Five ways to define the ball—radius, diameter, circumference, surface area, or volume—plus hollow shell, hemisphere, tank fill, density mass, multi-sphere totals, live diagrams, and a full unit table.
Input mode
Length unit
For radius, diameter, circumference, and surface-area inputs.
cm
5.00
Options
Diagram
Equator shown dashed (3D hint). Inner circle appears for hollow shells.
Great circle (cross-section)
A plane through the center cuts a great circle; its area is πr² (not the same as total surface area).
Results
Volume
523.60 cm³
full sphere
(4/3)πr³ or shell / hemi variants
Surface area
314.16 cm²
4πr²
4πr²
Diameter
10.0000 cm
2r
2r
Circumference
31.4159 cm
2πr
2πr
Radius
5.0000 cm
r
r
Multiple spheres
Total volume (N × V): 523.60 cm³
Spherical tank — fill level
Height h of liquid measured from the bottom point along the vertical through the center (0 to 2r). Uses spherical cap volume.
cm
Cap volume: —
Density → mass
Density in g/cm³. Mass = ρ × V.
Mass: 523.60 g (0.5236 kg)
Step-by-step
V = (4/3) × π × r³
= (4/3) × 3.141593 × 5.000000³
= 523.60 cm³
A = 4πr²
= 314.16 cm²
d = 2r = 10.000000 cm
C = 2πr = 31.415927 cm
Volume in all units
Unit
Value
m³
0.0005236
cm³
523.60
mm³
523,598.8
ft³
0.01849
in³
31.951958
yd³
0.0006848
L
0.5236
mL
523.60
gal (US)
0.1383
gal (UK)
0.1152
Real-world size
Your sphere (r ≈ 5.0000 cm) is almost exactly the same size as a billiard ball.
Choose input mode and units, enter the known value (slider optional), then read metrics, conversions, and steps.
Formula
V = (4/3)πr³; hemisphere V = (2/3)πr³; shell V = (4/3)π(r₁³−r₂³); cap V = πh²(3r−h)/3; A = 4πr²
Sphere volume — full reference
Use any known measurement, then read volume, surface area, and conversions. Hollow, hemisphere, and fill tools extend the basic V = ⁴⁄₃πr³ formula.
Five input modes (why they matter)
Most tools only accept radius. Here you can start from radius, diameter, circumference, surface area, or volume (reverse solve for r). Pick the length unit for geometry; for volume reverse, choose the volume unit that matches your measurement.
Hollow shell & hemisphere
Hollow uses inner radius r₂: shell volume (⁴⁄₃)π(r₁³−r₂³) and both spherical surfaces. Hemisphere uses half the full-sphere volume and includes the flat face in surface area (3πr²). Combining both follows the formulas shown in step-by-step output.
Tank fill, density, multiples
Fill level: spherical cap volume from fluid height h (bottom to surface along the vertical).
Density → mass: mass = ρ × V with ρ in g/cm³ (material presets included).
N spheres: total volume = N × V for identical balls.
FAQ
How do I convert diameter to volume?
Choose Diameter mode, enter d; the tool uses r = d/2 and computes V = (4/3)πr³.
What is the hollow sphere formula?
Volume of the material shell is (4/3)π(r_outer³ − r_inner³). Surface area counts both outer and inner spheres.
Hemisphere surface area — why 3πr²?
Curved half is 2πr²; the flat circular base adds πr², so total 3πr².
How does spherical tank fill work?
Enter fluid height h from the bottom point (same length unit as r). Volume uses the spherical cap formula πh²(3r−h)/3.
Are results guaranteed for exams?
For critical applications, verify units and formulas independently; this tool is for education and estimation.
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