SI Units

SI Model

Familiarity with the elements and structure of the International System of Units (SI), commonly known as the metric system, will prepare students to successfully make measurements in science, technology, engineering and mathematics (STEM) applications. The major SI elements are illustrated in this model.

Defining Constants

The SI rests on a foundation of seven (7) defining constants: the cesium hyperfine splitting frequency, the speed of light in vacuum, the Planck constant, the elementary charge (i.e. the charge on a proton), the Boltzmann constant, the Avogadro constant, and the luminous efficacy of a specified monochromatic source. NIST provides values and a searchable bibliography for the fundamental physical constants. 

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Base and Derived Units

Definitions of all seven (7) SI base units are expressed using an explicit-constant formulation and experimentally realized using a specific mises en pratique (practical technique).

The SI is made up of 7 base units that define the 22 derived units with special names and symbols, which are illustrated in NIST SP 1247, SI Base Units Relationship Poster.  The SI plays an essential role in international commerce and is commonly used in scientific and technological research and development. Learn more about the SI in NIST SP 330 and SP 811.

The seven SI base units, which are comprised of:

• Length - meter (m)
• Time - second (s)
• Amount of substance - mole (mol)
• Electric current - ampere (A)
• Temperature - kelvin (K)
• Luminous intensity - candela (cd)
• Mass - kilogram (kg)

Together the base units and derived units with special names (twenty-nine units) form the core set of SI units. All other SI units are combinations of some of these twenty-nine units. Any of the base units and derived units with special names can be constructed directly from the seven defining constants. Derived units with generic names reflect their mathe­matical derivation, such as area (m²), volume (m³), velocity (m/s), and acceleration (m/s²).

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Prefixes

Twenty-four prefixes ranging from 10³⁰ to 10⁻³⁰, are currently recognized for use. Values of quantities are expressed using Arabic sym­bols for numbers paired with a unit symbol, often a prefix symbol that modifies unit magni­tude. 

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Writing with the SI

A benefit of the International System of Units (SI) is that written technical information is effectively communicated, overcoming the variations of language, including spelling and pronunciation. Values of quantities are expressed using Arabic symbols for numbers paired with a unit symbol, often with a prefix symbol that modifies unit magnitude. Learn more about Writing with SI.

Scientists, Technologists, Engineers, and Mathematicians write with the SI. SI writing style is an essential literacy skill used by STEM professionals and the public to interpret, evaluate, synthesize, communicate, and apply measurement information. For STEM profession­als, SI skills are necessary to plan investigations, collect and document research data observations, analyze results, clearly communicate, share research, gain new information by interpreting the findings of others, develop technological solutions to improve the quality of life, design and build critical infrastructure, and develop new products for the marketplace. Using SI writing style helps prevent miscommunication, misinterpretation of data, and calculation errors. SI writing style is also important for consumers who will interpret and use quantities to make daily life decisions.

The International System of Units (SI), commonly known as the metric system, is the international standard for measurement. The International Treaty of the Meter was signed in Paris on May 20, 1875 by seventeen countries, including the United States and is now celebrated around the globe as World Metrology Day. NIST provides official U.S. representation in the various international bodies established by the Meter Convention: CGPM - General Conference on Weights and Measures; CIPM - International Committee for Weights and Measures; and BIPM - The International Bureau of Weights and Measures.

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Useful Definitions

• A quantity in the general sense is a property ascribed to phenomena, bodies, or substances that can be quantified for, or assigned to, a particular phenomenon, body, or substance. Examples are mass and electric charge.
• A quantity in the particular sense is a quantifiable or assignable property ascribed to a particular phenomenon, body, or substance. Examples are the mass of the moon and the electric charge of the proton.
• A physical quantity is a quantity that can be used in the mathematical equations of science and technology.
• A unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value.
• The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed.
• Example: the value of the height h_W of the Washington Monument is h_W = 169 m. Here h_W is the physical quantity, its value expressed in the unit "meter," unit symbol m, is 169 m, and its numerical value when expressed in meters is 169.

Resources for Students and Teachers

• Metric Estimation Game (SP 1336) - This fun, hands-on activity helps participants become familiar with SI measurements by practicing estimation skills. During this activity, participants will become familiar with using the metric system (International System of Units, SI) measurements on common, everyday items.
• SI Units Card Deck (SP 1297) – This activity offers a fun way to enhance understanding of the International System of Units, including the defining constants, base units, derived units with special names, and prefixes. (NIST)
• SI Base Units Relationships Poster (SP 1247) – A colorful poster illustrating the relationships of the International System of Units (SI) derived units with special names and symbols and the seven traditional base units. (NIST)
• Redefining the SI – In November 2018, the world’s measurement experts voted and unanimously approved a revision of the SI that establishes a measurement system entirely based on physical constants of nature. The changes became effective on World Metrology Day, May 20, 2019. (NIST)
• Learn more about the Road to the Revised SI.
• Learn more about the SI Redefinition. (NIST)
• The Last Artifact documentary and companion Grade 5 to 12 educational resources, which document the work that went on behind the scenes to modernize the International System of Units (SI). (Montana PBS)
• Metric Trivia Quiz – How much do you know about the metric system (SI)? Try the NIST Metric Trivia Quiz online or use the Alexa skill to test your knowledge and be on your way to thinking metric! (NIST)
• SI Education and Training – Explore NIST metric system education resources that build SI measurement system familiarity and fluency. (NIST)
• Kids Education Resources. (NIST)
• Top 10 Tips for Teaching the Metric System. (NIST Taking Measure Blog)
• Busting Myths about the Metric System. (NIST Taking Measure Blog)

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