The sphere calculator computes volume (V = 4/3πr³), surface area (A = 4πr²), and diameter from the radius or from any known measurement. Supports metric and imperial units.
Sphere Calculator
How to Use the Sphere Calculator
The sphere calculator solves for all sphere dimensions from any one known measurement — radius, diameter, volume, or surface area.
Volume Formula
V = (4/3)πr³. A basketball with diameter 24 cm (r=12 cm): V = (4/3)π×1728 ≈ 7238 cm³ ≈ 7.24 L. A tennis ball (d=6.7 cm, r=3.35): V = (4/3)π×37.6 ≈ 157.5 cm³ ≈ 157.5 mL.
Surface Area Formula
A = 4πr². Earth's surface area (r=6371 km): A = 4π×6371² ≈ 510 × 10⁶ km². About 71% is ocean (362 × 10⁶ km²) and 29% is land (148 × 10⁶ km²). The surface area of a sphere equals 4 times the area of a great circle: A = 4 × πr².
Finding Radius from Volume
r = ∛(3V / 4π). A container holds 500 mL = 500 cm³. r = ∛(1500/4π) = ∛(119.4) ≈ 4.93 cm. Enter volume in the input dropdown to solve backward.
FAQ
What is the volume of a sphere?
V = (4/3) × π × r³. Example: Earth's radius ≈ 6371 km → V = (4/3) × π × 6371³ ≈ 1.083 × 10¹² km³. A basketball (radius ≈ 12.0 cm) → V = (4/3) × π × 1728 ≈ 7238 cm³ ≈ 7.24 L.
What is the surface area of a sphere?
A = 4 × π × r². A sphere with radius 5 cm has surface area = 4π×25 ≈ 314.16 cm². Note: the surface area of a sphere equals 4 times the area of a great circle (cross-section). Earth's surface area ≈ 510 × 10⁶ km².
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
How do you find radius from volume?
Rearrange V = (4/3)πr³: r = ∛(3V/(4π)). Example: if V = 100 cm³, then r = ∛(75/π) = ∛(23.87) ≈ 2.879 cm. The calculator solves for r automatically from volume input.