How to Calculate the Weight of Sand

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Sand is a mix of several types of minerals, which have been worn down over time by wind and water. The properties of sand change depending on the part of the world where it is found. Sand is often composed of very small pieces of minerals such as quartz or gypsum, but can also have small pieces of organic material such as shells.

What is a Sand Weight Calculator?

In order to calculate the unit weight of sand, we need to know certain information, such as the volume of one unit of sand, the composition of the sand, and the mass densities of each component. A sand weight calculator would then take into account the composition of the sand, to calculate a unit weight.

Tips

  • To calculate the weight of sand, you need to determine the volume of each mineral in the sand, multiply the volume by the mass density. Then you can multiply the masses of each component mineral by the local acceleration of gravity, to determine the weight of the sand.

Example to Calculate: One Cubic Meter Sand Weight

Let's go through an example to determine a unit weight of sand, if we define one unit as one cubic meter of sand.

Because sand is made of several different types of minerals, we need to determine the percent composition of each mineral in the sand.

Let's take green sand, which is found at Papakolea Beach in Hawaii. It is largely composed of small pieces of olivine mixed with a small amount of basalt. For this quick example, let's estimate that one cubic meter of green sand is about 92 percent olivine and 8 percent basalt. That means that there are 0.92 cubic meters of olivine, and 0.08 cubic meters of basalt, in our unit of sand.

Next, we need the mass density of both minerals, which will tell us the mass of each mineral in the volume that it occupies. The average mass density of olivine is about 3.8 g/cm3, and the average mass density of basalt is about 3.0g/cm3.

The mass of each component is the volume of each multiplied by it's density. But don't forget to check units and convert when needed!

The mass of the olivine is 0.92 m3, or 920,000 cm3 times 3.8 g/cm3, gives 3,496,000 g. In kilograms, we have 3,496 kg.

Similarly, for the basalt, 0.08 m3 is 80000 cm3 times 3.0 g/cm3, which gives 240,000 g. In kilograms, the total mass of the mixture of olivine and basalt is 3,736 kg.

The weight is technically the mass times the acceleration of gravity: 3,736 kg × 9.8 m/s2 = 36,612.8 N. In metric tons (9806.65 N = 1 metric ton), this is about 3.7 metric tons of sand.

In many cases, you'll really need the mass of the sand, but you can always convert this into weight (the force due to the Earth's gravity acting on the mass) by multiplying by the 9.8 m/s2 acceleration due to gravity.

Generalizing This Method

Because sand is a general term which describes a substance made of small grains of several materials, we could apply the above method to any similar substance.

The general information you need to calculate the mass or weight of a substance is:

  1. What are the constituent materials of the substance? In the sand example, we assumed it was a mixture of the minerals olivine and basalt. For other types of sand, you may have mixtures of quarts, gypsum, or silica. 
  2. What is the volumetric percentage of each constituent material in one unit of the substance? This might be information you can estimate, or it may be provided. 
  3. What are the mass densities (or specific gravity) of the constituent materials? 
  4. From the volume and the mass densities, determine the mass of each material. Sum the masses to get the total mass of the substance, which is proportional to the total weight.

This method can even be generalized to other kinds of substances and solids, as well as liquids and gasses.

References

About the Author

Lipi Gupta is currently pursuing her Ph. D. in physics at the University of Chicago. She earned her Bachelor of Arts in physics with a minor in mathematics at Cornell University in 2015, where she was a tutor for engineering students, and was a resident advisor in a first-year dorm for three years. With this experience, when not working on her Ph. D. research, Gupta participates in STEM outreach activities to promote young women and minorities to pursue science careers.

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