Unit Conversion Cheatsheet

Cheatsheet Content

### Basic Conversions Unit conversion involves multiplying a quantity by one or more conversion factors. A conversion factor is a ratio of two equivalent measurements expressed in different units. 1. **Identify the given unit and the desired unit.** 2. **Find a conversion factor** that relates the given unit to the desired unit. If a direct conversion factor isn't available, use a series of factors. 3. **Set up the multiplication** so that the given unit cancels out, leaving the desired unit. **Common Prefixes (SI Units):** | Prefix | Symbol | Factor | |--------|--------|--------------| | Tera | T | $10^{12}$ | | Giga | G | $10^9$ | | Mega | M | $10^6$ | | Kilo | k | $10^3$ | | Hecto | h | $10^2$ | | Deka | da | $10^1$ | | Deci | d | $10^{-1}$ | | Centi | c | $10^{-2}$ | | Milli | m | $10^{-3}$ | | Micro | $\mu$ | $10^{-6}$ | | Nano | n | $10^{-9}$ | | Pico | p | $10^{-12}$ | **Example:** Convert 5 kilometers to meters. $$5 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} = 5000 \text{ m}$$ ### Area and Volume Conversions When converting units of area or volume, remember to apply the conversion factor for length the appropriate number of times. - **Area:** If $1 \text{ m} = 100 \text{ cm}$, then $1 \text{ m}^2 = (100 \text{ cm})^2 = 10000 \text{ cm}^2$. - **Volume:** If $1 \text{ m} = 100 \text{ cm}$, then $1 \text{ m}^3 = (100 \text{ cm})^3 = 1000000 \text{ cm}^3$. **Common Area/Volume Equivalents:** - $1 \text{ hectare (ha)} = 10^4 \text{ m}^2$ - $1 \text{ acre} \approx 4046.86 \text{ m}^2$ - $1 \text{ liter (L)} = 1 \text{ dm}^3 = 1000 \text{ cm}^3$ - $1 \text{ gallon (US)} \approx 3.785 \text{ L}$ **Example:** Convert 2 square meters to square centimeters. $$2 \text{ m}^2 \times \left(\frac{100 \text{ cm}}{1 \text{ m}}\right)^2 = 2 \text{ m}^2 \times \frac{10000 \text{ cm}^2}{1 \text{ m}^2} = 20000 \text{ cm}^2$$ ### Rate Conversions Rates involve two different units (e.g., speed, density). Convert each unit independently. **Example:** Convert 60 miles per hour to meters per second. Given: $1 \text{ mile} \approx 1609.34 \text{ m}$, $1 \text{ hour} = 3600 \text{ seconds}$. $$60 \frac{\text{miles}}{\text{hour}} \times \frac{1609.34 \text{ m}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ s}} \approx 26.82 \frac{\text{m}}{\text{s}}$$ ### Temperature Conversions Temperature conversions are not simple multiplicative factors. - **Celsius to Fahrenheit:** $F = C \times 1.8 + 32$ - **Fahrenheit to Celsius:** $C = (F - 32) / 1.8$ - **Celsius to Kelvin:** $K = C + 273.15$ - **Kelvin to Celsius:** $C = K - 273.15$ **Meaning:** - **Kelvin (K):** Absolute temperature scale, where 0 K is absolute zero (no molecular motion). Used extensively in scientific calculations, especially thermodynamics. A change of 1 K is equal to a change of 1 °C. - **Celsius (°C):** Based on the freezing (0 °C) and boiling (100 °C) points of water at standard atmospheric pressure. Widely used in most parts of the world. - **Fahrenheit (°F):** Based on a different set of reference points. Used primarily in the United States. A change of 1 °C is equivalent to a change of 1.8 °F. ### Energy Conversions Energy can appear in various forms (heat, work, electrical, chemical) and units. **Common Equivalents:** - $1 \text{ Joule (J)}$: SI unit of energy. The work done when a force of 1 Newton moves an object 1 meter. - $1 \text{ calorie (cal)} \approx 4.184 \text{ J}$: Energy needed to raise 1 gram of water by 1 °C. (Food calories, Cal, are actually kilocalories: $1 \text{ Cal} = 1000 \text{ cal}$). - $1 \text{ electron-volt (eV)} \approx 1.602 \times 10^{-19} \text{ J}$: The kinetic energy gained by an electron accelerating through an electric potential difference of 1 Volt. Used in atomic and particle physics. - $1 \text{ kilowatt-hour (kWh)} = 3.6 \times 10^6 \text{ J}$: A unit of energy representing one kilowatt of power sustained for one hour. Commonly used for billing of electrical energy. **Meaning:** - **Joule:** Fundamental unit of energy, work, or heat in the SI system. - **Calorie:** Historically defined based on water's thermal properties. Practical for chemistry and nutrition. - **Electron-volt:** Convenient for microscopic energy scales where Joules are too large. - **Kilowatt-hour:** Practical unit for large-scale energy consumption, e.g., household electricity. ### Pressure Conversions Pressure is force per unit area. **Common Equivalents:** - $1 \text{ Pascal (Pa)}$: SI unit of pressure. $1 \text{ Pa} = 1 \text{ N/m}^2$. - $1 \text{ atmosphere (atm)} = 101325 \text{ Pa} \approx 14.696 \text{ psi}$: Average atmospheric pressure at sea level. - $1 \text{ bar} = 10^5 \text{ Pa} \approx 0.9869 \text{ atm}$: A unit very close to 1 atmosphere. Commonly used in meteorology. - $1 \text{ torr} = 1 \text{ mmHg} \approx 133.322 \text{ Pa}$: Pressure exerted by a column of mercury 1 mm high. Used in vacuum measurements and blood pressure. - $1 \text{ pounds per square inch (psi)} \approx 6894.76 \text{ Pa}$: Used in the US for tire pressure, industrial pressure. **Meaning:** - **Pascal:** Derived SI unit, fundamental for scientific calculations. - **Atmosphere:** Useful for relating pressures to Earth's ambient conditions. - **Bar:** Convenient for expressing pressures slightly above or below atmospheric. - **Torr/mmHg:** Historically significant from barometer design, still used in specific fields. - **Psi:** Engineering unit in imperial system. ### Molar-Related Conversions In chemistry, the mole is a central unit for quantity of substance. **Key Concepts:** - **Mole (mol):** The amount of substance that contains as many elementary entities (atoms, molecules, ions, etc.) as there are atoms in 0.012 kilogram of carbon-12. This number is Avogadro's number ($N_A \approx 6.022 \times 10^{23}$). - **Molar Mass (g/mol):** The mass of one mole of a substance (numerically equal to its atomic/molecular weight in amu). - **Molarity (M or mol/L):** Moles of solute per liter of solution. - **Molality (m or mol/kg):** Moles of solute per kilogram of solvent. **Conversions:** - **Mass to Moles:** $n = \frac{\text{mass (g)}}{\text{Molar Mass (g/mol)}}$ - **Moles to Number of Particles:** $\text{Particles} = n \times N_A$ - **Molarity to Moles (given volume):** $\text{Moles} = \text{Molarity} \times \text{Volume (L)}$ **Meaning:** - **Mole:** Provides a bridge between the macroscopic mass of a substance and the microscopic number of particles. Essential for stoichiometry. - **Molar Mass:** Allows conversion between the mass of a substance and the number of moles. - **Molarity/Molality:** Express concentrations of solutions. Molarity is volume-dependent (changes with temperature), while molality is mass-dependent (temperature-independent), useful for colligative properties.