Unit Factor Converting Method

Overview

Engineering reference data for Unit Factor Converting Method in basics.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Conservation of Energy

$E_{in} = E_{out} + \Delta E_{stored}$

Energy balance.

Variables

Symbol	Description	Unit
$V$	Voltage	V
$I$	Current	A
$R$	Resistance	Ω
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/s²

Expanded Formulas & Derivations

The factor-label method allows chaining multiple conversion factors. The general formula for sequential conversions is:

$$\frac{a \, (\text{u1})}{1} \cdot \frac{y \, (\text{u2})}{x \, (\text{u2})} \cdot \frac{z \, (\text{u3})}{y \, (\text{u3})} \cdot \frac{1}{z \, (\text{u4})} = \frac{a \cdot y \cdot z}{x \cdot z} \, (\text{u4})$$

Simplifying the unit factor for converting feet to millimeters (mm/ft) using eq. (4):

$$\frac{25.4 \, \text{mm}}{1 \, \text{in}} \cdot \frac{12 \, \text{in}}{1 \, \text{ft}} = 304.8 \, \frac{\text{mm}}{\text{ft}}$$

Applying this unit factor to convert a length value:

$$304.8 \, \frac{\text{mm}}{\text{ft}} \cdot b \, (\text{ft}) = b \cdot 304.8 \, (\text{mm})$$

Key Definitions

• Unit Factor: A ratio equal to 1 that expresses the relationship between two different units (e.g., $\frac{25.4 \, \text{mm}}{1 \, \text{in}} = 1$). It is derived by dividing both sides of a fundamental unit equivalence.
• Factor-Label Method: A systematic process for unit conversion that involves multiplying the original quantity by a sequence of unit factors. Units are treated algebraically, allowing unwanted dimensions to cancel out, leaving only the desired final unit.

References

• Original Source