Calculate the volume and surface area of a sphere. Solve from radius, diameter, circumference, surface area, or volume. Includes presets for common spheres like basketballs and Earth.
A sphere is the most perfectly symmetric three-dimensional shape — every point on its surface is exactly the same distance from the center. From tiny ping pong balls to the enormous Earth itself, spheres and near-spheres are everywhere in nature, sports, engineering, and astronomy.
The volume of a sphere is V = ⁴⁄₃πr³, and its surface area is A = 4πr². These formulas, first derived by Archimedes over 2,200 years ago, reveal a beautiful relationship: the surface area of a sphere equals exactly four times the area of its great circle (πr²), and its volume equals exactly two-thirds the volume of the smallest cylinder that encloses it.
A key property of the sphere is that it has the smallest surface area for a given volume of any shape. This is why soap bubbles are spherical — surface tension minimizes surface area. The volume-to-surface-area ratio (r/3) increases with radius, meaning larger spheres are more "volume efficient," which has implications in biology (cell size), engineering (tank design), and physics (heat transfer).
This calculator lets you work forward or backward: enter the radius, diameter, circumference, surface area, or volume, and it computes everything else. Presets for common spherical objects — from tennis balls to celestial bodies — let you explore instantly.
This calculator is useful any time a sphere is described in a form other than radius. Real measurements often begin with diameter, circumference, filled volume, or even known surface area from a coating or material requirement. Converting those values by hand is straightforward in theory, but easy to mix up when units, cubes, and square roots all appear in the same problem.
It also helps when you want more than one answer. Instead of stopping at volume alone, you can immediately compare surface area, great-circle area, circumference, and the volume-to-surface-area ratio. That broader view is valuable in geometry classes, packaging design, tank sizing, sports equipment comparisons, and science problems involving heat transfer or scaling.
Volume: V = ⁴⁄₃πr³ Surface Area: A = 4πr² Diameter: d = 2r Circumference: C = 2πr Great Circle Area: A_gc = πr² V/SA Ratio: r/3
Result: Volume ≈ 7424.1 cm³, surface area ≈ 1839.7 cm², and circumference ≈ 76.03 cm.
With solveFrom set to radius and inputVal = 12.1, the calculator uses r = 12.1 cm directly. It computes volume with (4/3)πr³, giving about 7424.1 cm³, surface area with 4πr², giving about 1839.7 cm², and circumference with 2πr, giving about 76.03 cm. That is a useful approximation for a regulation basketball-sized sphere.
A sphere is a classic example of how three-dimensional and two-dimensional measurements grow at different rates. Volume depends on r³, while surface area depends on r². If you double the radius, the surface area becomes four times as large, but the volume becomes eight times as large. That difference explains why larger tanks, planets, and balls gain capacity much faster than they gain exterior material.
In many real problems, you do not begin with radius. A sports ball might be measured by circumference, a tank might be specified by total volume, and a manufacturing part might be described by outside area for painting or coating. Solving backward from those values is where a sphere calculator becomes especially useful, because it removes the extra algebra and immediately translates one known measurement into the full set of related properties.
Once you have the computed dimensions, pay attention to units and interpretation. Surface area is always in square units and volume is always in cubic units, so unit mistakes can make an answer look reasonable while still being wrong. The cross-section area is the area of the great circle through the center, and the V/SA ratio shows how efficiently the sphere encloses space. Those outputs are often as informative as the main volume number itself when comparing different spherical objects.
V = ⁴⁄₃πr³, where r is the radius. For a sphere with radius 10, volume = ⁴⁄₃ × π × 1000 ≈ 4,188.79.
Rearrange: r = ∛(3V / 4π). The calculator does this automatically in "Solve from Volume" mode.
A = 4πr². This equals exactly four times the area of the great circle (the largest cross section).
Measure the circumference (C) with a flexible tape, then r = C / (2π). Or measure the diameter with calipers and halve it.
For a fixed volume, the sphere minimizes surface area. This is the isoperimetric inequality in 3D and explains why bubbles, droplets, and planets tend toward spherical shapes.
The volume-to-surface-area ratio (r/3 for a sphere) indicates how much interior volume each unit of surface encloses. It matters in heat transfer, biology (cell size limits), and tank design.