Radius of three
For r = 3, volume is 36π, approximately 113.0973355 cubic units. Surface area is also 36π numerically, but it is measured in square units.
Sphere Calculator inputs
Changing the unit relabels the numbers. Convert measurements to one common unit before entering them.
Volume input is cubic units and surface area input is square units. The radius is measured from the center to the surface. Positive measurements must be from 0.000000001 to 1,000,000,000; derived defining lengths must also remain in this range.
Calculated measurements
Volume
113.0973355 units³
| Measurement | Value |
|---|---|
| Volume | 113.0973355 units³ |
| Surface area | 113.0973355 units² |
| Radius | 3 units |
| Diameter | 6 units |
| Great-circle area | 28.27433388 units² |
Formula: V = 4πr³/3; S = 4πr²; d = 2r
A perfect sphere with no wall thickness. Surface input uses square units; volume input uses cubic units.
Results use full floating-point precision internally and display up to 10 significant digits. Angles are in degrees.
Calculations run locally in your browser. Measurement values are not sent to a calculation service. The downloadable text contains your selected inputs and computed results.
How to use the Sphere Calculator
- 01
Choose the sphere measurement you know.
- 02
Enter radius or diameter as a length, surface area in square units, or volume in cubic units.
- 03
Check the derived radius and compare the sphere surface with its great-circle area.
- 04
Copy or download a labeled result summary.
Examples
A larger ball
A diameter of 10 units gives radius 5, surface area 100π, and volume 500π/3. Doubling that diameter multiplies surface by four and volume by eight.
Infer size from a volume
A volume near 33.51032164 cubic units gives radius near 2 and diameter near 4. The cube root is required to recover a length from volume.
Three dimensions change the scaling
A sphere’s volume is 4πr³/3 and its surface is 4πr². Radius therefore affects the two answers differently: scaling every length by k multiplies surface area by k² and volume by k³. This is useful when checking a result after changing diameter or comparing two similarly shaped objects.
Recover radius from an indirect measurement
The volume mode uses r = ∛(3V/(4π)); surface mode uses r = √(S/(4π)). A diameter input is divided by two first. These modes describe the same ideal shape, so a forward calculation followed by its inverse should recover the original radius apart from numeric rounding.
Great-circle area is a flat cross section
A plane through the center slices a disk of area πr². The whole curved surface has area 4πr², four times that disk. A cross section away from the center is smaller. The tool reports only the maximum central cross section, rather than the area of every possible slice.
Hollow objects need inner and outer sizes
For a hollow spherical shell, material volume is the outer sphere volume minus the inner sphere volume. This calculator takes one radius at a time and does not infer wall thickness, mass, density, or internal capacity from an external diameter. Real balls and tanks may also depart from a perfect sphere.
What to know
- Perfect full spheres only; no ellipsoids, caps, or built-in shell thickness.
- Positive input values and derived radius are bounded to 10⁻⁹–10⁹ in their corresponding units.
Common questions
Is this a hemisphere calculator?
The outputs describe a complete sphere. A hemisphere has half the sphere volume, while its closed surface also includes a circular base.
Does surface area include the equator disk?
No. Sphere surface area is the exterior curved skin. Great-circle area is shown separately as a flat cross section.
Are volume and surface area interchangeable?
No. Even when their displayed numeric values match for a particular radius, their units and physical meanings differ.
Can I calculate mass?
Mass requires density and a material model. This calculator reports geometry only.