How to Calculate Unit Weight

Unit weight is one of a number of related basic physics terms that leads some students to confusion. Also called ​specific weight​, unit weight is in a family of terms that, loosely speaking, define and relate ​size​ (​volume​), ​amount​ (​mass​), concentration (​density​) and ​force​ (​weight​), along with ​specific gravity.

Most of the confusion over which term is best suited for a particular physical situation stems from the common and incorrect equating of mass and weight, a point addressed later in this article in detail.

Weight is the product of mass, a quantity that simply describes how much atomic and molecular "stuff" is present, and the acceleration due to ​gravity​, which has units of m/s2.

Unit Weight Defined

Unit weight, typically assigned the Greek letter gamma (γ) is simply weight ​W​ per unit volume ​V​ of a material in which the matter, or mass ​m​ is assumed to be uniformly distributed. That is, the density – defined as mass divided by volume, represented by the Greek letter rho (ρ) – at any randomly chosen point within the material represents the density of the entire sample with high fidelity.

Since ​Wγ= m​g​ and γ = ​W​/V,:

\gamma = \frac{mg}{V}=\rho g
  • SI units are N/m3.  

Why Not Just Density?

On the surface it is difficult to see why unit weight is even needed, since it just seems to be taking density and multiplying it by gravity. But it is useful for several reasons. For one thing, though the value of ​g​ is usually treated as a constant for Earth problems, in reality its value decreases with increasing distance from Earth, albeit very slowly.

Also, some products sold by unit weight do not always have the same density. Different shipments of the same kind of concrete might be more or less dense owing to settling of contents during transport or a result pressure differences. In any case, when a more surgical level of precision is needed that mere density, unit weight can come in handy.

Those Pesky Pounds

You may have wondered by now why there are separate units for mass (kg) and weight (N) in the metric system pounds (pounds, or lb), whereas in the imperial or "traditional" system, the notion of mass appears to have been swallowed up in the definition of a pound, which is, in theory, a unit of weight.

You may have been told that 2.204 lb is equal to 1 kilogram or that 1 lb equals 0.454 kg, but what this really means is that a force of 2.204 lb results from that object's mass times the local value of gravity in some units or another.

A unit called the ​slug​, equal to 32.17 "mass-pounds" or 14.6 kg, can be used to convert between pounds in the usual (force) sense and pounds in the mass sense, but for the most part it is better to duck the problem and stick with the metric system.

Unit Weight Calculator

Soil is a product commonly sold by unit weight. Soil consists of dirt, water and organic matter. The ​dry unit weight​ of soil is a helpful figure as it can be used to establish a standard of sale between a purchaser and a soil vendor. It can be measured after when the "void spaces" of the soil (which are sort of like the holes in a sponge) are filled with air, with no water remaining.

The dry unit weight formula is

\gamma_D=\frac{W_s}{V_{tot}}

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