Sphere Volume Calculator (often searched as 'Volume of a Circle')
This calculator finds the volume and surface area of a sphere based on its radius or diameter.
Understanding "Volume of a Circle": Many users search for the "volume of a circle". However, a circle is a flat, 2D shape and has Area, not Volume. Volume measures 3D space. When searching for the volume of a circle, people usually mean the volume of a Sphere – a perfectly round 3D object like a ball. This tool calculates that sphere volume accurately.
Enter either the radius (r) or the diameter (d) of the sphere below to calculate its Volume (V) and Surface Area (SA). The correct formula for volume of circle-related sphere is used.
Enter Sphere Dimension
Enter EITHER Radius OR Diameter. The other will be calculated.
Understanding Sphere Volume & Formulas
What is a Sphere?
A sphere is the three-dimensional counterpart of a two-dimensional circle. It is a perfectly round geometrical object that, mathematically, is the set of points that are equidistant from a given point at its center. The distance between the center and any point on the sphere is the radius (r). Likely the most commonly known spherical object is a perfectly round ball. The longest line segment that connects two points of a sphere through its center is called the diameter (d), where d = 2r.
The Sphere Volume Formula (The "Volume of a Circle Formula" for 3D)
The equation for calculating the volume of a sphere, often sought when searching for the "formula of volume of circle", is:
V = (4/3) * π * r³
Where:
- V is the Volume
- π (Pi) is a mathematical constant, approximately 3.14159...
- r is the radius of the sphere
This volume of the circle formula (applied to a sphere) tells you how much 3D space the sphere occupies.
Sphere Surface Area Formula
The total area of the outside surface of the sphere is calculated using:
SA = 4 * π * r²
Where SA is the Surface Area, π is Pi, and r is the radius.
Example Calculation (Provided in Original Text)
EX: Claire wants to fill a perfectly spherical water balloon with radius 0.15 ft with vinegar. The volume in a circle (meaning, the sphere) necessary can be calculated using the sphere volume equation:
V = (4/3) * π * (0.15 ft)³ ≈ 0.0141 cubic feet (ft³).
Real-Life Sphere Volume Examples
Click on an example to see the step-by-step calculation:
Example 1: Basketball Volume
Scenario: Calculate the volume of air inside a standard NBA basketball.
1. Known Value: Standard diameter (d) ≈ 9.5 inches.
2. Find Radius: r = d / 2 = 9.5 inches / 2 = 4.75 inches.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (4.75)³ ≈ (4/3) * π * 107.171875
5. Result: V ≈ 448.92 cubic inches.
Conclusion: A standard basketball holds approximately 449 cubic inches of air.
Example 2: Golf Ball Volume
Scenario: Determine the volume of a standard golf ball.
1. Known Value: Standard diameter (d) ≈ 1.68 inches.
2. Find Radius: r = d / 2 = 1.68 inches / 2 = 0.84 inches.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (0.84)³ ≈ (4/3) * π * 0.592704
5. Result: V ≈ 2.48 cubic inches.
Conclusion: A golf ball has a volume of about 2.5 cubic inches.
Example 3: Orange Volume (Approximate)
Scenario: Estimate the volume of a medium-sized orange.
1. Known Value: Approximate diameter (d) ≈ 3 inches.
2. Find Radius: r = d / 2 = 3 inches / 2 = 1.5 inches.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (1.5)³ = (4/3) * π * 3.375
5. Result: V ≈ 14.14 cubic inches.
Conclusion: A medium orange has roughly 14 cubic inches of volume.
Example 4: Ball Bearing Volume
Scenario: Find the volume of a small steel ball bearing.
1. Known Value: Diameter (d) = 0.5 inches.
2. Find Radius: r = d / 2 = 0.5 inches / 2 = 0.25 inches.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (0.25)³ ≈ (4/3) * π * 0.015625
5. Result: V ≈ 0.065 cubic inches.
Conclusion: The small ball bearing has a volume of about 0.065 cubic inches.
Example 5: Large Exercise Ball Volume
Scenario: Calculate the volume of air needed to inflate a large exercise ball.
1. Known Value: Typical diameter (d) = 65 cm.
2. Find Radius: r = d / 2 = 65 cm / 2 = 32.5 cm.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (32.5)³ ≈ (4/3) * π * 34328.125
5. Result: V ≈ 143799 cubic cm (or about 143.8 Liters).
Conclusion: A 65 cm exercise ball holds approximately 144,000 cubic centimeters (144 Liters) of air.
Example 6: Marble Volume
Scenario: Find the volume of a standard glass marble.
1. Known Value: Typical diameter (d) ≈ 1.6 cm.
2. Find Radius: r = d / 2 = 1.6 cm / 2 = 0.8 cm.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (0.8)³ ≈ (4/3) * π * 0.512
5. Result: V ≈ 2.14 cubic cm (or 2.14 mL).
Conclusion: A standard marble has a volume of just over 2 cubic centimeters.
Example 7: Earth's Volume (Approximate)
Scenario: Estimate the volume of the planet Earth, treating it as a perfect sphere.
1. Known Value: Approximate mean radius (r) ≈ 6,371 kilometers (km).
2. Formula: V = (4/3) * π * r³
3. Calculation: V = (4/3) * π * (6371)³ ≈ (4/3) * π * 2.586 × 10¹¹
4. Result: V ≈ 1.083 × 10¹² cubic kilometers.
Conclusion: The approximate volume of Earth is over a trillion cubic kilometers!
Example 8: Soap Bubble Volume
Scenario: Calculate the volume of air inside a soap bubble.
1. Known Value: Let's assume the bubble has a diameter (d) of 10 cm.
2. Find Radius: r = d / 2 = 10 cm / 2 = 5 cm.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (5)³ = (4/3) * π * 125
5. Result: V ≈ 523.6 cubic cm (or 523.6 mL).
Conclusion: A 10 cm diameter soap bubble encloses about 524 cubic centimeters of air.
Example 9: Tennis Ball Volume
Scenario: Find the volume of a standard tennis ball.
1. Known Value: Average diameter (d) ≈ 2.63 inches.
2. Find Radius: r = d / 2 = 2.63 inches / 2 = 1.315 inches.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (1.315)³ ≈ (4/3) * π * 2.273
5. Result: V ≈ 9.52 cubic inches.
Conclusion: A tennis ball has a volume of approximately 9.5 cubic inches.
Example 10: Decorative Garden Globe Volume
Scenario: Calculate the volume of a glass garden globe.
1. Known Value: Diameter (d) = 12 inches.
2. Find Radius: r = d / 2 = 12 inches / 2 = 6 inches.
3. Formula: V = (4/3) * π * r³
4. Calculation: V = (4/3) * π * (6)³ = (4/3) * π * 216
5. Result: V ≈ 904.78 cubic inches.
Conclusion: A 12-inch diameter garden globe has a volume of about 905 cubic inches.
Understanding Volume Measurement
Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for volume is the cubic meter (m³), but many other units are used depending on the context (liters, gallons, cubic feet, etc.). This calculator provides the numerical result; the units depend on the units used for the radius or diameter input.
Common Volume Units Reference
Ensure your input radius or diameter uses a consistent unit. The result will be in corresponding cubic units for volume and square units for surface area.
| Unit | Cubic Meters (m³) | Liters (L) | Milliliters (mL/cm³) | Gallons (US) | Cubic Feet (ft³) |
|---|---|---|---|---|---|
| cubic centimeter (mL) | 0.000001 | 0.001 | 1 | 0.000264 | 0.0000353 |
| liter (L) | 0.001 | 1 | 1,000 | 0.264172 | 0.035315 |
| cubic meter (m³) | 1 | 1,000 | 1,000,000 | 264.172 | 35.3147 |
| cubic inch (in³) | 0.00001639 | 0.01639 | 16.387 | 0.004329 | 0.0005787 |
| cubic foot (ft³) | 0.028317 | 28.317 | 28,316.8 | 7.48052 | 1 |
| gallon (US gal) | 0.003785 | 3.785 | 3,785.41 | 1 | 0.133681 |
Frequently Asked Questions about Sphere Volume
1. What is the formula for the volume of a sphere (or the 'volume of a circle' in 3D)?
The correct volume formula of circle-related sphere is V = (4/3) * π * r³, where 'r' is the radius.
2. How do I use this calculator if I only know the diameter (d)?
You can enter the diameter directly into the "Diameter (d)" field. The calculator will automatically find the radius (r = d/2) and use it for the calculations.
3. Why can't I calculate the 'volume of a circle'?
Volume measures 3D space. A circle is a flat 2D shape; it only has area (A = π * r²) and circumference (C = 2 * π * r). A sphere is the 3D equivalent, and it has volume.
4. What's the difference between Sphere Volume and Sphere Surface Area?
Volume is the space *inside* the sphere. Surface Area is the total area of the sphere's *outer surface*. This calculator provides both values.
5. What units should I use for radius or diameter?
You can use any unit of length (e.g., meters, feet, inches, cm), but be consistent. If you enter the radius in inches, the volume will be in cubic inches (in³) and the surface area in square inches (in²).
6. Is the circle volume equation the same as the sphere volume equation?
Technically, there is no "circle volume equation". The equation V = (4/3) * π * r³ is specifically for the volume of a sphere. People searching for a "circle volume equation" almost always need this sphere formula.
7. What is Pi (π)?
Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It's approximately 3.14159, but the calculator uses a more precise value available in JavaScript (`Math.PI`).
8. How accurate is this calculation?
The calculation uses standard mathematical formulas and a precise value for Pi. The accuracy of the result depends entirely on the accuracy of the radius or diameter you provide.
9. Can I calculate the volume of half a sphere (hemisphere)?
Yes. Calculate the full sphere volume using this tool, then simply divide the result by 2. The formula is V_hemisphere = (2/3) * π * r³.
10. What are some real-world examples of spheres?
Examples include balls (basketball, soccer ball, golf ball), ball bearings, bubbles, water droplets (approximately), and planets or stars (approximately spherical).
11. What's the easiest way to find the radius if I have the circumference?
The formula for circumference is C = 2 * π * r. So, if you know C, you can find the radius using r = C / (2 * π). You can then enter this radius into the calculator.
