Sphere Density
Calculate sphere density from mass and radius using ρ = m / (4/3 × π × r³). Free online physics calculator with instant results, volume computation, interactive charts, and formula breakdown.
About This Calculator
The Sphere Density Calculator computes the density of a spherical object given its mass and radius. It uses the standard physics formula ρ = m / V, where the sphere volume V is derived from the radius using V = (4/3) × π × r³. This tool is ideal for students studying mechanics and material science, engineers working with spherical components, and hobbyists calculating densities of balls, marbles, beads, or planets.
The calculation proceeds in two steps: first the sphere volume is computed from the radius input, then the density is obtained by dividing mass by that volume. All four values — density, mass, radius, and volume — are displayed in the results section along with an interactive bar or pie chart and a detailed breakdown table for easy reference.
How to use
Enter the mass of your sphere in kilograms and the radius in meters, then click Calculate. The result shows the sphere density in kg/m³, the computed volume, and a comparison chart. The shareable URL saves your inputs so you can bookmark or share the exact calculation with classmates or colleagues.
Frequently Asked Questions
What is the formula for density of a sphere?
The density of a sphere is calculated using the formula ρ = m / (4/3 × π × r³), where ρ is density, m is mass, and r is the radius of the sphere. First compute the sphere volume V = (4/3) × π × r³, then divide mass by that volume.
How do I find the mass of a sphere given density and radius?
To find the mass of a sphere given its density and radius, first calculate the volume using V = (4/3) × π × r³, then multiply the volume by the density: mass = density × volume. The combined formula is mass = density × (4/3) × π × r³.
How do I find the radius of a sphere given density and mass?
To find the radius from density and mass, first compute the volume from density using V = mass / density. Then solve for radius using r = ³√(3V / (4π)). The combined formula is r = ³√(3 × mass / (4 × π × density)).
What units should I use for sphere density calculations?
For best results use consistent SI units: mass in kilograms (kg), radius in meters (m). Density will be in kg/m³. You can also use grams and centimeters to get g/cm³ — 1 g/cm³ = 1000 kg/m³.
Can I calculate sphere volume with this calculator?
Yes, the calculator automatically computes the sphere volume using V = (4/3) × π × r³ as an intermediate step. The volume is displayed alongside the density, mass, and radius in the results section and breakdown table.
Is this sphere density calculator free?
Yes, it is completely free to use with no registration or hidden charges. You can bookmark or share your calculation via the URL.
How accurate are the results?
Density and volume are computed to 4 decimal places using the standard sphere density formula with the JavaScript Math.PI constant. Results are suitable for physics homework, engineering calculations, and scientific analysis.
What are typical densities of common sphere materials?
Common material densities include: steel ~7800 kg/m³, aluminum ~2700 kg/m³, glass ~2500 kg/m³, wood ~600-800 kg/m³, and polystyrene foam ~50 kg/m³. Enter the mass and radius of your sphere to find its density and identify the material.