SI QUICK REFERENCE GUIDE: International System of Units (SI) The Modernized Metric System*
UNITS
The International System of Units (SI) is based on seven fundamental (base) units: Base Units
Quantity length mass time electric current thermodynamic temperature amount of substance luminous intensity Name metre kilogram second ampere kelvin mole candela Symbol m kg s A K mol cd
and a number of derived units which are combinations of base units and which may have special names and symbols: Examples of Derived Units
Quantity acceleration angular linear angle plane solid area Celsius temperature density heat flux mass current energy, enthalpy work, heat specific entropy heat capacity specific flow, mass flow, volume force frequency periodic rotating inductance magnetic flux mass flow moment of a force potential,electric power, radiant flux pressure, stress resistance, electric thermal conductivity velocity angular Expression Name Symbol
rad/s2 m/s2 dimensionless dimensionless m2 K W/m2 kg/m3 A/m2 N•m J/kg J/K J/(kg•K) kg/s m3/s kg•m/s2 1/s rev/s Wb/A V• s kg/s N•m W/A J/s N/m2 V/A W/(m•K) rad/s joule J radian steradian degree Celsius rad sr °C
newton hertz henry weber
N Hz H Wb
volt watt pascal ohm
V W Pa
linear viscosity dynamic (absolute)() kinematic () volume volume, specific
*For complete information see IEEE/ASTM SI-10.
m/s Pa•s m2/s m3 m3/kg
SYMBOLS
Symbol Name Quantity Formula
A ampere Bq becquerel C coulomb °C degree Celsius cd candela F farad Gy gray g gram H henry Hz hertz ha hectare* J joule K kelvin kg kilogram L litre lm lumen lx lux m metre mol mole N newton ohm Pa pascal rad radian (dimensionless) S siemens Sv sievert s second sr steradian (dimensionless) T tesla t tonne, metric ton Mg V volt W watt Wb weber *allowed with SI
electric current activity (of a radio nuclide) electric charge temperature interval luminous intensity electric capacitance absorbed dose mass inductance frequency area energy, work, heat temperature mass volume luminous flux illuminance length amount of substance force electric resistance pressure, stress plane angle electric conductance dose equivalent time solid angle magnetic flux density mass electric potential power, radiant flux magnetic flux
base unit 1/s A• s °C = K base unit C/V J/kg kg/1000 Wb/A 1/s 10 000 m2 N•m base unit base unit m3/1000 cd•sr lm/m2 base unit base unit kg•m/s2 V/A N/m2 m/m A/V J/kg base unit m2/m2 Wb/m2 1000 kg; W/A J/s V• s
Use of Symbols The correct use of symbols is important because an incorrect symbol may change the meaning of a quantity. Some SI symbols are listed in the Symbol table. SI has no abbreviations—only symbols. Therefore, no periods follow a symbol except at the end of a sentence. Examples: A, not amp; s, not sec; SI, not S.I. Symbols appear in lower case unless the unit name has been taken from a proper name. In this case the first letter of the symbol is capitalized. Examples: m, metre; Pa, pascal; W, watt
Exception: L, litre Symbols and prefixes are printed in upright (roman) type regardless of the type style in surrounding text. Example: . . . a distance of 73 km between . . . Unit symbols are the same whether singular or plural. Examples: 1 mm, 100 mm; 1 kg, 65 kg
Leave a space between the value and the symbol. Examples: 115 W, not 115W; 0.75 L, not 0.75L 88 °C, not 88°C or 88° C No space is left between the numerical value 73°, not 73 ° and symbol for degree of plane angle.
Exception: Examples:
Note: Symbol for coulomb is C; for degree Celsius it is °C Do not mix symbols and names in the same expression. Examples: radians per second or rad/s not radians/second; not radians/s m/s or metres per second, not metres/second; not metres/s J/kg or joules per kilogram, not joules/kilogram; not joules/kg
Symbol for product—use the raised dot ( • ) Examples: N•m; mPa•s; W/(m2•K)
Symbol for quotient—use one of the following forms: Examples: m/s or m or use negative exponent
Note: Use only one solidus ( / ) per expression and parentheses to avoid any ambiguity. Do not use modifying terms such as electrical, alternating current, etc. Examples: kPa (gage); MW (e); V (ac)
PREFIXES
Most prefixes indicate orders of magnitude in steps of 1000 and provide a convenient way to express large and small numbers and to eliminate nonsignificant digits and leading zeros in decimal fractions. Examples: 64 000 watts is the same as 64 kilowatts* 0.057 metre is the same as 57 millimetres 16 000 metres is the same as 16 kilometres* *except for intended accuracy
Prefix yotta Symbol Y Represents 1024
zetta exa peta tera giga mega kilo hecto deka deci centi milli micro nano pico femto atto zepto yocto
Z E P T G M k h* da* d* c* m n p f a z y
1021 1018 1015 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 10-21 10-24
To realize the full benefit of the prefixes when expressing a quantity by numerical value, choose a prefix so that the number lies between 0.1 and 1000. For simplicity, give preference to prefixes representing 1000 raised to an integral power (i.e., m, mm, km). *Exceptions: In expressing area and volume, the prefixes hecto, deka, (L), square hectometre (hectare), cubic centimetre. Tables of values of the same quantity. Comparison of values. For certain quantities in particular applications. For example, the millimetre is used for linear dimensions in architectural and engineering drawings even when the values lie far outside the range of 0.1 mm to 1000 mm; the centimetre is usually used for anatomical measurements and clothing sizes. Compound units. A compound unit is a derived unit expressed with two or more units. The prefix is attached to a unit in the numerator. Examples: V/m not mV/mm MJ/kg not kJ/g
deci, and centi may by required; for example, cubic
decimetre
Compound prefixes formed by a combination of two or more prefixes are not used. Use only one prefix. Examples: 2 nm not 2 mm 6 m3 not 6 kL 6 MPa not 6 kkPa
Exponential Powers. An exponent attached to a symbol containing a prefix indicates that the multiple (of the unit with its prefix) is raised to the power of 10 expressed by the exponent. Examples: 1 mm3 = (10-3 m)3 = 10-9 m3 1 ns-1 = (10-9 s)-1 = 109 s-1 1 mm2/s = (10-3 m)2/s = 10-6 m2/s
NUMBERS
International practice separates the digits of large numbers into groups of three, counting from the decimal to the left and to the right, and inserts a space to separate the groups. In numbers of four digits, the space is not necessary except for uniformity in tables. Examples: 6.358 568; 85 365; 51 845 953; 88 000; 0.246 113 562; 7 258
Small Numbers. When writing numbers less than one, always put a zero before the decimal marker. Example: 0.046 Decimal Marker. The recommended decimal marker is a dot on the line (period). (In some countries, a comma is used as the decimal marker.) Because billion means a million million in most countries but a thousand million in the United States, avoid using billion in technical writing.
DO’S AND DON’TS
The units in the international system of units are called SI units—not Metric Units and not SI Metric Units. Non-SI units in the US are called Inch-Pound units (I-P units)—not conventional units, not U.S. customary units, not English units, and not Imperial units.) Treat all spelled out names as nouns. Therefore, do not capitalize the first letter of a unit except at the beginning of a sentence or in capitalized material such as a title. Examples: Exception: watt; pascal; ampere; volt; newton; kelvin Always capitalize the first letter of Celsius.
Do not begin a sentence with a unit symbol—either rearrange the words or write the unit name in full. Use plurals for spelled out words when required by the rules of grammar. Examples: Irregular: metre—metres; henry—henries; kilogram—kilograms; kelvin—kelvins hertz—hertz; lux—lux; siemens—siemens
Do not put a space or hyphen between the prefix and unit name. Examples: kilometre not kilo metre or kilo-metre; milliwatt not milli watt or milli-watt
When a prefix ends with a vowel and the unit name begins with a vowel, retain and pronounce both vowels. Example: Exceptions: kiloampere hectare; kilohm; megohm
When compound units are formed by multiplication, leave a space between units that are multiplied. Examples: newton metre, not newton-metre; volt ampere, not volt-ampere
Use the modifier squared or cubed after the unit name.
Example: Exception: Example:
metre per second squared For area or volume the modifier may be placed square millimetre; cubic metre
before the units.
When compound units are formed by division, use the word per, not a solidus ( / ). Examples: metre per second, not metre/second; watt per square metre, not watt/square meter
Do not use modifying terms such as electrical, alternating current, etc. after the symbol. Examples: kPa (gage); MW (e); V (ac)
SELECTED CONVERSION FACTORS
CAUTION: These conversion values are rounded to three or four significant figures, which is sufficiently accurate for most applications. When making conversions, remember that a converted value is no more precise than the original value. Round off the final value to the same number of significant figures as those in the original value. See ANSI SI 10 for additional conversions with more significant figures. Multiply acre atmosphere, standard bar barrel (42 US gal, petroleum) Btu, (International Table) Btu/lb•°F (specific heat, cp) bushel calorie, kilogram (kilocalorie) candle, candlepower centipoise, dynamic vicosity, centistokes, kinematic viscosity, ft ft ft/min, fpm ft/s, fps ft of water ft2 ft2/s, kinematic viscosity, ft3 ft3 ft3/h, cfh ft3/min, cfm ft3/s, cfs footcandle ft•lbf (torque or moment) ft•lbf (work) ft•lbf/lb (specific energy) ft•lbf/min (power) gallon, US (*231 in3) gph gpm gpm/ft2 gr/gal horsepower (550 ft•lbf/s) inch in of mercury (60°F) in of water (60°F) in•lbf (torque or moment) in2 in3 (volume) in3 (section modulus) in4 (section moment) By 0.4047 *101.325 *100 159 1.055 4.184 0.03524 4.187 *1.0 *1.00 *1.00 *0.3048 *304.8 *0.00508 *0.3048 2.99 0.09290 92 900 28.32 0.02832 7.866 0.4719 28.32 10.76 1.36 1.36 2.99 0.0226 3.785 1.05 0.0631 0.6791 17.1 0.746 *25.4 3.377 248.8 113 645 16.4 16 400 416 200 To Obtain ha kPa kPa L kJ kJ/(kg•K) m3 kJ cd mPa•s mm2/s m mm m/s m/s kPa m2 mm2/s L m3 mL/s L/s L/s lx N•m J J/kg W L mL/s L/s L/(s•m2) g/m3 kW mm kPa Pa mN•m mm2 mL mm3 mm4
km/h kWh kip/in2 (ksi) litre micron (m) of mercury (60°F) mil (0.001 in.) mile mile, nautical mph mph millibar mm of mercury (60°F) mm of water (60°F) ounce (mass, avoirdupois) ounce (force of thrust) ounce (liquid, US) ounce (avoirdupois) per gallon pint (liquid, US) pound lbm (mass) lbm (mass) lbf (force or thrust) lbm/ft (uniform load) lbm/(ft•h) (dynamic viscosity, ) lbm/(ft•s) (dynamic viscosity, ) lbf•s/ft2 (dynamic viscosity, ) lbm/min lbm/h lbf/ft2 lbm/ft2 lbm/ft3 (density, ) lbm/gallon ppm (by mass) psi quad (1015 Btu) quart (liquid, US) rpm tablespoon (approx.) teaspoon (approx.) therm (100,000 Btu) ton, short (2000 lb) yd yd2 yd3
*Conversion factor is exact.
0.278 *3.60 6.895 *0.001 133 *25.4 1.61 1.85 1.61 0.447 *0.100 0.133 9.80 28.35 0.278 29.6 7.49 473 0.4536 453.6 4.45 1.49 0.413 1490 47 880 0.00756 0.126 47.9 4.88 16.0 120 *1.00 6.895 1.06 0.946 0.105 15 5 105.5 0.907 *0.9144 0.836 0.7646
m/s MJ MPa m3 mPa m km km km/h m/s kPa kPa Pa g N mL kg/m3 mL kg g N kg/m mPa•s mPa•s mPa•s kg/s g/s Pa kg/m2 kg/m3 kg/m3 mg/kg kPa EJ L rad/s mL mL MJ Mg; t (tonne) m m2 m3
Note: In this list the kelvin (K) expresses temperature intervals. The degree Celsius symbol (°C) may be used for this purpose as well.