Sphere Volume Calculator
Calculate the volume of a sphere quickly and accurately. Enter the radius, diameter, or circumference and get instant results in multiple units. Perfect for students, engineers, and anyone working with 3D geometry.
What Is a Sphere?
A sphere is a perfectly round three-dimensional object where every point on its surface is equidistant from its center. It is the three-dimensional analog of a circle. Spheres are among the most common shapes in nature and mathematics — from planets and bubbles to balls and bearings.
The volume of a sphere is the amount of space it occupies. It is calculated by the formula:
V = ⁴⁄₃ × π × r³
Where:
V = Volume of the sphere
π (Pi) ≈ 3.14159
r = Radius of the sphere (distance from center to surface)
Alternative formulas:
Using diameter: V = ⁴⁄₃ × π × (d/2)³ = (πd³)/6
Using circumference: V = C³ / (6π²)
The calculator also computes the surface area of the sphere (A = 4πr²), which is the total area of the sphere's outer surface.
How Does the Sphere Volume Calculator Work?
Simply enter the radius, diameter, or circumference of the sphere, and the calculator will instantly compute the volume, surface area, and all other properties. You can choose your preferred unit system and output format.
The calculator handles the conversion between measurement units automatically:
- Metric: Centimeters (cm) → Cubic centimeters (cm³) or Liters
- Imperial: Inches (in) → Cubic inches (in³) or Gallons
Why Use This Sphere Volume Calculator?
- Fast & Accurate: Get precise results with zero math errors.
- Multiple Inputs: Enter radius, diameter, or circumference.
- Multiple Units: Supports metric and imperial, plus liters and gallons.
- Comprehensive: Calculates volume, surface area, and all sphere properties.
- Free & Private: No registration, no data storage.
Real-World Applications of Sphere Volume
- Engineering & Design: Calculating the capacity of spherical tanks, pressure vessels, and ball bearings.
- Astronomy: Estimating the volume and mass of planets, stars, and celestial bodies.
- Sports: Determining the volume and weight of balls used in various sports.
- Manufacturing: Calculating material needed for spherical objects and components.
- Everyday Life: Estimating the capacity of fishbowls, decorative spheres, and more.
❓ Sphere Volume FAQ
What is the formula for the volume of a sphere?
The formula is V = ⁴⁄₃πr³, where V is the volume, r is the radius, and π is approximately 3.14159.
How do I calculate the volume of a sphere using diameter?
If you know the diameter (d), use the formula V = (πd³)/6, or V = ⁴⁄₃ × π × (d/2)³.
How do I calculate the volume of a sphere using circumference?
If you know the circumference (C), use the formula V = C³ / (6π²).
What is the surface area of a sphere?
The surface area of a sphere is A = 4πr². This calculator automatically computes it for you.
What is the difference between a sphere and a circle?
A circle is a two-dimensional shape (flat), while a sphere is a three-dimensional shape (solid). A circle has area; a sphere has volume.
What is a hemisphere?
A hemisphere is exactly half of a sphere. The volume of a hemisphere is half the volume of a sphere: V = ⅔πr³.
How do I find the radius of a sphere if I know the volume?
Rearrange the formula: r = (3V / (4π))^(1/3). Take the cube root of (3 × Volume ÷ 4π).
How do I find the diameter of a sphere if I know the volume?
d = (6V / π)^(1/3). Take the cube root of (6 × Volume ÷ π).
What is the volume of a sphere with radius 5?
Using V = ⁴⁄₃πr³ = ⁴⁄₃ × π × 5³ = ⁴⁄₃ × π × 125 ≈ 523.60 cubic units.
What is the volume of a sphere with diameter 10?
Radius = 5. Volume = ⁴⁄₃ × π × 5³ ≈ 523.60 cubic units.
How do I convert sphere volume to liters?
1 cubic centimeter (cm³) = 0.001 liters. 1 cubic meter (m³) = 1000 liters. Our calculator can display results in liters automatically.
How do I convert sphere volume to gallons?
1 US gallon = 231 cubic inches. 1 US gallon ≈ 3.785 liters. Our calculator includes gallons as an output option.
How does the volume change if I double the radius?
Volume is proportional to the cube of the radius. Doubling the radius increases the volume by a factor of 8 (2³).
How does the volume change if I double the diameter?
Doubling the diameter also doubles the radius, which increases the volume by a factor of 8.
What is the volume of a sphere in terms of diameter?
V = (πd³)/6, where d is the diameter.
What is the volume of a sphere in terms of circumference?
V = C³ / (6π²), where C is the circumference.
What is the difference between volume and capacity?
Volume is the amount of space a solid object occupies. Capacity is the amount of liquid or gas a container can hold. For a sphere, the volume and capacity are numerically equal when measured in the same units.
Can I use this calculator for a sphere with different units?
Yes. You can enter dimensions in centimeters, meters, inches, or feet. The calculator will display the volume in the corresponding cubic units, liters, or gallons.
What is the volume of the Earth?
The Earth's radius is approximately 6,371 km. Its volume is roughly 1.083 × 10¹² km³ (1.083 trillion cubic kilometers).