Sphere Volume & Surface
Compute the volume and surface area of a sphere from its radius, with formulas, a worked r = 3 example and how doubling the radius scales each result.
Results
Volume
- Surface area
- 113.097336
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Formula / how it works
Volume = (4/3) π r³. Surface area = 4 π r². Doubling r multiplies the volume by 8 and the surface area by 4.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
A sphere is perfectly round in three dimensions, defined by a single measurement: its radius. The volume is four-thirds of π times the radius cubed, and the surface area is four times π times the radius squared. These formulas are used for balls, tanks, bubbles, planets and any rounded vessel. This calculator takes the radius and returns the volume and the surface area. The radius is half the diameter, so convert diameters before you enter. Volume is in cubic units of the length unit and area is in square units. Because volume scales with the cube of the radius, small changes in size make a big difference to capacity.
When to use / who it helps
- You need the capacity of a spherical tank or ball.
- You are estimating the material needed to cover a sphere.
- You are checking geometry homework.
- You want to compare spheres of different sizes.
- You are modelling bubbles, droplets or planets.
How to use
Steps
- Enter the radius, which is half the diameter.
- Use any length unit consistently.
- Read the volume.
- Read the surface area.
- Convert cubic units to litres if needed.
- Remember that the diameter is twice the radius.
How to interpret results
- Volume is in cubic units and area in square units.
- Doubling the radius multiplies the volume by 8.
- Doubling the radius multiplies the area by 4.
- The volume-to-surface-area ratio equals r ÷ 3.
- The two numbers match only when r = 3 because of that ratio.
Common mistakes & gotchas
- Entering the diameter as the radius.
- Mixing up volume and surface units.
- Using r² instead of r³ in the volume.
- Forgetting to convert units.
- Rounding π too coarsely.
Worked example
Worked example — radius 3
- Volume: (4/3) × π × 3³ = (4/3) × π × 27 = 36π ≈ 113.097.
- Surface area: 4 × π × 3² = 36π ≈ 113.097.
- The two numbers are equal here because the volume-to-area ratio is r ÷ 3 = 1.
- For radius 2: volume ≈ 33.510 and surface area ≈ 50.265.
Result: A sphere of radius 3 has a volume of about 113.10 and a surface area of about 113.10.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Volume = (4/3) π r³. Surface area = 4 π r². Doubling r multiplies the volume by 8 and the surface area by 4.
Frequently asked questions
What is the volume formula for a sphere?
(4/3) π r³.
What is the surface area formula?
4 π r².
How do I use the diameter?
Divide it by 2 to get the radius.
Why are the two results equal in the example?
At r = 3 the volume and surface area values coincide numerically; the units differ.
How do I convert volume to litres?
Cubic centimetres divided by 1,000, or cubic metres times 1,000.
What happens if I double the radius?
Volume increases by 8 times, and surface area by 4 times.