Sphere Density Calculator
Calculate density, mass, radius, and volume of spherical objects with precise physics formulas
Calculate Sphere Properties
Total mass of the spherical object
Distance from center to surface
Sphere Properties Results
Formulas used: ρ = m/V, V = (4/3)πr³, A = 4πr²
Volume formula: V = (4/3) × π × r³
Surface area formula: A = 4 × π × r²
Physical Analysis
Example Calculations
Steel Ball Bearing
Given: Radius = 1 cm, Mass = 32.7 g
Volume: V = (4/3)π(0.01)³ = 4.189 × 10⁻⁶ m³
Density: ρ = 0.0327 kg / 4.189 × 10⁻⁶ m³ = 7,806 kg/m³
Material: Matches steel density (~7,800 kg/m³)
Ping Pong Ball
Given: Radius = 2 cm, Mass = 2.7 g
Volume: V = (4/3)π(0.02)³ = 3.351 × 10⁻⁵ m³
Density: ρ = 0.0027 kg / 3.351 × 10⁻⁵ m³ = 80.6 kg/m³
Note: Much less dense than water due to hollow structure
Common Material Densities
Sphere Formulas
Density
ρ = m/V
Mass per unit volume
Volume
V = (4/3)πr³
Space inside the sphere
Surface Area
A = 4πr²
Outer surface area
Diameter
d = 2r
Distance across center
Understanding Sphere Density
What is Density?
Density is a fundamental physical property that describes how much mass is contained in a given volume of space. For spheres, density helps us understand the material composition and can be used to identify unknown materials or verify the purity of known ones.
Sphere Geometry
- •Perfect 3D round shape - all points equidistant from center
- •Volume increases with the cube of radius (r³)
- •Surface area increases with the square of radius (r²)
- •Maximum volume for minimum surface area
Mathematical Relationships
Basic Density Formula
ρ = m/V
Where ρ is density, m is mass, and V is volume
Sphere Volume Formula
V = (4/3)πr³
Volume is proportional to the cube of radius
Note: Small changes in radius lead to large changes in volume and mass.
Real-World Applications
Material Identification
Compare calculated density with known material properties to identify unknown spherical objects or verify material composition.
Quality Control
Manufacturing processes use density measurements to ensure spherical products meet specifications and detect defects.
Scientific Research
Planetary science, materials research, and particle physics often involve spherical objects and density calculations.
Measurement Tips
Measuring Mass
- • Use precise digital scales for accuracy
- • Account for air buoyancy for very precise measurements
- • Ensure the sphere is clean and dry
- • Take multiple measurements and average
Measuring Dimensions
- • Use calipers for diameter measurement
- • Measure at multiple orientations
- • For volume: water displacement method
- • Consider surface irregularities