Units and Conversions

Units

• Mass
  • SI Unit: grams ( $\text{m}$ )
  • Other
    • pounds ( avoirdupois ) ( $\text{lb}$ )
    • ounce ( avoirdupois ) ( $\text{oz}$ )
    • pounds ( apothecary ) ( $\text{℔}$ )
    • ounce ( apothecary ) ( $\text{℥}$ )
    • dram( $\text{ʒ}$ )
    • scruple ( $\text{℈}$ )
    • grain ( $\text{gr}$ )
• Volume
  • Derived
    • cubic centimeter ( $\text{cc}\text{or}{\text{cm}}^3$ )
  • SI Unit: liters ( $\text{L}$ )
  • Other
    • gallon ( $\text{gal}$ )
    • quart ( $\text{qt}$ )
    • pint ( $\text{pt}$ )
    • fluid ounce ( $\text{fl ℥}$ )
    • fluid dram ( $\text{fl ʒ}$ )
    • minim ( $\text{minim}$ )
• Length
  • SI Unit: meter ( $\text{m}$ )
  • Other
    • Inches ( $\text{in}\text{or}\prime \prime$ )
    • Foot ( $\text{ft}\text{or}\prime$ )
    • Yard ( $\text{yd}$ )
• Pressure
  • Derived
    • millimeter of mercury ( $\text{mmHg}$ )
    • newton per square meter ( $\text{N}/{\text{m}}^2$ )
    • pounds per square inch ( $\text{psi}\text{or}\text{lb}/{\text{in}}^2$ )
  • SI Unit: pascal ( $\text{Pa}$ )
  • Other
    • standard atmosphere ( $\text{atm}$ )
    • torr ( $\text{Torr}$ )
• Time
  • SI Unit: Seconds ( $\text{s}$ )
  • Other
    • Minutes ( $\text{m}$ )
    • Hours ( $\text{h}$ )
    • Days ( $\text{day}$ )
• Concentration
  • Derived Units
    • Molarity ( $\text{M}$ or $\text{n}/\text{L}$)

SI Units

SI units share a base10 system, which allows you to make sub-units to represent bigger or smaller values that would be a hassle to write in the base unit:

Example: milligrams are better for smaller vales.

$0.001\text{g}=1\text{mg}$

Example: kilograms are better for larger values.

$1000\text{g}=1\text{kg}$

Prefixes of SI Units

The sub-units are made of the base unit with a prefix depending on its power of 10.

Relation to Base	Prefix	Symbol
$10^{-21}\text{ of base unit}$	zepto-	$\text{z}$
$10^{-18}\text{ of base unit}$	atto-	$\text{a}$
$10^{-15}\text{ of base unit}$	femto-	$\text{f}$
$10^{-12}\text{ of base unit}$	pico-	$\text{p}$
$10^{-9}\text{ of base unit}$	nano-	$\text{n}$
$10^{-6}\text{ of base unit}$	micro-	$\mu$
$10^{-3}\text{ of base unit}$	milli-	$\text{m}$
$10^{-2}\text{ of base unit}$	centi-	$\text{c}$
$10^{-1}\text{ of base unit}$	deci-	$\text{d}$
$10\text{ of base unit}$	deka-	$\text{da}$
$10^2\text{ of base unit}$	hecto-	$\text{h}$
$10^3\text{ of base unit}$	kilo-	$\text{k}$
$10^6\text{ of base unit}$	mega-	$\text{M}$
$10^9\text{ of base unit}$	giga-	$\text{G}$
$10^{12}\text{ of base unit}$	tera-	$\text{T}$
$10^{15}\text{ of base unit}$	peta-	$\text{P}$
$10^{18}\text{ of base unit}$	exa-	$\text{E}$
$10^{21}\text{ of base unit}$	zetta-	$\text{Z}$

Derived Units

Derived units are units that are made from performing arithmetic operations on units of measurements. Derived units can be expressed as their

Conversion Factors

Simply multiply these factors to your given to get the desired converted value.

Note I: Conversion factors will only cover milli-units to kilo-units; the same rules apply for bigger and smaller units.

Note II: to do the reversed conversion, use a reciprocal of the conversion factor

Mass

• Grams to kilograms: $\left(\frac{1\text{kg}}{1000\text{g}}\right)$
• Grams to hectograms: $\left(\frac{1\text{hg}}{100\text{g}}\right)$
• Grams to dekagrams: $\left(\frac{1\text{dag}}{10\text{g}}\right)$
• Grams to decigrams: $\left(\frac{10\text{dg}}{1\text{g}}\right)$
• Grams to centigrams: $\left(\frac{100\text{cg}}{1\text{g}}\right)$
• Grams to milligrams: $\left(\frac{1000\text{mg}}{1\text{g}}\right)$
• Grams to grains: $\left(\frac{15.432\text{gr}}{1\text{g}}\right)$
• Grams to scruples: $\left(\frac{1\text{℈}}{1.3\text{g}}\right)$
• Grams to drams: $\left(\frac{1\text{ʒ}}{3.89\text{g}}\right)$
• Grams to ounces ( apothecary ): $\left(\frac{1\text{℥}}{31.1\text{g}}\right)$
• Grams to pounds ( apothecary ): $\left(\frac{1\text{℔}}{373\text{g}}\right)$
• Grams to ounces ( avoirdupois ): $\left(\frac{1\text{oz}}{28.35\text{g}}\right)$
• Grams to pounds ( avoirdupois ): $\left(\frac{1\text{lb}}{454\text{g}}\right)$

Volume

• Liters to kiloliters: $\left(\frac{1\text{kL}}{1000\text{L}}\right)$
• Liters to hectoliters: $\left(\frac{1\text{hL}}{100\text{L}}\right)$
• Liters to dekaliters: $\left(\frac{1\text{daL}}{10\text{L}}\right)$
• Liters to deciliters: $\left(\frac{10\text{dL}}{1\text{L}}\right)$
• Liters to centiliters: $\left(\frac{100\text{cL}}{1\text{L}}\right)$
• Liters to milliliters: $\left(\frac{1000\text{mL}}{1\text{L}}\right)$
• Liters to cubic centimeters: $\left(\frac{1000\text{cc}}{1\text{L}}\right)\text{or}\left(\frac{1000{\text{cm}}^2}{1\text{L}}\right)$
• Millilters to minim: $\left(\frac{16.23\text{min}}{1\text{mL}}\right)$
• Millilters to fluid dram: $\left(\frac{1\text{fl ʒ}}{3.69\text{mL}}\right)$
• Millilters to fluid ounce: $\left(\frac{1\text{fl ℥}}{29.57\text{mL}}\right)$
• Millilters to pints: $\left(\frac{1\text{pt}}{473\text{mL}}\right)$
• Millilters to quarts: $\left(\frac{1\text{qt}}{946\text{mL}}\right)$
• Millilters to gallons: $\left(\frac{1\text{gal}}{3785\text{mL}}\right)$

Length

• Meters to kilometers: $\left(\frac{1\text{km}}{1000\text{m}}\right)$
• Meters to hectometers: $\left(\frac{1\text{hm}}{100\text{m}}\right)$
• Meters to dekameters: $\left(\frac{1\text{dam}}{10\text{m}}\right)$
• Meters to decimeters: $\left(\frac{10\text{dc}}{1\text{m}}\right)$
• Meters to centimeters: $\left(\frac{100\text{cm}}{1\text{m}}\right)$
• Meters to millimeters: $\left(\frac{1000\text{mm}}{1\text{m}}\right)$
• Meters to inches: $\left(\frac{39.37\text{in}}{1\text{m}}\right)$
• Meters to foot: $\left(\frac{3.28\text{ft}}{1\text{m}}\right)$
• Meters to yard: $\left(\frac{1.09\text{yd}}{1\text{m}}\right)$
• Centimeters to inches: $\left(\frac{1\text{in}}{2.54\text{cm}}\right)$

Pressure

• Pascals to kilopascals: $\left(\frac{1\text{kPa}}{1000\text{Pa}}\right)$
• Pascals to hectopascals: $\left(\frac{1\text{hPa}}{100\text{Pa}}\right)$
• Pascals to dekapascals: $\left(\frac{1\text{daPa}}{10\text{Pa}}\right)$
• Pascals to decipascals: $\left(\frac{10\text{dPa}}{1\text{Pa}}\right)$
• Pascals to centipascals: $\left(\frac{100\text{cPa}}{1\text{Pa}}\right)$
• Pascals to millipascals: $\left(\frac{1000\text{mPa}}{1\text{Pa}}\right)$
• Pascals to torr: $\left(\frac{1\text{Torr}}{133.322\text{Pa}}\right)$
• Pascals to standard atmosphere: $\left(\frac{1\text{atm}}{101325\text{Pa}}\right)$
• Pascals to millimeters of mercury: $\left(\frac{1\text{mmHg}}{133.322\text{Pa}}\right)$
• Pascals to newtons per square meter: $\left(\frac{1\text{N}/{\text{m}}^2}{1\text{Pa}}\right)$
• Pascals to pounds per square inch: $\left(\frac{1\text{psi}}{6894.74\text{Pa}}\right)\text{or}\left(\frac{1\text{lbf}/{\text{in}}^2}{6894.74\text{Pa}}\right)$

Time

• Seconds to kiloseconds:
• Seconds to hectoseconds:
• Seconds to dekaseconds:
• Seconds to deciseconds:
• Seconds to centiseconds:
• Seconds to milliseconds:
• Seconds to minutes:
• Seconds to hours:
• Seconds to days:

Other Conversions

The contents of this section are units that are not convertible through conversion factors, ratios, or proportions.

Temperature

• Degrees fahrenheit to degrees celsius: $°\text{C}=(°\text{F}-32)\times \frac{5}{9}$
• Degrees celsius to degrees fahrenheit: $°\text{F}=\left(°\text{C}\times \frac{9}{5}\right)+32$
• Degrees celsius to kelvin: $K=°C+273.15$