Sphere Calculator
Calculate sphere volume, surface area, diameter, and circumference from radius. Includes hemisphere, spherical cap, hollow sphere, and weight from density.
cm
Volume
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Surface Area —
Diameter —
Circumference (great circle) —
Extended More scenarios, charts & detailed breakdown ▾
cm
Volume (cm³)
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Surface Area (cm²) —
Diameter (cm) —
Professional Full parameters & maximum detail ▾
Hemisphere
Hemisphere Volume (cm³) —
Hemisphere Total SA (cm²) —
Spherical Cap & Hollow
Spherical Cap Volume (cm³) —
Hollow Sphere Volume (cm³) —
Weight & Geometry
Weight (g) —
Inscribed Cube Side (cm) —
How to Use This Calculator
- Enter Radius to calculate volume, surface area, diameter, and circumference.
- Use the From Diameter tab if you know diameter.
- Use the From Volume tab to find radius from a known volume.
- The Professional tab covers hemisphere, spherical cap, hollow sphere, and weight calculation.
Formula
Volume: V = (4/3)πr³ | SA: A = 4πr² | Diameter: d = 2r | Circumference: C = 2πr
Example
r=5 cm → V ≈ 523.60 cm³, SA ≈ 314.16 cm², d = 10 cm.
Frequently Asked Questions
- The volume of a sphere is V = (4/3)πr³, where r is the radius. For a sphere with radius 5 cm: V = (4/3) × π × 5³ = (4/3) × π × 125 ≈ 523.60 cm³. Note that volume scales as the cube of the radius — doubling the radius multiplies the volume by 8. A common error is using the diameter instead of the radius: if you know the diameter d, compute r = d/2 first. For d=10 cm, r=5 cm, so V ≈ 523.60 cm³.
- The surface area of a sphere is SA = 4πr². For a sphere with radius 5 cm: SA = 4 × π × 25 ≈ 314.16 cm². Interestingly, the surface area of a sphere equals exactly 4 times the area of a great circle (a cross-section through the center). Surface area scales as the square of the radius — doubling the radius quadruples the surface area. To find radius from surface area: r = √(SA / (4π)).
- Rearrange V = (4/3)πr³ to solve for r: r = ∛(3V / (4π)). Example: V = 523.60 cm³ → r = ∛(3 × 523.60 / (4π)) = ∛(1570.8 / 12.566) = ∛(125) = 5 cm. For V = 100 cm³: r = ∛(300 / (4π)) = ∛(23.873) ≈ 2.879 cm. The cube root step means you need to take the third root, not the square root. This calculator performs this calculation automatically.
- A spherical cap is the region of a sphere above (or below) a flat cutting plane. If h is the height of the cap (from the cut to the top of the sphere) and R is the sphere radius, then: Cap volume = πh²(3R − h)/3, and Cap curved surface area = 2πRh. For a hemisphere (h = R): V = πR²(3R−R)/3 = 2πR³/3 = half the sphere volume, and SA = 2πR² = half the sphere surface area. Spherical caps appear in lens design, tank dome calculations, and geography (polar caps).
- A hollow sphere (spherical shell) has an outer radius R and inner radius r, with a wall of thickness R − r. Its volume equals the outer sphere minus the inner cavity: V = (4/3)π(R³ − r³). Surface area depends on context: the total area of both surfaces (outer + inner) = 4πR² + 4πr². Example: R = 6 cm, r = 5 cm → V = (4/3)π(216 − 125) = (4/3)π(91) ≈ 381.7 cm³. Hollow spheres appear in pressure vessels, balloon problems, and atom models.