What you get
A sphere has four properties that all derive from each other: radius, diameter, surface area, and volume. Knowing any one, you can compute the other three. Pick which value you have, type it in, get everything else.
The calculator also shows the great-circle circumference (the longest line that fits on the sphere’s surface, equator length) since that’s frequently useful in geographic and physics calculations.
The formulas
- Diameter = 2 × radius
- Surface area = 4 × π × radius²
- Volume = (4/3) × π × radius³
- Great-circle circumference = 2 × π × radius
The cube in the volume formula is what makes spheres grow so fast, doubling the radius increases volume by 8× (2³). This is why a tennis ball and a basketball look not-that-different in size but a basketball holds vastly more air.
When this matters
- Physics homework: drag, buoyancy, gravitational mass, anything involving spherical objects.
- Astronomy: planets are nearly spherical. Knowing radius gives surface area and volume of any celestial body.
- Engineering: tank capacity, ball-bearing weight, pressure-vessel stress calculations.
- Cooking/food: meatballs, dumplings, surface area drives browning, volume drives cooking time.
- Everyday curiosity: how much air is in a soccer ball? How much surface does a basketball have?
Reference values
For calibration:
| Object | Radius | Volume | Surface area |
|---|---|---|---|
| Tennis ball | 3.35 cm | 158 cm³ | 141 cm² |
| Basketball | 12 cm | 7,238 cm³ | 1,810 cm² |
| Earth | 6,371 km | 1.08 × 10¹² km³ | 510 million km² |
| Sun | 696,000 km | 1.41 × 10¹⁸ km³ | 6.09 × 10¹² km² |
Earth and Sun aren’t perfect spheres but the approximation is close enough for most purposes.
Frequently asked questions
Why is the volume formula different from a cylinder? A sphere has the highest volume-to-surface ratio of any shape. That’s why bubbles are spherical (minimize surface energy) and droplets pull spherical (surface tension).
What’s a “great circle”? Any circle on the sphere’s surface that passes through the center, the equator is one, longitudinal meridians are others. All great circles have the same length: 2πr. Used in navigation for shortest-distance routes.
What about an oblate spheroid (like Earth)? This calculator handles perfect spheres only. For ellipsoids (oblate or prolate), the formulas use semi-major and semi-minor axes and produce different volumes. Earth’s “official” geoid model is a much more complex shape.
Why does my Excel formula give a different answer? Likely a precision difference in π. Most calculators use ~3.14159265 (15 significant digits); this tool uses JavaScript’s Math.PI which is the same precision. If your Excel uses a rounded value (3.14 or 3.1416), the answers diverge in later decimal places.