Volume of a Sphere Calculator
Calculate the volume, surface area, diameter, and circumference of a sphere from its radius. See also Volume of Hemisphere Calculator and Volume of Ellipsoid Calculator.
How to Calculate the Volume of a Sphere
To find the volume of a sphere, measure the radius — the distance from the center to any point on the surface. Cube the radius, multiply by π, then multiply by 4/3. The result is the total space enclosed within the sphere. If you know the diameter, divide it by 2 to get the radius first. This calculator also computes the surface area, diameter, and circumference automatically.
Sphere Volume Formula
V = (4/3) × π × r³
SA = 4 × π × r²
Diameter: d = 2r
Circumference: C = 2πr
Example
Find the volume of a sphere with radius 5:
V = (4/3) × π × r³
V = (4/3) × π × 5³
V = (4/3) × π × 125
V ≈ 523.5988 cubic units
Sphere Volume Reference Table
| Radius | Volume | Surface Area | Diameter |
|---|---|---|---|
| 1 | 4.1888 | 12.5664 | 2 |
| 2 | 33.5103 | 50.2655 | 4 |
| 3 | 113.0973 | 113.0973 | 6 |
| 4 | 268.0826 | 201.0619 | 8 |
| 5 | 523.5988 | 314.1593 | 10 |
| 6 | 904.7787 | 452.3893 | 12 |
| 7 | 1436.7550 | 615.7522 | 14 |
| 8 | 2144.6606 | 804.2477 | 16 |
| 9 | 3053.6281 | 1017.8760 | 18 |
| 10 | 4188.7902 | 1256.6371 | 20 |
| 15 | 14137.1669 | 2827.4334 | 30 |
| 20 | 33510.3216 | 5026.5482 | 40 |
| 25 | 65449.8469 | 7853.9816 | 50 |
| 50 | 523598.7756 | 31415.9265 | 100 |
| 100 | 4188790.2048 | 125663.7061 | 200 |
Solved Examples
Example 1: Volume of a Basketball
A standard basketball has a diameter of 24.26 cm. Find its volume.
Radius = 24.26 / 2 = 12.13 cm
V = (4/3) × π × 12.13³
V = (4/3) × π × 1786.33
V ≈ 7,481.13 cm³
Example 2: Water Balloon Capacity
A water balloon is approximately spherical with radius 7 cm. How many milliliters of water can it hold? (1 cm³ = 1 mL)
V = (4/3) × π × 7³
V = (4/3) × π × 343
V ≈ 1,436.76 cm³ = 1,436.76 mL ≈ 1.44 liters
Example 3: Marble Volume
A glass marble has a diameter of 1.6 cm. What is its volume?
Radius = 1.6 / 2 = 0.8 cm
V = (4/3) × π × 0.8³
V = (4/3) × π × 0.512
V ≈ 2.145 cm³
Example 4: Earth's Volume
Earth has an average radius of approximately 6,371 km. Estimate its volume.
V = (4/3) × π × 6371³
V = (4/3) × π × 2.586 × 10¹¹
V ≈ 1.083 × 10¹² km³
Practice Questions
Q1: Find the volume of a sphere with radius 9 cm.
Answer: V = (4/3) × π × 9³ = (4/3) × π × 729 ≈ 3,053.63 cm³
Q2: A soccer ball has a diameter of 22 cm. What is its volume?
Answer: r = 11 cm; V = (4/3) × π × 11³ ≈ 5,575.28 cm³
Q3: A sphere has a volume of 904.78 cm³. What is its radius?
Answer: r = ∛(3V / 4π) = ∛(3 × 904.78 / 4π) = ∛(215.98) ≈ 6 cm
Q4: How many spherical marbles (r=1 cm) fit by volume in a container of radius 10 cm?
Answer: Container V ≈ 4188.79 cm³; Marble V ≈ 4.19 cm³; Ratio ≈ 1000 marbles (by volume)
Q5: If the radius of a sphere is doubled, how does the volume change?
Answer: V₂ = (4/3)π(2r)³ = 8 × V₁. The volume increases by a factor of 8.
Q6: Find the surface area and volume of a sphere with radius 3.5 m.
Answer: V = (4/3) × π × 3.5³ ≈ 179.59 m³; SA = 4 × π × 3.5² ≈ 153.94 m²
Common Mistakes
Using diameter instead of radius: The formula requires the radius. Always divide the diameter by 2 first. Using diameter directly gives a volume 8× too large.
Forgetting to cube the radius: Volume is 3D — the radius must be raised to the third power, not squared.
Omitting the 4/3 factor: Writing V = πr³ instead of V = (4/3)πr³ is incorrect. The coefficient is essential.
Mixing up units: If the radius is in cm, the volume is in cm³. Ensure consistent units before calculating.
Key Takeaways
- The sphere volume formula is V = (4/3)πr³ — memorize the 4/3 coefficient.
- Doubling the radius increases volume by 8× (since 2³ = 8).
- A sphere has the smallest surface area for a given volume of any 3D shape.
- Always convert diameter to radius (r = d/2) before using the formula.
- Volume is in cubic units — match the unit to the radius measurement.
- A hemisphere is exactly half the sphere volume: V = (2/3)πr³.
Frequently Asked Questions
What is the volume of a sphere?
The volume of a sphere is the total three-dimensional space enclosed within its surface. It is measured in cubic units and calculated using V = (4/3)πr³, where r is the radius.
How do I find the volume if I know the diameter?
Divide the diameter by 2 to get the radius, then use V = (4/3)πr³. For example, a sphere with diameter 10 has radius 5, so V = (4/3) × π × 125 ≈ 523.60 cubic units.
What is the surface area of a sphere?
The surface area of a sphere is the total area of its outer surface, calculated as SA = 4πr². For a sphere with radius 5, SA = 4 × π × 25 ≈ 314.16 square units.
What is the difference between a sphere and a hemisphere?
A hemisphere is exactly half of a sphere. Its volume is (2/3)πr³ — half the sphere volume. A hemisphere also has a flat circular base that adds to its total surface area.
What units is the volume in?
The volume is in cubic units of whatever unit the radius is in. If the radius is in centimeters, the volume is in cubic centimeters (cm³). If in meters, the volume is in cubic meters (m³).