HVAC Construction Math for Construction Management and Jobsite Maintenance (Outcome 6.1)

Volume

The amount of space inside a 3D object.

Surface area

How much outside area an object has.

Level of precision

The specified accuracy required for measurements, often rounded at the end of calculations.

Rectangular prism

A three-dimensional shape used for duct sections and equipment pads.

Volume formula for a rectangular prism

$V = L \times W \times H$.

Surface area formula for a rectangular prism

$SA = 2(LW + LH + WH)$.

Cylinder

A 3D shape used for pipes and round ducts.

Volume formula for a cylinder

$V = \frac{22}{7}r^2h$.

Surface area formula for a cylinder (total)

$SA = 2\frac{22}{7}r^2 + 2\frac{22}{7}rh$.

Lateral surface area

The surface area of the side of a cylinder, excluding the ends.

Triangular prism

A 3D shape used for duct transitions and wedge-shaped curbs.

Volume formula for a triangular prism

$V = A_{\triangle}L$.

Basic angle conversion to degrees

When in right triangles, use trigonometric functions to denote angle relations.

Dimensional analysis

A method for converting units by multiplying by conversion factors.

Perpendicular

A relationship between two lines that meet at a right angle.

Proportional reasoning

Comparing two ratios to establish equal relationships.

Pythagorean theorem

In a right triangle, $c^2 = a^2 + b^2$ where $c$ is the hypotenuse.

Measurement scale

A controlled ratio between the size on a drawing and the real size in the field.

Builder’s level

A tool used to transfer elevations across a site.

Grade rod

A graduated rod used with a level to read elevations.

Percent change formula

$\text{new} = A(1 + \frac{p}{100})$ for increases.

Volume conversion reminder

Volume scales by the cube: $1 \text{ft}^3 = 1728 \text{in}^3$.

Temperature conversion from Fahrenheit to Celsius

$C = (F-32) \frac{5}{9}$.

Common units for area

$1 \text{ft}^2 = 144 \text{in}^2$.

Standard pressure conversion equivalence

$1 \text{psi} = 6.895 \text{kPa}$.

Angle measurement tool

A protractor is used for measuring angles.

Convert mixed number to improper fraction

If you have $a \frac{b}{c}$, then it equals $\frac{ac+b}{c}$.

Common mistake in volume calculation

Failing to convert all dimensions to the same unit.

Measurement tool selection

Choose based on accuracy and measurement needs.

Rounding off errors

Rounding too early in calculations can misrepresent final values.

Common unit mistake

Adding/subtracting dimension strings incorrectly.