume (2/3)πr³.