Comprehensive Technical Conversion Factors and Unit Equivalencies Study Guide

Length Conversion Factors

Linear measurements are fundamental to physical sciences, bridging the Imperial and Metric systems. The primary length conversions involve the inch, foot, mile, and meter. Specifically, one inch is defined as $1\,\text{inch (in.)} = 2.54\,\text{cm}$. Larger Imperial units such as the foot and the mile are converted as follows: $1\,\text{foot (ft)} = 30.48\,\text{cm}$ and $1\,\text{mile (mi)} = 1.609\,\text{km}$. To convert from the metric base unit to Imperial, the relationship is established as $1\,\text{meter} = 39.37\,\text{in.}$

Mass and Weight Classification

Mass and weight conversions define the relationships between kilograms, pounds, and slugs across the SI and Imperial systems. The conversion for the kilogram is listed as $1\,\text{kilogram (kg)} = 2.2046\,\text{pounds (lb)}$ and simultaneously as $1\,\text{kilogram (kg)} = 0.06852\,\text{slug}$. The relationship for weight in grains or grams is noted as $1\,\text{lb} = 453.6\,\text{g}$. The slug, a unit of mass in the Imperial system, is quantified as $1\,\text{slug} = 32.174\,\text{lb}$.

Volume and Liquid Capacity Measure

Volumetric data covers a wide range of applications from liquid measurement to container capacity. The liter (alternatively transcribed as 1, I, or l) is defined as $1\,\text{liter} = 1000\,\text{cm}^3$. Other equivalents for the liter include $1\,\text{liter} = 1.057\,\text{quart (qt)}$, $1\,\text{liter} = 61.02\,\text{in}^3$, and $1\,\text{liter} = 0.03532\,\text{ft}^3$. Larger cubic volumes include the cubic meter: $1\,\text{cubic meter (m}^3) = 1000\,\text{l}$ and $1\,\text{cubic meter (m}^3) = 35.32\,\text{ft}^3$. The cubic foot is represented by several identities: $1\,\text{cubic foot (ft}^3) = 7.481\,\text{U.S. gal}$, $1\,\text{cubic foot (ft}^3) = 0.02832\,\text{m}^3$, and $1\,\text{cubic foot (ft}^3) = 28.32\,\text{l}$. The U.S. gallon is defined as $1\,\text{U.S. gallon (gal)} = 231\,\text{in}^3$ or $1\,\text{U.S. gallon (gal)} = 3.785\,\text{l}$.

Force and Gravitational Benchmarks

Force conversions involve the Newton ($\text{N}$), dyne, pound-force ($\text{lb}_f$), and poundals. One Newton is equivalent to $1\,\text{newton (N)} = 10^5\,\text{dynes}$, $1\,\text{newton (N)} = 0.1020\,\text{kg}_1$, $1\,\text{newton (N)} = 0.2248\,\text{lb}_f$, and $1\,\text{newton (N)} = 7.239\,\text{poundals}$. Pound weight ($\text{lb}$) is converted as $1\,\text{pound weight (lb)} = 4.448\,\text{N}$, $1\,\text{pound weight (lb)} = 0.4536\,\text{kg}_1$, and $1\,\text{pound weight (lb)} = 32.17\,\text{poundals}$. Additional measurements include $1\,\text{kilogram weight (kg)} = 2.205\,\text{lb}_f$ and an secondary entry for pound weight as $1\,\text{pound weight (lb.)} = 9.807\,\text{N}$. For heavy loads, the conversions are: $1\,\text{U.S. short ton} = 2000\,\text{lb}_1$, $1\,\text{long ton} = 2240\,\text{lb}$, and $1\,\text{metric ton} = 2205\,\text{lb}$.

Energy and Work Equivalencies

Energy is measured in Joules, ergs, foot-pounds, calories, and British thermal units. The Joule is defined as $1\,\text{Joule} = 1\,\text{Nm}$, with variations including $1\,\text{Joule} = 10^7\,\text{ergs}$, $1\,\text{Joule} = 0.7376\,\text{ft-lb}$, $1\,\text{Joule} = 0.2389\,\text{cal}$, and $1\,\text{Joule} = 9.481 \times 10^4\,\text{Btu}$. The foot-pound follows the relations $1\,\text{ft lb} = 1.356\,\text{joules}$, $1\,\text{ft lb} = 0.3239\,\text{cal}$, and $1\,\text{ft lb} = 1.285 \times 10^3\,\text{Btu}$. One calorie is given as $1\,\text{calorie (cal)} = 4.186\,\text{Joules}$, and also relates to Imperial units: $1\,\text{calorie (cal)} = 3.087\,\text{ft lb}_f$ and $1\,\text{calorie (cal)} = 3.968 \times 10^3\,\text{Btu}$. The British thermal unit relates to work and power-time as $1\,\text{Btu} = 778\,\text{ft lb}$, $1\,\text{Btu} = 1055\,\text{Joules}$, and $1\,\text{Btu} = 0.293\,\text{watt hour}$. Electrical energy units include the kilowatt hour as $1\,\text{kilowatt hour (kw hr)} = 3.60 \times 10^6\,\text{J}$, $1\,\text{kilowatt hour (kw hr)} = 860\,\text{kcal}$, and $1\,\text{kilowatt hour (kw hr)} = 3413\,\text{Btu}$. The electron volt for atomic energy is $1\,\text{electron volt (ev)} = 1.602 \times 10^{-19}\,\text{Joule}$.

Power and Rate of Work Standards

Power is the rate at which work is performed, primarily defined by the Watt ($\text{W}$) and Horsepower ($\text{hp}$). One Watt equals $1\,\text{watt} = 1\,\text{Joule/sec}$, $1\,\text{watt} = 10^7\,\text{ergs/sec}$, and $1\,\text{watt} = 0.2389\,\text{cal/sec}$. Mechanical power measured in horsepower is equal to $1\,\text{horsepower (hp)} = 550\,\text{ft lb/sec}$, $1\,\text{horsepower (hp)} = 33,000\,\text{ft lb/min}$, and $1\,\text{horsepower (hp)} = 745.7\,\text{watts}$. Kilowatt conversions are specified as $1\,\text{kilowatt (kw)} = 1.341\,\text{hp}$, $1\,\text{kilowatt (kw)} = 737.6\,\text{ft lb/sec}$, and $1\,\text{kilowatt (kw)} = 0.9483\,\text{Btu/sec}$.

Pressure and Stress Measurements

Pressure conversions describe force distributed over an area, utilizing Newtons per square meter, dynes per square centimeter, atmospheres, and pounds per square inch ($\text{lb/in}^2$ or $\text{psi}$). One Newton per square meter is $1\,\text{N/m}^2 = 10\,\text{dynes/cm}^2$, $1\,\text{N/m}^2 = 9.869 \times 10\%\,\text{atmosphere}$, and $1\,\text{N/m}^2 = 2.089 \times 10^{-2}\,\text{lb/ft}^2$. Pounds per square inch relate to other units as $1\,\text{lb/in}^2 = 6895\,\text{N/m}^2$, $1\,\text{lb/in}^2 = 5.171\,\text{cm mercury}$, and $1\,\text{lb/in}^2 = 27.68\,\text{in water}$. A full atmosphere ($\text{atm}$) is measured as $1\,\text{atmosphere (atm)} = 1.013 \times 10^5\,\text{N/m}^2$, $1\,\text{atmosphere (atm)} = 1.013 \times 10^6\,\text{dynes/cm}^2$, $1\,\text{atmosphere (atm)} = 14.70\,\text{lb/in}^2$, $1\,\text{atmosphere (atm)} = 76\,\text{cm mercury}$, and $1\,\text{atmosphere (atm)} = 406.8\,\text{in. water}$.