Approximate Estimates. Approximate estimates are obtained with varying degrees of accuracy by several methods, the most convenient and reliable of which is the system of cubing; i.e., the cubical contents of the proposed building is obtained and multiplied by a given price per cubic foot. This rate is obtained by careful comparison of the plans and requirements with similar buildings which have been erected under conditions as like as possible to the conditions under which the proposed building can be erected.

Several methods are used to determine the cubical units, depending upon the size and shape of the proposed building. One method is to multiply the square feet in the plan of the building by the height from half-way the depth of foundations to half-way up the roof. Another system uses the height from the bottom of the foundation, and another obtains the actual cubical contents. Any of these may be used if the data for comparison is obtained in the same way, but all are subject to important variations which experience and judgment alone will determine. For instance, if the contour of the building is very uneven, with low portions, such as porches and sheds, and high portions, such as towers and cupolas, these must either be omitted from the whole and compared separately, or a lump sum be added or subtracted according to the size and elaboration of these members.

Another variation arises in the size of rooms, giving a ratio of partitions and division walls which is not constant, and of course a large building with many duplicate parts will require a different rating from a smaller one, so that the method of estimating by cubing is at best approximate, and its degree of accuracy depends largely upon the experience and judgment of the contractor. Even long experience will afford no safe-guard against unusual elaboration of interior or exterior, so that cube rates can only be applied to buildings of ordinary character, and comparisons are only reliable between buildings of like description and uses, as the treatment of even the same materials will vary largely in buildings of varying uses.

The height of the building will not increase the cube rate proportionately, unless the internal voids are alike, although it is certain that the higher one builds from the ground, the more time and expense it requires to put the material in place, to say nothing of thicker walls and necessarily heavier construction.

Estimating by the Square. A convenient method of estimating is by the square of one hundred surface feet. This is especially applicable to office buildings, schools, mills, stables, and all buildings where the floors are few in number or similar in plan. For one story buildings the price per square is taken to include the roof, walls, floor, and foundations, but for buildings of two or more stories the price per square should be taken separately for each floor, the lower floor being priced to include the foundations and the top floor to include the roof.

This method of estimating by the square is not so accurate as by cubical contents, but the results are often more convenient and adaptable, because the tabulation of the square area of the various floors may be easily reduced to terms of accommodation for public buildings or shops. For instance, a given floor area in a school house means accommodation for a certain number of pupils; in a church, a certain number of sittings; in factories for the manufacture of staple goods, a certain number of machines and operatives.

This unit of accommodation is sometimes carried further, and, by the reverse process, made the basis of another method of estimating the approximate cost of such buildings as the above mentioned, i.e., schools, churches, factories, hospitals, etc. This is also a method by comparison, the known data being supplied by previous experience or calculation, and it is often valuable as a means of determining the approximate cost of buildings necessary to accommodate a given number of individuals or machines, even before any definite plans have been drawn. All of these methods are approximate, with varying degrees of accuracy, and should never be advanced as accurate, or used as the basis of a contract, unless the contractor has had a long and varied experience and feels absolutely certain of his judgment, or unless a proper margin is added for possible variations.

Estimating by Quantities. The only sure and correct method of estimating is by taking off the actual quantities in detail and carrying out the prices accurately with the cost of labor, the percentage for profit, and contingencies added.

For this, accurate and complete drawings and specifications are necessary to give the absolute quantity and quality of materials and labor. The various items are then taken off, similar portions grouped, the amount of labor estimated, and a complete and classified schedule prepared and priced at current rates; the cost of transportation, board of men, and any other contingencies noted, a percentage of profit added, and a sum total reached which should be correct if faithfully done.

This, of course, takes considerable time, but is well worth the expense and trouble if a definite contract is to be made.

Preparation. In order to estimate to a sufficient degree of accuracy, some things other than the possession of plans and specifications are necessary. A visit to the site should be made, to ascertain the nature of the soil, the levels of the lot, the distance from railroad or wharf, the condition of the roads, if a long haul is necessary, and the preparation of the site necessary to receive and dispose of materials. Some knowledge should be obtained of the nature of the sub-soil, the presence of ledges or water below the surface which will require especial or costly treatment, etc. Often a deposit of sand will be found upon the site which will not only save carting away of material excavated, but, if of proper quality, it may be used for the work. Such items are constantly occurring so that a knowledge of existing conditions will be of great advantage to the estimator.

Regarding underground conditions, there is always an element of chance, as the most thorough examination will not always reveal hidden perils; the author knows of a case where a mason had contracted for the building of a sewer, and was in a fair way to make a good profit, when a narrow vein of quicksand was uncovered, to overcome which not only took away all the anticipated profit but caused a severe loss to the contractor besides.

Ground water is another source of danger and it will be well for the contractor to closely examine his contract, to see to what extent he is to furnish protection from this source, as a vein of water which may have been temporarily stopped or diverted by the operation of building, will sometimes unexpectedly make its presence known during or after the completion of the work, when it may become a source of great annoyance and expense to the contractor if he has agreed to insure a waterproof job. Numerous illustrations could be given of the danger from unforeseen causes which can at best be only partially obviated by the most careful examination.

In order to accurately take off a building either by quantities, square or cube, a good knowledge of arithmetic is necessary; and, while we may assume that the reader already possesses this knowledge, it may be well to include some of the essential rules of that branch of arithmetic which is known as mensuration.

This consists primarily in the science of obtaining definite data regarding given figures or surfaces, such as areas, solids, capacity, linear dimensions, and comparisons of bodies.

Definitions. The area, or superficial dimension of any figure is the measure of its surface, without regard to its thickness or any other dimension.

The cubical contents of any figure is the measure of its solidity, or whole capacity, and has reference to the three dimensions, length, breadth, and thickness.

If the figure is considered as hollow, then the cubical contents becomes its capacity or capability of containing matter.

The linear dimension of a figure is expressed by its length in a direct line in any direction and has no regard to breadth or thickness.

Units. The application of these dimensions is made by fixing a unit by which the figure may be compared and the required dimension obtained; thus, for calculating the area of a figure the unit is usually a square, one side of which is the unit of length, and the area becomes the square measure of the figure.

This is expressed in common terms by square inch, square foot, square yard, or any other given unit and the measure of the surface is computed by obtaining the number of these square units which are contained in the figure, the process being called squaring.

In a similar manner the cubical contents or solidity of a figure is obtained by computing the number of cubical units which it contains, which is called cubing it.

Rules. Numerous rules have been adopted for obtaining these dimensions when given dimensions are known, and a tabulation of some of the more important and useful of these follows, by means of which it is hoped that the student may be able to solve most of the ordinary problems which will arise in common practice.