🔵 Sphere Volume Calculator
Calculate volume, radius, diameter, or surface area of a sphere
Enter Radius
r = radius, d = diameter
📊 Results
Radius (r)
10 cm
Diameter (d)
20 cm
Volume
4,188.79 cm³
Surface Area
1,256.64 cm²
Circumference
62.83 cm
V in Liters
4.19 L
📝 Step-by-Step Solution
Given: r = 10 cm
Volume formula: V = (4/3)πr³
V = (4/3) × π × 10³ = (4/3) × π × 1000
V = 4188.79 cm³ = 4.19 liters
Surface area: SA = 4πr² = 4 × π × 100 = 1256.64 cm²
📐 Sphere Formulas
Volume: V = (4/3)πr³ = (π/6)d³
Surface Area: SA = 4πr² = πd²
Radius from Volume: r = ∛(3V / 4π)
Radius from Surface: r = √(SA / 4π)
Circumference: C = 2πr = πd
Understanding Spheres
🔵 Perfect Symmetry
All points equidistant from center. Spheres have infinite rotational symmetry. Most efficient shape for enclosing volume.
📐 The 4/3 Factor
V = (4/3)πr³. Derived from calculus (integration of circular disks). The 4/3 comes from the integration process.
📏 Diameter = 2r
Diameter is twice the radius. Use d = 2r to convert. Volume formula with diameter: V = (π/6)d³.
🌍 Real-World Spheres
Planets, balls, bubbles, atoms. Nature prefers spheres for minimum surface tension and maximum efficiency.
Frequently Asked Questions
What is the volume formula for a sphere?
V = (4/3)πr³. Four-thirds times pi times radius cubed. With
diameter: V = (π/6)d³.
How do I find radius from volume?
r = ∛(3V / 4π). Cube root of (3 times volume divided by 4π).
Rearrange V = (4/3)πr³.
What is surface area of a sphere?
SA = 4πr². Four times pi times radius squared. Exactly 4 times the
area of the great circle.
Why is the formula 4/3?
Calculus integration. Integrating πr² dh from stacked disks. The
4/3 emerges from the mathematics.
How do I use diameter instead of radius?
r = d/2. Substitute in formulas. Or use V = (π/6)d³ and SA = πd²
directly.
What is a great circle?
Largest circle on a sphere. Passes through center. Area = πr².
Equator is Earth's great circle.
How do I convert to liters?
1 L = 1000 cm³. Divide cm³ by 1000. Our calculator shows liters
automatically.
What is circumference of a sphere?
C = 2πr = πd. Great circle circumference. Same formula as circle
with same radius.
How does surface area relate to volume?
SA = 3V/r. Or V = SA×r/3. Spheres minimize SA for given volume
(efficient shape).
What is a hemisphere?
Half a sphere. Volume = (2/3)πr³. Surface area = 2πr² (curved) +
πr² (flat base).
How accurate is this calculator?
Mathematically exact. Uses π to full precision. Results match
calculus integration.
What is the volume of Earth?
~1.08 × 10¹² km³. Radius ≈ 6,371 km. V = (4/3)π(6371)³.
Can I calculate hollow sphere volume?
Subtract inner from outer. Shell volume = (4/3)π(R³ - r³). Where R
= outer, r = inner radius.
What is spherical cap volume?
V = (πh²/3)(3r - h). Slice of sphere with height h. Different
formula from full sphere.
Why are spheres efficient?
Minimum surface for maximum volume. Isoperimetric inequality.
That's why bubbles are spherical.
How do I find diameter from volume?
d = ∛(6V / π). Cube root of (6 times volume divided by π). Or find
r first, then d = 2r.
What is the ratio of surface to volume?
SA/V = 3/r. Smaller spheres have higher ratio. Important for heat
transfer and reactions.