1.4 Units of Measurement in Chemistry – SI Units

Temperature determines which way heat flows, density determines whether one liquid floats on another, and a single wrong unit can destroy an entire calculation. For students aiming at AP Chemistry, A-Level Chemistry, IB Chemistry HL, College Chemistry, and Olympiad exams, mastering the metric system and SI units is not memorization, it is the language you will use for every measurement from now on. This guide rebuilds that language from the ground up using the framework of The Central Science, so you will master base units, prefixes, length and mass, temperature conversions, derived units, volume relationships, and density with worked examples and exam-tested problem solving.

Key Insights

• SI units provide seven base units from which all other scientific units are derived.
• Metric prefixes scale base units by powers of ten and require exponential notation.
• Kelvin is the SI temperature unit and equals Celsius in size, with absolute zero at 0 K.
• Volume is a derived unit from length, with 1 L equal to 1 dm3 and 1 mL equal to 1 cm3.
• Density equals mass divided by volume and is temperature dependent and intensive.

Units of Measurement

Many properties of matter are quantitative, that is, associated with numbers. When a number represents a measured quantity, the units of that quantity must be specified. To say that the length of a pencil is 17.5 is meaningless. Expressing the number with its units, 17.5 centimeters, properly specifies the length. The units used for scientific measurements are those of the metric system.

The metric system, developed in France during the late eighteenth century, is used as the system of measurement in most countries. The United States has traditionally used the English system, although use of the metric system has become more common. Metric measurements are increasingly common in the United States, as exemplified by the volume printed on a soda can in both English units, fluid ounces, and metric units, milliliters.

The power of the metric system is its decimal nature. All larger and smaller units are powers of ten from a base unit, making conversions a matter of moving a decimal point rather than remembering arbitrary factors like 12 inches to a foot.

Callout Box: The Scientific Method - How Measurements Become Laws> Science does not begin with facts, it begins with observation and experiment. Scientists collect information, look for repeatable patterns and trends, formulate a tentative explanation called a hypothesis that proposes a mechanism and makes testable predictions, and then test it. If a hypothesis is sufficiently general and repeatedly effective at predicting future experiments, it becomes a theory, an explanation of the general causes of phenomena with considerable supporting evidence. Einstein's theory of relativity succeeded because it predicted new results that earlier theories could not explain. Even landmark theories are never said to be proven, because future data and better equipment may require modification. When many observations are tied together in a concise verbal statement or mathematical equation summarizing a wide variety of experiences, we have a scientific law. Laws do not make nature obey them, they describe how matter behaves.

SI Units

In 1960 an international agreement was reached specifying a particular choice of metric units for use in scientific measurements. These preferred units are called SI units, after the French Systeme International d'Unites. This system has seven base units from which all other units are derived. In this chapter we will consider the base units for length, mass, and temperature, but you should know the full set.

Physical Quantity	Name of Unit	Abbreviation
Mass	Kilogram	kg
Length	Meter	m
Time	Second	s or sec
Temperature	Kelvin	K
Amount of substance	Mole	mol
Electric current	Ampere	A or amp
Luminous intensity	Candela	cd

Seven SI base units displayed as realistic 3D objects on white background - kilogram cylinder weight, meter stick, stopwatch for second, thermometer for Kelvin, molecular models for mole, copper wire for Ampere, glowing bulb for candela

All other units in chemistry are derived from these seven by combining them mathematically. Speed, for example, is distance divided by time, so its SI unit is meters per second, m/s.

With SI units, prefixes are used to indicate decimal fractions or multiples of various units. For example, the prefix milli- represents a 10 to the minus 3 fraction, one-thousandth, of a unit. A milligram, mg, is 10 to the minus 3 gram, g, and a millimeter, mm, is 10 to the minus 3 meter, m.

Prefix	Abbreviation	Meaning	Example
Peta	P	10 to the 15	1 petawatt PW = 1 x 1015 watts
Tera	T	1012	1 terawatt TW = 1 x 1012 watts
Giga	G	109	1 gigawatt GW = 1 x 109 watts
Mega	M	106	1 megawatt MW = 1 x 106 watts
Kilo	k	103	1 kilowatt kW = 1 x 103 watts
Deci	d	10-1	1 deciwatt dW = 1 x 10-1 watt
Centi	c	10-2	1 centiwatt cW = 1 x 10-2 watt
Milli	m	10-3	1 milliwatt mW = 1 x 10-3 watt
Micro	µ	10-6	1 microwatt µW = 1 x 10-6 watt
Nano	n	10-9	1 nanowatt nW = 1 x 10-9 watt
Pico	p	10-12	1 picowatt pW = 1 x 10-12 watt
Femto	f	10-15	1 femtowatt fW = 1 x 10-15 watt
Atto	a	10-18	1 attowatt aW = 1 x 10-18 watt
Zepto	z	10-21	1 zeptowatt zW = 1 x 10-21 watt

The watt, W, is the SI unit of power, which is the rate at which energy is either generated or consumed. The SI unit of energy is the joule, J, where 1 J equals 1 kg times m squared per s squared and 1 W equals 1 J per s. The Greek letter mu, µ, is pronounced mew.

Although non-SI units are being phased out, some are still commonly used by scientists. Whenever we first encounter a non-SI unit, the SI unit will also be given. Relations between non-SI and SI units you will use most frequently appear on standard reference tables, and you will learn to convert between them using dimensional analysis.

Pro Tip for Exams:You must be comfortable with exponential notation. Which quantity is smallest: 1 mg, 1 µg, or 1 pg? Convert to grams: 1 mg = 10^-3 g, 1 µg = 10^-6 g, 1 pg = 10^-12 g. Therefore 1 pg is smallest by a factor of a million compared to 1 µg. AP and IB will hide this in unit conversion chains.

Exam Trap:The abbreviation for micro is µ, not m. Students frequently write m for both milli and micro, losing marks. Also, the kilogram is the only SI base unit whose name already contains a prefix, kilo, which is why we add prefixes to gram, not kilogram, to make milligram, microgram, etc.

Sample work with prefixes: What is the name of the unit that equals 10 to the minus 9 gram? Nanogram, ng. 10 to the minus 6 second? Microsecond, µs. 10 to the minus 3 meter? Millimeter, mm.

Practice in reverse: How many picometers are in one meter? 1 pm = 10^-12 m, so 1 m = 10¹² pm. Express 6.0 x 10³ m using a prefix: 6.0 km. Use exponential notation to express 4.22 mg in grams: 4.22 x 10^-3 g. Use decimal notation: 0.00422 g.

Length and Mass

The SI base unit of length is the meter, a distance slightly longer than a yard. Common laboratory lengths are centimeters and millimeters for small objects and kilometers for large distances.

Mass is a measure of the amount of material in an object. The SI base unit of mass is the kilogram, kg, which is equal to about 2.2 pounds. This base unit is unusual because it uses a prefix, kilo-, instead of the word gram alone. We obtain other units for mass by adding prefixes to the word gram.

Callout Box: Mass vs Weight - A Critical Distinction> Mass and weight are often incorrectly thought to be the same. The weight of an object is the force exerted on its mass by gravity. In space, where gravitational forces are very weak, an astronaut can be weightless, but he or she cannot be massless. The astronaut's mass in space is the same as it is on Earth. A balance measures mass, a spring scale measures weight. In chemistry, we always report mass, not weight.

Temperature

Temperature, a measure of the hotness or coldness of an object, is a physical property that determines the direction of heat flow. Heat flows spontaneously from a substance at higher temperature to one at lower temperature. Thus, we feel the influx of heat when we touch a hot object, and we know that the object is at a higher temperature than our hand.

The temperature scales commonly employed in science are the Celsius and Kelvin scales. The Celsius scale was originally based on the assignment of 0°C to the freezing point of water and 100°C to its boiling point at sea level.

The Kelvin scale is the SI temperature scale, and the SI unit of temperature is the kelvin, K. Zero on the Kelvin scale is the lowest attainable temperature, minus 273.15°C, referred to as absolute zero. The Celsius and Kelvin scales have equal-sized units, that is, a kelvin is the same size as a degree Celsius. Thus, the Kelvin and Celsius scales are related according to:

K = °C + 273.15

The freezing point of water, 0°C, is 273.15 K. Notice that we do not use a degree sign with temperatures on the Kelvin scale. We write 273 K, not 273°K.

The common temperature scale in the United States is the Fahrenheit scale, which is not generally used in science. Water freezes at 32°F and boils at 212°F. The Fahrenheit and Celsius scales are related according to:

°C = 5/9 (°F - 32) or °F = 9/5 (°C) + 32

Three realistic glass thermometers on white background showing Kelvin Celsius Fahrenheit scales aligned with water boiling, body temperature, and water freezing points marked

True or false: The size of a degree on the Celsius scale is the same as the size of a degree on the Kelvin scale. True, because both scales have 100 units between freezing and boiling of water, while Fahrenheit has 180 units for the same interval.

Worked example: A weather forecaster predicts the temperature will reach 31°C. What is this temperature in K and in °F?

Using K = °C + 273.15, we have K = 31 + 273 = 304 K. Using °F = 9/5 (°C) + 32, we have °F = 9/5 (31) + 32 = 56 + 32 = 88°F.

Ethylene glycol, the major ingredient in antifreeze, freezes at minus 11.5°C. What is the freezing point in K and °F? K = -11.5 + 273.15 = 261.7 K. °F = 9/5 (-11.5) + 32 = -20.7 + 32 = 11.3°F.

Pro Tip for Exams:For conversions between Kelvin and Celsius, use 273.15 for precise work, but many textbooks and AP problems approximate as 273. Always add, never multiply. A common error is writing K = °C x 273.15. Also, never put a degree symbol before K.

Exam Trap:Students forget that temperature differences are the same in Kelvin and Celsius, but not in Fahrenheit. A temperature change of 1°C equals a change of 1 K, but equals a change of 1.8°F. When a problem says temperature increases by 10°C, it also increases by 10 K.

Derived SI Units

The SI base units are used to obtain derived units. To do so, we use the defining equation for the quantity, substituting the appropriate base units. For example, speed is defined as the ratio of distance traveled to elapsed time. Thus, the SI unit for speed, m/s, read meters per second, is a derived unit, the SI unit for distance, length, m, divided by the SI unit for time, s. Two common derived units in chemistry are those for volume and density.

Volume

The volume of a cube is its length cubed, length to the third power. Thus, the derived SI unit of volume is the SI unit of length, m, raised to the third power. The cubic meter, m³, is the volume of a cube that is 1 m on each edge. Each cubic meter contains 1000 cubic decimeters. One liter is the same volume as one cubic decimeter, 1 L = 1 dm³. Each cubic decimeter contains 1000 cubic centimeters, 1 dm³ = 1000 cm³. One cubic centimeter equals one milliliter, 1 cm³ = 1 mL. Smaller units, such as cubic centimeters, sometimes written cc, are frequently used in chemistry.

Another volume unit used in chemistry is the liter, L, which equals a cubic decimeter, dm³, and is slightly larger than a quart. The liter is the first metric unit we have encountered that is not an SI unit. There are 1000 milliliters, mL, in a liter, and 1 mL is the same volume as 1 cm³: 1 mL = 1 cm³.

How many 1-L bottles are required to contain 1 m³ of liquid? Since 1 m³ = 1000 dm³ = 1000 L, you need 1000 bottles.

The devices used most frequently in chemistry to measure volume are graduated cylinders, syringes, burets, pipets, and volumetric flasks. Graduated cylinders, syringes, and burets deliver variable volumes, with burets using a stopcock, a valve to control liquid flow, for high precision. Syringes, burets, and pipets deliver amounts of liquids with more precision than graduated cylinders. Volumetric flasks are used to contain specific volumes of liquid. A pipet delivers a specific volume, while a volumetric flask contains a specific volume.

Volume relationships with large 1 cubic meter cube, medium 1 cubic decimeter cube equals 1 liter, small 1 cubic centimeter cube equals 1 milliliter, plus realistic volumetric glassware - graduated cylinder syringe buret pipet volumetric flask

Callout Box: Which Quantity Represents Volume?> Ask yourself about units. 15 m² is area, meters squared, not volume. 2.5 x 10² m³ is volume, meters cubed. 5.77 L/s is flow rate, volume per time, not volume alone. Only units with length cubed, L³, or liters count as volume.

Pro Tip for Exams:In the lab, never confuse delivers versus contains. A 10 mL pipet delivers 10.00 mL when you drain it, but a 100 mL volumetric flask contains 100.00 mL when filled to the mark. Using a flask to deliver will be inaccurate.

Density

Density is defined as the amount of mass in a unit volume of a substance:

Density = mass / volume

The densities of solids and liquids are commonly expressed in either grams per cubic centimeter, g/cm³, or grams per milliliter, g/mL, which are numerically identical because 1 cm³ = 1 mL. The density of water is 1.00 g/mL at near room temperature. It is no coincidence: the gram was originally defined as the mass of 1 mL of water at a specific temperature. Because most substances change volume when they are heated or cooled, densities are temperature dependent, and so temperature should be specified when reporting densities. If no temperature is reported, we assume 25°C, close to normal room temperature.

Substance	Density at 25°C (g/cm3)
Air	0.001
Balsa wood	0.16
Ethanol	0.79
Water	1.00
Ethylene glycol	1.09
Table sugar	1.59
Table salt	2.16
Iron	7.9
Gold	19.32

The terms density and weight are sometimes confused. A person who says that iron weighs more than air generally means that iron has a higher density than air. One kilogram of air has the same mass as one kilogram of iron, but the iron occupies a much smaller volume, thereby giving it a higher density. If we combine two liquids that do not mix, the less dense liquid will float on the denser liquid.

Density is an intensive property, excellent for identifying substances, and it connects mass and volume in problem solving. You can rearrange the equation to find any one variable if you know the other two: mass = density x volume, volume = mass / density.

Worked example: Calculate the density of mercury if 1.00 x 10² g occupies a volume of 7.36 cm³.

Density = mass / volume = 100 g / 7.36 cm³ = 13.6 g/cm³.

Calculate the volume of 65.0 g of liquid methanol, wood alcohol, if its density is 0.791 g/mL.

Volume = mass / density = 65.0 g / 0.791 g/mL = 82.2 mL.

What is the mass in grams of a cube of gold, density 19.32 g/cm³, if the length of the cube is 2.00 cm?

Volume of a cube is length cubed: Volume = (2.00 cm)³ = 8.00 cm³. Mass = volume x density = 8.00 cm³ x 19.32 g/cm³ = 155 g.

Pro Tip for Exams:Density problems are unit conversion problems in disguise. Always check that mass is in grams and volume in cm³ or mL before dividing. If volume is in liters, convert to mL by multiplying by 1000 first. On A-Level and AP, they often give density in g/cm³ and volume in dm³ to test conversion.

Exam Trap:Students think 1 kg of iron weighs more than 1 kg of feathers. Mass is same, density differs. Also, density of water is 1.00 g/mL only near 4°C, but we approximate as 1.00 at 25°C for general chemistry. For precise work, temperature matters.

Practice Questions

MCQs (Multiple Choice Questions)

01. Which of the following is an SI base unit?

1. Liter
2. Gram
3. Kilogram
4. Milliliter

Correct: C - Kilogram is the SI base unit for mass. Liter, gram, and milliliter are metric but not SI base units.

02. What does the prefix nano- represent?

1. 10^-3
2. 10^-6
3. 10^-9
4. 10^-12

Correct: C - Nano is 10^-9. Milli is 10^-3, micro is 10^-6, pico is 10^-12.

03. Which quantity is smallest: 1 mg, 1 µg, 1 pg?

1. 1 mg
2. 1 µg
3. 1 pg
4. They are equal

Correct: C - 1 pg = 10^-12 g, 1 µg = 10^-6 g, 1 mg = 10^-3 g. Picogram is smallest.

04. Convert 31°C to Kelvin.

1. 304 K
2. -242 K
3. 31 K
4. 88 K

Correct: A - K = °C + 273.15 ≈ 304 K.

05. Which temperature change is same size as 1 K increase?

1. 1°F increase
2. 1°C increase
3. 1.8°C increase
4. 273°C increase

Correct: B - Kelvin and Celsius degrees are same size.

06. How many milliliters are in 1 cubic meter?

1. 1000 mL
2. 1,000,000 mL
3. 100 mL
4. 1 mL

Correct: B - 1 m³ = 1000 L = 1,000,000 mL because 1 L = 1000 mL.

07. Which device delivers variable volumes with highest precision?

1. Graduated cylinder
2. Beaker
3. Buret
4. Volumetric flask

Correct: C - Buret with stopcock delivers variable volumes precisely. Flask contains specific volume.

08. Density is defined as:

1. Weight times volume
2. Mass divided by volume
3. Volume divided by mass
4. Mass times volume

Correct: B - Density = mass / volume.

09. A sample of copper has mass 374.5 g and volume 41.8 cm³. Its density is:

1. 8.96 g/cm³
2. 0.112 g/cm³
3. 15,654 g/cm³
4. 41.8 g/cm³

Correct: A - 374.5 / 41.8 = 8.96 g/cm³, matches known density of copper.

10. Which quantity represents a volume measurement?

1. 15 m²
2. 5.77 L/s
3. 2.5 x 10² m³
4. 9.8 m/s²

Correct: C - m³ is length cubed, a volume. m² is area, L/s is flow rate, m/s² is acceleration.

FRQs (Free Response Questions)

FRQ 1: SI Prefixes and Exponential Notation
A student measures a DNA strand as 2.5 x 10^-9 m long and a nanoparticle as 4500 pm diameter.
(a) Express DNA length in nanometers.
(b) Express nanoparticle diameter in nanometers and micrometers.
(c) Which is larger?

Rubric:

• (a) 1 nm = 10^-9 m, so 2.5 x 10^-9 m = 2.5 nm (2 pts)
• (b) 4500 pm = 4500 x 10^-12 m = 4.5 x 10^-9 m = 4.5 nm = 0.0045 µm (3 pts)
• (c) Nanoparticle 4.5 nm > 2.5 nm (1 pt)

FRQ 2: Temperature Conversion and Heat Flow
Ethylene glycol freezes at -11.5°C. Explain in terms of heat flow why it is used as antifreeze, and convert its freezing point to K and °F.

Rubric:

• Heat flows from higher to lower temperature, ethylene glycol mixture stays liquid at lower temperature than pure water, preventing engine freeze (2 pts)
• K = -11.5 + 273.15 = 261.7 K (2 pts)
• °F = 9/5(-11.5)+32 = 11.3°F (2 pts)

FRQ 3: Volume Relationships
Show using dimensional analysis that 1 L = 1000 cm³ and calculate how many 355 mL soda cans can be filled from 1 m³ of soda.

Rubric:

• 1 L = 1 dm³ = (10 cm)³ = 1000 cm³ (2 pts)
• 1 m³ = 1000 L = 1,000,000 mL (2 pts)
• Number cans = 1,000,000 / 355 = 2816 cans (2 pts)

FRQ 4: Density as Identification and Separation
You have two unlabeled liquids, ethanol density 0.79 g/cm³ and ethylene glycol 1.09 g/cm³. You have a sample mass 50.0 g and volume 63.3 mL. Identify liquid and explain how density determines layering if mixed with water.

Rubric:

• Density = 50.0 g / 63.3 mL = 0.790 g/cm³, matches ethanol (3 pts)
• Less dense floats on denser, ethanol 0.79 will float on water 1.00, ethylene glycol will sink slightly or mix (3 pts)

FRQ 5: Derived Units and Lab Equipment Choice
A lab requires 19.0 mL of ethanol for reaction. Student has graduated cylinder, buret, and volumetric pipet. Which should be used for most precise variable delivery and why? Calculate mass of 25.0 mL mercury density 13.6 g/mL.

Rubric:

• Buret most precise for variable volume because stopcock and fine graduations, pipet delivers fixed volume only, graduated cylinder least precise (3 pts)
• Mass = volume x density = 25.0 mL x 13.6 g/mL = 340 g (3 pts)

Frequently Asked Questions

What are the 7 SI base units in chemistry?

The seven SI base units are kilogram for mass, meter for length, second for time, kelvin for temperature, mole for amount, ampere for electric current, and candela for luminous intensity. All other units are derived from these.

What is the difference between mass and weight?

Mass measures amount of material and is constant, measured in kilograms. Weight is force of gravity on mass. An astronaut is weightless in space but retains same mass. Chemistry uses mass, not weight.

How do you convert Celsius to Kelvin?

Add 273.15 to Celsius degrees: K = °C + 273.15. Kelvin and Celsius degrees are same size, so a 1°C change equals 1 K change. Never use degree symbol with Kelvin.

How many mL in a cubic centimeter?

One milliliter equals one cubic centimeter exactly: 1 mL = 1 cm³. One liter equals one cubic decimeter: 1 L = 1 dm³ = 1000 cm³. One cubic meter equals 1000 liters.

Why is density temperature dependent?

Most substances expand when heated, increasing volume while mass stays same, so density decreases. That is why you should report temperature with density values, normally assumed 25°C if not stated.

Which is more precise for volume: graduated cylinder or buret?

A buret is more precise for variable volumes because it has a stopcock and finer markings. Syringes and pipets are also more precise than graduated cylinders. Volumetric flasks contain a specific volume, not deliver variable volumes.

What does the prefix micro mean?

Micro means 10 to the minus 6, one millionth. One microgram is 10^-6 gram and one micrometer is 10^-6 meter. Do not confuse micro symbol µ with milli m.

How do you calculate density from mass and volume?

Density equals mass divided by volume. Use grams for mass and cubic centimeters or milliliters for volume to get g/cm³ or g/mL. Rearranged, mass equals density times volume and volume equals mass divided by density.

Exam Mapping

Concept	A-Level Chemistry	AP Chemistry	IB Chemistry HL	College Chemistry 1	USNCO / IChO
SI Units and Base Units	3.1.2 Amount of substance, SI units	Unit 1 - Units and dimensional analysis	Topic 1.1 - SI units and fundamental quantities	Ch 1.4 - SI base units	Lab practical - SI units required
Metric Prefixes	3.1.1 Calculations with prefixes	Unit 1 - Prefix conversions, exponential notation	Topic 1.1 - Prefixes nano to giga	Ch 1.4 - Prefix table and conversions	Theory - prefix and scientific notation
Length and Mass vs Weight	Practical skills - mass measurement	Unit 1 - Mass vs weight distinction	Topic 1.2 - Mass measurement	Ch 1 - Mass vs weight explanation	Lab - proper use of balance
Temperature Scales	3.2.1 Enthalpy, temperature conversion	Unit 6 - Temperature and heat, K = °C + 273	Topic 5 - Temperature scales, absolute zero	Ch 1.4 - Celsius Kelvin Fahrenheit equations	Theory - absolute zero concept
Derived Units Volume	3.1.2 Ideal gas equation, cm3 and dm3	Unit 1 - Derived units, volume conversions	Topic 1.2 - Volume relationships	Ch 1.4 - Volume as length cubed	Theory - volume conversions
Density	3.1.2 Density calculations, identification	Unit 1 - Density as intensive property	Topic 1.1 - Density calculations	Ch 1.4 - Density = mass/volume	Lab - density identification of unknowns

Conclusion

You now control the measurement system that underpins all quantitative chemistry. You know the seven SI base units and why kilogram is the only base unit with a prefix in its name. You can fluently apply metric prefixes from zepto to peta using exponential notation, distinguish mass which is invariant from weight which depends on gravity, convert between Celsius, Kelvin, and Fahrenheit with the exact equations, derive volume from length with the critical relationships 1 L equals 1 dm³ equals 1000 cm³ and 1 mL equals 1 cm³, choose the correct volumetric glassware for variable versus fixed volumes, and use density as mass over volume to identify substances and predict whether one liquid will float on another. With these tools, every calculation in stoichiometry, gas laws, thermochemistry, and solutions becomes a unit conversion you can handle confidently on AP, A-Level, IB, and Olympiad papers.

References

• Chemistry: The Central Science by Brown, LeMay, Bursten, Murphy, Woodward, and Stoltzfus - Latest Edition - Section 1.4 Units of Measurement
• SI Brochure and NIST Reference on SI Units and Metric Prefixes for scientific measurement standards