A sphere is fixed by one number, so any measurement you have gives all the others. A ball 22 cm across has a radius of 11 cm, a circumference of 69.1 cm, a surface of 1,520.5 cm² and a volume of 5,575 cm³, about 5.6 liters. Choose what you know – radius, diameter, circumference, surface area or volume – and the calculator finds the radius first, then everything else, with each step written out.
The four formulas
| Quantity | Formula | Radius from it |
|---|---|---|
| Diameter | d = 2r | r = d ÷ 2 |
| Circumference | C = 2πr | r = C ÷ 2π |
| Surface area | A = 4πr² | r = √(A ÷ 4π) |
| Volume | V = 4/3 πr³ | r = ∛(3V ÷ 4π) |
Double the radius and the area grows four times, the volume eight times. That is why a slightly bigger orange holds much more juice.
Balls by the rules
Sports bodies fix ball sizes by circumference or diameter. Here they are turned into volume and surface with the formulas above:
| Ball and official size | Diameter | Volume | Surface |
|---|---|---|---|
| Soccer ball, size 5: circumference 68–70 cm (IFAB Laws of the Game) | 21.65–22.28 cm | 5,310–5,792 cm³ | 1,472–1,560 cm² |
| Tennis ball: diameter 6.54–6.86 cm (ITF) | 6.54–6.86 cm | 146.5–169 cm³ | 134.4–147.8 cm² |
| Golf ball: diameter at least 42.67 mm (1.680 in) | 4.27 cm | 40.7 cm³ | 57.2 cm² |
A 2 cm spread in a soccer ball’s circumference makes a 9% difference in the air it holds.
Planets are nearly spheres
| Body (mean radius) | Diameter | Circumference | Surface | Volume |
|---|---|---|---|---|
| Earth (6,371 km) | 12,742 km | 40,030 km | 510.1 million km² | 1.083 trillion km³ |
| Moon (1,737.4 km) | 3,474.8 km | 10,916 km | 37.9 million km² | 21.97 billion km³ |
Earth is slightly flattened at the poles, so these are averages; the Moon would fit inside Earth about 49 times by volume.
The calculator keeps working in airplane mode once zet4u is saved (works offline).
Frequently asked questions
What is the formula for the volume of a sphere?
V = 4/3 × π × r³. A ball with an 11 cm radius (22 cm across) has a volume of 4.18879 × 1,331 = 5,575 cm³, about 5.6 liters.
What is the surface area of a sphere?
A = 4 × π × r², exactly four times the area of a circle with the same radius. For r = 11 cm: 1,520.5 cm².
How do I find the radius from the circumference?
Divide by 2π. A ball that measures 69 cm around has a radius of 69 ÷ 6.28318 = 10.98 cm and a diameter of 21.96 cm.
How do I find the radius from the volume?
Take the cube root of 3V ÷ 4π. For a volume of 1,000 cm³ (one liter): ∛(3,000 ÷ 12.566) = 6.2 cm.
What about a hemisphere?
Half the volume of the sphere and half its curved surface. With the flat circle added, a closed hemisphere has three quarters of the sphere's area: 3πr².
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