Specific Weight Calculator

Specific weight is the weight of a substance per unit volume. Although it sounds similar to density, they are not the same thing. While density indicates how much mass there is in a given space, specific weight measures the magnitude of the force that a substance exerts downward due to gravity. This calculator allows for two methods of calculation: either by measuring the weight and volume of a sample or starting with the density and local gravitational acceleration. By entering known values and leaving one field blank, this field can be calculated, allowing for back-calculations of weight, volume, density, and gravitational acceleration.

What is specific gravity?

Density is usually represented by the Greek letter gamma and is the weight of a substance divided by its volume. Since weight is a force, the unit for density in the SI system is newtons per cubic meter while it is pounds per cubic foot in the US system. The density of water at 4 degrees Celsius is about 9,810 newtons per cubic meter which is equivalent to 9.81 kilonewtons per cubic meter or 62.4 pounds per cubic foot. Under normal earth gravity, water exerts a force of about 9,810 newtons per cubic meter downward.

Gravity is the key to distinguishing between specific gravity and density. Density is a property of matter itself and does not change with location while specific gravity varies. Although the amount of mass in one cubic meter of water is the same on the moon as it is on Earth, the weight will be about one-sixth that on Earth because of lower gravity. Therefore, specific gravity decreases due to weaker gravity while density remains unchanged.

Two formulas

There are two ways to express specific gravity and this calculator supports both. The direct definition is the weight divided by the volume.

where gamma is the specific gravity, W is the total weight as a force and V is the volume. The second formula relates specific gravity to density. Since weight is mass times acceleration due to gravity and density is mass divided by volume, then weight per unit of volume is equal to density times acceleration due to gravity.

In this formula rho is the density and g is the acceleration due to gravity. These two equations are equivalent because they describe the same quantity from different starting points. The result can be checked by multiplying the units. This means that multiplying kilograms per cubic meter by meters per square second gives newtons per cubic meter. This is because a newton is equal to one kilogram times meters per square second.

Example calculation:

For example, water at 10 degrees Celsius has a density of about 999.75 kilograms per cubic meter and under standard gravity of 9.81 meters per square second its weight is as follows.

Air is a much lighter material. At 20 degrees Celsius it has a density of about 1.2 kilograms per cubic meter, so its specific weight is only about 11.8 Newtons per cubic meter. In contrast, mercury, which is at the other end of the spectrum, has a specific weight of nearly 133,000 Newtons per cubic meter. The following table shows each symbol and their example values.

Specific gravity and relative density.

Density is also called relative density. It compares the density of a material to that of water and is expressed as a simple dimensionless number. If the relative density is less than 1, then the material floats on water; if it's greater than 1, then it sinks. Concrete has a relative density of about 2.4, steel about 7.9, and gasoline about 0.72. This also explains why fuel spreads out over the surface of a puddle when it is spilled. This calculator gives both density and specific weight at the same time so you can get answers to buoyancy questions directly.

Applications of specific gravity

The most common application is for calculating hydrostatic pressure. The gauge pressure at any depth of a stationary liquid is the product of specific weight and depth. This calculator allows you to convert specific weight into pressure at a given depth. Civil engineers use this in designing dams, aquariums, and retaining walls while geotechnical engineers use soil specific weight to calculate bearing pressures and analyze slope stability. In fluid mechanics, specific weight determines buoyancy and establishes the material load acting on a structure.

Tips to improve accuracy of results

Make sure the weight you enter is a force in Newtons or pounds-force and not just mass. If only mass is given, multiply it by 9.81 to convert it into Newtons first. Always use the same system of units. Mixing kilograms-force with cubic feet will give results that are off by several orders of magnitude. As materials expand and contract, their specific weight changes slightly with temperature. For liquids near phase transitions, make sure you're using a reference value appropriate for current conditions. For gases, the specific weight is highly dependent on pressure and temperature, so it's hard to account for this with a single standard value.