The SI Guide

2.1 In SI, each physical quantity has only one unit. The base and derived units may be modified by prefixes as indicated in Section 4. All derived units are formed as combinations of base units linked by the algebraic relations connecting the quantities represented. The basic simplicity of the system can only be kept by adhering to the approved units.

2.2 Angle. The unit of plane angle is the radian. The degree and its decimal fractions may be used, but the minute and second should not be used.

2.3 Area. The unit of area is the square metre. Large areas are expressed in hectares (ha) or square kilometres (km²). The hectare is restricted to land or sea areas and equals 10 000 m².

2.4 Energy. The unit of energy, work, and quantity of heat is the joule (J). The kilowatthour (kWh) is presently allowed as an alternative in electrical applications, but should not be introduced in new applications.
1 kilowatthour (kWh) = 3.6 megajoules (MJ)
The unit of power and heat flow rate is the watt (W).
1 watt (W) = 1 joule per second (J/s)

2.5 Force. The unit of force is the newton (N). The newton is also used in derived units that include force.
Examples:
pressure or stress = N/m² = Pa (pascal)
work = N·m = J (joule)
power = N·m/s = W (watt)

2.6 Length. The unit of length is the metre. The millimetre is used on architectural or construction drawings and mechanical or shop drawings. The symbol mm does not need to be placed after each dimension; a note, “All dimensions in mm,” is sufficient.

The centimetre is used only for cloth, clothing sizes, and anatomical measurements. The metre is used for topographical and plot plans. It is always written with a decimal and three figures following the decimal (e.g., 38.560).

2.7 Mass. The unit of mass is the kilogram (kg). The unit of mass is the only unit whose name, for historical reasons, contains a prefix. Names of multiples of the unit mass are formed by attaching prefixes to the word gram. The megagram, Mg (1000 kg, metric ton or tonne, t), is the appropriate unit for describing large masses. Do not use the term weight when mass is intended.

2.8 Pressure. The unit of stress or pressure, force per unit area, is the newton per square metre. This unit is called the pascal (Pa). SI has no equivalent symbol for psig or psia. If a misinterpretation is likely, spell out Pa (absolute) or Pa (gage).

2.9 Volume. The unit of volume is the cubic metre. Smaller units are the litre, L (m³/1000); millilitre, mL; and microlitre, μL. No prefix other than m or μ is used with litre.

2.10 Temperature. The unit of thermodynamic (absolute) temperature is the Kelvin. Celsius temperature is measured in degrees Celsius. Temperature intervals may be measured in kelvins or degrees Celsius and are the same in either scale. Thermodynamic temperature is related to Celsius temperature as follows:
t_c = T – T₀

where
t_c= Celsius temperature, °C
T = thermodynamic temperature, kelvins (K)
T₀ = 273.15 K by definition

2.11 Time. The unit of time is the second, which should be used in technical calculations. However, where time relates to life customs or calendar cycles, the minute, hour, day, and other calendar units may be necessary.
Exception: Revolutions per minute may be used, but revolutions per second is preferred.

3.1 The correct use of symbols is important because an incorrect symbol may change the meaning of a quantity. Some SI symbols are listed in Table 3.

3.2 SI has no abbreviations—only symbols. Therefore, no periods follow a symbol except at the end of a sentence.
Examples: SI, not S.I.; s, not sec; A, not amp

3.3 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; W, watt; Pa, pascal
Exception: L, litre

3.4 Symbols and prefixes are printed in upright (roman) type regardless of the type style in surrounding text.
Example: . . . a distance of 56 km between . . .

3.5 Unit symbols are the same whether singular or plural.
Examples: 1 kg, 14 kg; 1 mm, 25 mm

3.6 Leave a space between the value and the symbol.
Examples: 55 mm, not 55mm; 100 W, not 100W
Exception: No space is left between the numerical value and symbol for degree Celsius and degree of plane angle (e.g., 20°C, not 20 °C or 20° C; 45°, not 45 °). Note: Symbol for degree Celsius is °C; for coulomb, C.

3.7 Do not mix symbols and names in the same expression.
Examples:
m/s or metres per second, not metres/second; not metres/s
J/kg or joules per kilogram, not joules/kilogram; not joules/kg

3.8 Symbol for product—use the raised dot (·).
Examples: N·m; mPa·s; W/(m² ·K)

3.9 Symbol for quotient—use a solidus (/) or a negative exponent. Note: Use only one solidus per expression.
Examples:
m/s; ms^-1
m/s² or (m/s)/s, not m/s/s
kJ/(kg·K) or (kJ/kg)/K, not kJ/kg/K

3.10     Place modifying terms such as electrical, alternating current, etc. parenthetically after the symbol with a space in between.
Examples:
MW (e), not MWe; not MW(e)
V (ac), not Vac; not V(ac)
kPa (gage), not kPa(gage); not kPa gage

4.1 Most prefixes indicate orders of magnitude in steps of 1000. Prefixes provide a convenient way to express large and small numbers and to eliminate nonsignificant digits and leading zeros in decimal fractions. Some prefixes are listed in Table 4.
Examples:
126 000 watts is the same as 126 kilowatts
0.045 metre is the same as 45 millimetres
65 000 metres is the same as 65 kilometres

4.2 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 (e.g., μm, mm, km).
Exceptions:

1. For area and volume, the prefixes hecto, deka, deci, and centi are sometimes used; for example, cubic decimetre (L), square hectometre (hectare), cubic centimetre.
2. Tables of values of the same quantity.
3. Comparison of values.
4. For certain quantities in particular applications. For example, the millimetre is used for linear dimensions in engineering drawings even when the values lie far outside the range of 0.1 mm to 1000 mm; the centimetre is usually used for body measurements and clothing sizes.

4.3 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
mN·m not N·mm (torque)
MJ/kg not kJ/g

4.4 Compound prefixes formed by a combination of two or more prefixes are not used. Use only one prefix.
Examples:
2 nm not 2 mmm
6 MPa not 6 kkPa

4.5 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

5.1 Large 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: 2.345 678; 73 846; 635 041; 600.000; 0.113 501; 7 258

5.2 Small Numbers. When writing numbers less than one, always put a zero before the decimal marker.
Example: 0.046

5.3 Decimal Marker. The recommended decimal marker is a dot on the line (period). (In some countries, a comma is used as the decimal marker.)

5.4 Billion. Because billion means a thousand million in the United States and a million million in most other countries, avoid using the term in technical writing.

5.5 Roman Numerals. Do not use M to indicate thousands (MBtu for a thousand Btu), nor MM to indicate millions, nor C to indicate hundreds; they conflict with SI prefixes.

6.1 The units in the international system of units are called SI units—not Metric Units and not SI Metric Units. (Inch-Pound units are called I-P units—not conventional units, not U.S. customary units, not English units, and not Imperial units.)

6.2 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: watt; pascal; ampere; volt; newton; kelvin
Exception: Always capitalize the first letter of Celsius.

6.3 Do not begin a sentence with a unit symbol—either rearrange the words or write the unit name in full.

6.4 Use plurals for spelled out words when required by the rules of grammar.
Examples: metre — metres; henry — henries; kilogram — kilograms; kelvin — kelvins
Irregular: hertz — hertz; lux — lux; siemens — siemens

6.5 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

6.6 When a prefix ends with a vowel and the unit name begins with a vowel, retain and pronounce both vowels.
Example: kiloampere
Exceptions: hectare; kilohm; megohm

6.7 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

6.8 Use the modifier squared or cubed after the unit name.
Example: metre per second squared
Exception: For area or volume, place the modifier before the units (e.g., square millimetre, cubic metre)

6.9 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 metre

7.1 Conversions are produced by multiplying the original value by a factor, then rounding so that it implies the same accuracy as in the original units. The same number of significant digits should be retained in the converted value. To convert a value, multiply it by the conversion factor (as found in Tables 6 and 7) and then round to the appropriate number of significant digits. For example, to convert 3 feet 6 7/8 inches to metres:
(3 ft · 0.3048 m/ft) + (6.875 in · 0.0254 m/in) = 1.089 025 m,
which rounds to 1.089 m.
When making conversions, remember that a converted value is no more precise than the original value. For many applications, rounding off the converted value to the same number of significant figures as those in the original value provides acceptable accuracy.

7.2 Significant digits are defined as those “necessary to define a numerical value of a quantity” (IEEE/ASTM 2011). Identification of significant digits requires a judgment based on the context of the original measurement or rounding. For example, a drawing notation of “4 ft above finished floor” is unlikely to require a converted SI value of 1.2192 m; a more reasonable value is 1.2 m or 1200 mm.

7.3 Substitutions define a new rational value for the measurement, using the original value as a guide in selecting a logical size in the alternative units.
Examples:
1. A 100 yard foot race converts to 91.44 m; however, a substitution of 100 m is made, for a more rational race distance.
2. A 12 in. pipe size converts to 305 mm. However, if a more logical SI pipe size is 300 mm, to match the size available where a project will be built, 300 mm would be a substitution.

7.4 Generally, for projects in which items from one system of units must fit together with those using another system, conversions should be used. Substitutions should be used when the entire item or system can be specified with the new, more logical value.

7.5 The terms conversion and substitution should be used to differentiate between direct conversions and the choice of a new size for a value. The terms hard conversion and soft conversion should not be used.

ASHRAE. 2013. Chapter 38, Units and conversions. In ASHRAE Handbook—Fundamentals.

IEEE/ASTM. 2011. American National Standard for Metric Practice. ANSI/IEEE/ ASTM SI 10™-2010. Institute of Electrical and Electronics Engineers, New York; ASTM International, West Conshohocken, PA.

© 2013 ASHRAE. All rights reserved.
ASHRAE® has compiled this publication with care, but ASHRAE has not investigated, and ASHRAE expressly disclaims any duty to investigate, any product, service, process, procedure, design, or the like that may be described herein. The appearance of any technical data or editorial material in this publication does not constitute endorsement, warranty, or guaranty by ASHRAE of any product, service, process, procedure, design, or the like. ASHRAE does not warrant that the information in this publication is free of errors. The entire risk of the use of any information in this publication is assumed by the user.

This guide is based in large part on ANSI/IEEE/ASTM SI 10™-2010, American National Standard for Metric Practice (IEEE/ASTM 2011). See ANSI/IEEE/ASTM SI 10™-2010 for more information and a complete list of conversion factors with more significant digits.