`m = [4/3 * pi * "r" ^3] * rho `

Enter a value for all fields

The Mass or Weight of a Sphere calculator computes the mass or weight of a sphere based on the radius (r) and the mean density (ρ).

INSTRUCTIONS: Choose units and enter the following:

• (r) Radius of Sphere
• (ρ) Density of Sphere

Mass of Sphere (m) : The calculator returns the mass of the sphere in kilograms (kg).  However, this can be automatically converted to other mass or weight units (e.g., pounds, tons) via the pull-down menu next to the answer.  NOTE: To find the mean density (ρ) of many common substances, elements, liquids and materials, CLICK HERE (e.g., the density of water is 1,000 kg/m³).

The Math / Science

The formula for the mass of a sphere:

    M = 4/3⋅π⋅r³⋅mD

where:

• M is the mass of the sphere
• r is the radius of the sphere
• mD is the mean density of the material

The mass of a sphere calculator first computes the volume of the sphere based on the radius.  With the computed volume, this formula then executes the simple equation below to compute the approximate mass of the object.

         Mass = Volume ⋅ Density

See the mean density (ρ) of many common substances

Above the formula for mass and volume of a sphere are combined.

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Common Mean Densities

Fluids Pure Water - 1,000 kg/m³  Seawater - 1,022 kg/m³  Milk - 1,037 kg/m³  Olive Oil - 860 kg/m³ Cement Slurry - 1,442 kg/m³  Fuels Diesel Fuel - 885 kg/m³  Crude Oil - 870 kg/m³  to 920 kg/m³  Fuel Oil -  890 kg/m³  Ethanol - 789 kg/m³  Gasoline (petrol) - 737 kg/m³  Propane - 493 kg/m3 Liquid Natural Gas - 430 to 470 kg/m3 Market-Ready Grains Corn - 56 lb/bu (721 kg/m3) Wheat - 60 lb/bu (772 kg/m3) Barley - 48 lb/bu (618 kg/m3) Oats - 32 lb/bu (412 kg/m3) Rye - 56 lb/bu (721 kg/m3) Soybean - 60 lb/bu (772 kg/m3)

Metals Aluminum - 2700 kg/m³ Brass - 8530 kg/m³ Bronze - 8150 kg/m³ Chromium - 7190 kg/m3 Cobalt - 8746 kg/m3 Copper - 8920 kg/m³ Gallium - 5907 kg/m3  Gold - 19300 kg/m³ Iridium - 22560 kg/m3 Iron - 7847.0 kg/m³  Lead - 11340 kg/m³ Molybdenum - 10280 kg/m3 Nickle - 8908  kg/m3  Palladium -  12160 kg/m³ Platinum - 21450.0 kg/m³ Rhodium - 12410 kg/m3 Steel - 7850 kg/m³ Silver - 10490 kg/m³ Titanium - 4500 kg/m³ Tungsten - 19600 kg/m³ Zinc - 7135 kg/m³ Zirconium - 6570 kg/m³

Mean Density is the average amount of mass within a volume for a substance.  Note, volume of a material is often highly subject to the temperatures, since materials expand as they warm.  For that reason, mean densities of substances are often cited with a set of nominal conditions such as temperature and barometric pressure. 

The formula for mean density is:

μD = V / m

where:

• μD = mean density
• V = Volume in units like cubic meters or cubic inches
• m = Mass in units like kilograms or pounds

Mean density is also often indicated as the Greek symbol rho (ρ).

Mass and Weight

Density is a function of mass.  However, converting from mass to weight is trivial under the right conditions.  Fortunately those conditions are generally true anywhere on the surface of the Earth, so the conversions built into the vCalc engine can be assumed to be fairly accurate unless you require weight at very high altitudes or in space.

CLICK HERE  for a pop-up function that provides the mean density (mD or μD) of many common substances, elements, liquids and materials.

Mean Density Units

Mean density is scientifically volume divided by mass.  There are  various unit for density adopted by cultures and industries. Common units for density included the following:

• kilograms per cubic meter (kg/m³)
• grams per cubic centimeter (g/cm³)
• grams per liter (g/L)
• pounds per cubic feet (lb/ft³)
• ounces per cubic inch (oz/in³)
• pounds per barrel (lb/bbl)
• pounds per bushel (lb/bu)

vCalc provides for automatic conversions between density units via the pull-down menus.

 

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Sphere Calculators

• Sphere Surface Area based radius (r)
• Sphere Surface Area from Volume
• Sphere Volume from Radius
• Sphere Volume from Circumference
• Sphere Volume from Surface Area
• Sphere Volume from Mass and Density
• Sphere Radius from Volume
• Sphere Radius from Surface Area
• Sphere Weight (Mass) from volume and density
• Sphere Density
• Area of Triangle on a Sphere
• Distance between Two Points on a Sphere
• Sphere Cap Surface Area
• Sphere Cap Volume
• Sphere Cap Weight (Mass) 
• Sphere Segment Volume
• Sphere Segment Weight (Mass)
• Sphere Segment Wall Surface Area (without the circular top and bottom ends)
• Sphere Segment Full Surface Area  (with the top and bottom circles, aka ends)
• Volume of Spherical Shell
• Mass of Spherical Shell

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Astronomy Calculators

• Schwarzschild Radius
• Hill Sphere Radius
• Escape Velocity
• Mass of a Black Hole
• Density of a Sphere
• Mass of a Sphere
• Kepler's 3^rd Law formula T² = (4π • R³)/(G • M)
  • (M) - mass of the system. 
  • (T) - period of the orbit.
  • (R) - separation distance between the two objects.
  • (G) - universal gravity constant
• Small Angle Formula Small Angle Formula    α = S / D
  • (α) - angle
  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
• Flux and Magnitude formulas
  • Change in Magnitude from Flux Ratio
  • Flux Ratio from Magnitudes
• Telescope formulas
  • Resolving Power of a Telescope
  • Magnification of a Telescope
• Mass formulas
  • Mass from Luminosity
  • Mass from Acceleration and Radius
  • Mass from Speed and Separation
  • Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
  • Mass of extra-solar planet from mass and velocity of star and velocity of planet
• Relative Size Formulas
  • Relative Size from Relative Temperature and Luminosity
  • Relative Temperature from Relative Size and Luminosity
  • Relative Luminosity from Relative Temperature and Size
• Wavelength Formulas
  • Velocity from shift in Wavelength and Unshifted Wavelength
  • Wavelength Shift from Wavelength and Speed
  • Blackbody Wavelength from Temperature
  • Blackbody Temperature from Peak Wavelength
  • Photon Energy from Wavelength
  • Photon Wavelength from Energy
• Luminosity and other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Luminosity from Mass

A word on Mass and Weight

Converting from mass to weight is trivial under the right conditions.  Fortunately those conditions are generally true anywhere on the surface of the Earth, so the conversions built into the vCalc unit conversion engine can be assumed to be fairly accurate unless you require weight at very high altitudes or in space.