How do you calculate grains of sand?

Mathematician Marcus du Sautoy replies: Sand is rock with a diameter of between 0.625mm and 0.2mm. Assuming a grain of sand is roughly spherical, the average volume of a grain is 4/3 x pi x r3=0.00947mm3, where r is the radius. So how many grains of sand are there in a metre cube box? It has 109mm cubes inside (10N is how mathematicians write a 1 followed by N zeros), and if they are arranged randomly, about 65% of the box will be sand and the rest air. So we can estimate that the number of grains of sand in a metre cube box is 109 x 0.65/0.00947, or roughly 70bn grains. Now, let's go for an average of 5% of the surface of the Earth being covered in sand with a depth of 100m. The surface area of the Earth is 4 x pi x r2 where r is the radius of the Earth, which is 6,378,000 metres. So the volume of sand comes out at: 2.5 x 1015m3. So my rough estimate is that the number of grains of sand on the Earth is a number with 27 digits.

Marcus du Sautoy is author of The Number Mysteries (Fourth Estate).

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Use this calculator to estimate how much sand in volume (cubic ft, cubic yards, or cubic meters) or weight (tons & pounds, tonnes and kilograms) you would need. It uses conventional sand density.

    Quick navigation:

  1. Calculating how much sand you need
    • Square or rectangular area
    • Round area
    • Irregularly shaped area
  2. Sand basics
  3. Types and grades of sand
    • What is the density of sand?
    • How much does a cubic meter of sand weigh?
    • How much is a tonne of sand?

    Calculating how much sand you need

Many builders and gardeners are faced with calculating or estimating the amount of sand they need to fill a given space with sand. Our sand calculator is of great utility in such cases, but you should keep in mind that the results will only be as good as the measurements entered. The calculation process is as follows:

  1. Estimate the volume of sand needed, using geometrical formulas and plans or measurements.
  2. The approximate density of sand is 1600 kg/m3 (100 lb/ft3).
  3. Multiply the volume by the density (in the same units) to get the weight

There is finer and more coarse sand, so the density, measured for dry sand in kg per cubic meter or pounds per cubic feet, of your particular shipment may vary. For this reason, and due to potential loses / waste, you should consider buying 5-6% more sand than estimated so you don't run just short of what you need in the end.

Square or rectangular area

The volume formula for a rectangular (or square) box in cubic feet is height(ft) x width(ft) x length(ft), as seen in the figure below:

How do you calculate grains of sand?

For example, to fill a box with a width of 3ft and a length of 6ft, to a depth of 1ft, you need to multiply 1ft x 3ft x 6ft = 18ft3 (cubic feet) of sand.

Round area

If the area you want to cover, or the shape you want to fill is round, the calculation is a bit different:

How do you calculate grains of sand?

The volume of a figure with a round foundation is its height times the area of its foundation. To calculate the foundation area we need its diameter, since the formula is π x r2, where r is the radius, or diameter/2.

Irregularly shaped area

In case the area you are calculating has an irregular shape what you want to do is divide it in several regularly-shaped sections, calculate their volume and sand requirements and then sum them up together. In case you end up needing to do this for a large number of sections, you might use our summation calculator.

    Sand basics

Sand is a naturally occurring granular material which is composed of finely divided rock and mineral particles, rounded and polished to a varying extent. Sand can be thought of as finer gravel, or coarser silt. In some cases, "sand" refers to a textural class of soil, that is - a soil which has more than 85% of its mass comprised of sand-sized particles. Sand is a renewable resource in the long run, but in human timescale it is practically non-renewable. Sand is a major component of concrete and due to the high demand for concrete for construction, suitable for concrete sand is also in high demand.

The most common constituent of sand in inland continental settings and non-tropical coastal settings is silica quartz (silicon dioxide - SiO2). The second most common type of sand, mostly encountered in islands and near the sea, is calcium carbonate which is created by various life-forms, like coral and shellfish. Of course, the exact composition will vary depending on local rock sources and conditions during the formation of the pebbles.

How do you calculate grains of sand?

Sand for domestic or garden use is usually sold in small packets of several pounds / kilograms, and for larger projects in bags of 40, 60 or 80 lbs - 25kg or 50kg in Europe and other places. For construction work, concrete mixing, etc. it is sold by the tonne and comes in trucks.

    Types and grades of sand

Contrary to what you may think, there is more than one type of sand, by the size of its pebbles and it's intended use [2]. Selecting the right type and size is crucial, as some sands have a different application than others.

Sand types
20-30 Sand n-standard sand, graded to pass a 850μm sieve and be retained on a 600μm sieve.
Graded Sand n-standard sand, graded between the 600μm sieve and the 150μm sieve.
Standard Sand n-silica sand, composed almost entirely of naturally rounded grains of nearly pure quartz (used for mortars and testing of hydraulic cements).

Standard sand, in addition, shall be light grey or whitish color, should be free from silt and the grains should be angular, but a small percentage of flaky or rounded particles are permissible. Some manufacturers express the grade and type of the sand in other ways, e.g. "river sand" (a.k.a. "sharp sand", "builder's sand", "grit sand", "concrete sand"), "masonry sand", "M-10 sand" (granite sand), "play sand", each being finer and more expensive than the previous one.

What is the density of sand?

The density of typical sand is 100 lb/ft3 (1600 kg/m3). This corresponds to moderately damp sand and is the number used in the calculator.

How much does a yard3 of sand weigh?

A cubic yard of typical sand weighs about 2700 pounds or 1.35 tons. A square yard of a sandbox with a depth of 1 foot (30.48 cm) weighs about 900 pounds (410 kg) or slightly less than half a ton. The water content of the sand is assumed to be moderate.

How much does a cubic meter of sand weigh?

A cubic meter of typical sand weighs 1,600 kilograms 1.6 tonnes. A square meter sandbox with a depth of 35 cm weighs about 560 kg or 0.56 tonnes. The numbers are obtained using this sand calculator.

How much is a ton of sand? A ton of sand is typically about 0.750 cubic yards (3/4 cu yd), or 20 cubic feet. Sand is assumed relatively damp, since adding water can increase or decrease the density of the sand considerably (e.g. if it was raining or if you dig up and leave sand under the sun so water evaporates).

How much is a tonne of sand?

A tonne of moderately damp sand typically fills about 0.625 m3 (cubic meters). It can be more or less dense depending on water content and the size of the sand particles.

Ton vs tonne, tons vs tonnes

When calculating the sand's weight, make sure you do not confuse the tonne (metric ton) with the ton (short ton). The first one is used by all countries in the world and is defined to be equal to 1000 kg by the international body of standardization. The ton is currently only used in the United States and is equal to 2000 pounds (2000 lbs). The difference between the two is not huge but can quickly add up to a significant number as the amount increases.


[1] Krinsley D.H., Smalley I.J. (1972) "Sand", American Scientist 60:286-291

[2] ASTM C-778 - 17 "Standard Specification for Standard Sand"

How do you calculate the number of grains of sand?

on the number of sand grains in a bucket and the number of buckets filled by a square metre of sand, multiplied by the surface area of the beach. difference, it is the mean grain size which determines the number of grains in the bucket or on the beach.

How do you calculate grain?

Divide the total grams of creditable grains in the recipe (Step 5) by the number of servings (yield) in the recipe to determine the amount of creditable grains per serving. For example 367.5 g creditable grains ÷ 20 servings in the Blueberry Muffins recipe = 18.375 g creditable grains per serving .

What does 1 million grains of sand look like?

Each grain is 1/1,000th of a foot wide, so it takes 1,000 x 1,000 or about 1 million grains of sand to cover just 1 square foot. That's just a thin layer of single grains…if you want a few inches of sand, you need hundreds of layers, giving us over a billion grains for a grown-up!

How many grains of sand are in a cubic meter?

So we can estimate that the number of grains of sand in a metre cube box is 109 x 0.65/0.00947, or roughly 70bn grains.