SI Units and Conversions

Whenever a measurement is taken, a measurement system must be used. If you live in the United States, it is common to measure length in inches or feet. The units of inches and feet are part of the Imperial System of Measurement.

In many scientific disciplines, such as chemistry and physics, the system of measurement used is the SI system, which comes from the French Système international d’unités.

In this post, we will explore:

• The SI base units

• How SI prefixes are used

• Conversions between SI units

• Conversions between SI units and their imperial counterparts

• How to correctly set up and solve conversion problems using dimensional analysis

---

SI Base Units

Some fundamental SI units are listed below.

Physical Quantity	Name of Unit	Abbreviation
Mass	kilogram	kg
Length	meter	m
Time	second	s
Temperature	kelvin	K
Electric Current	ampere	A
Amount of Substance	mole	mol
Luminous Intensity	candela	cd
Volume	cubic meter	m3

Mass

Mass is the amount of matter in an object. Mass is different from weight, because it includes the effect of gravity on an object. On Earth, mass and weight are often treated as equivalent in everyday contexts, but scientifically, they are not the same.

The SI base unit for mass is the kilogram (kg). In many situations, especially in chemistry, grams (g) are more convenient. Always refer to the context or formula to determine which unit is appropriate.

Length

Length is the measured distance of an object. It is a one-dimensional quantity, meaning it is measured in only one direction. The SI base unit for length is the meter (m).

Time

Time measures duration or how long an event lasts. The SI base unit for time is the second (s). Minutes and hours are also commonly used, depending on the context.

Temperature

Temperature is a measure of the average kinetic energy of particles in a system. In everyday language, temperature describes how hot or cold something feels.

The SI base unit for temperature is the kelvin (K). In the United States, degrees Fahrenheit (°F) are commonly used, while degrees Celsius (°C) are often used in scientific contexts. When working with formulas, it is important to use the correct temperature unit required by the equation.

Electric Current

Electric current measures the rate of flow of electric charge. The SI base unit for electric current is the ampere (A), often shortened to amp.

Amount of Substance

The amount of substance measures the number of specified particles, such as atoms, molecules, ions, or electrons. The SI base unit is the mole (mol).

One mole contains exactly 6.02214076 × 10²³ particles, a value known as Avogadro’s number.

Luminous Intensity

Luminous intensity measures visible light emitted from a source as perceived by the human eye. It does not account for all electromagnetic radiation; it only accounts for visible light. The SI base unit is the candela (cd).

Volume

Volume measures the three-dimensional space occupied by matter. The SI unit for volume is the cubic meter (m³). In practice, volume is often measured in liters (L), especially in chemistry. Always check which unit is required when using formulas.

---

SI Prefixes

While SI base units are standard, they are not always the most practical for every measurement. SI prefixes are used to adjust units to a more convenient magnitude.

For example, while the meter is the base unit of length, it would be impractical to measure the length of an ant in meters. A smaller unit, such as millimeters, is more appropriate.

SI prefixes are placed before the base unit to indicate magnitude. The only exception is the kilogram, which already includes a prefix. When converting mass units, prefixes are applied to the gram.

Below are common SI prefixes used in introductory science courses.

Prefix	Symbol	Meaning	Exponential Notation
Tera	T	1,000,000,000,000	1012
Giga	G	1,000,000,000	109
Mega	M	1,000,000	106
Kilo	k	1,000	103
Hecto	h	100	102
Deka	da	10	101
Base Unit	—	1	100
Deci	d	0.1	10-1
Centi	c	0.01	10-2
Milli	m	0.001	10-3
Micro	µ	0.000001	10-6
Nano	n	0.000000001	10-9
Pico	p	0.000000000001	10-12

---

Using SI Prefixes

SI prefixes allow scientists to express measurements at appropriate scales.

For example, to measure the length of an ant, millimeters (mm) are more practical than meters.

• Prefix + unit: milli + meter = millimeter

• Symbol: m (milli) + m (meter) = mm

One millimeter equals 0.001 meters, or 10⁻³ meters.

The “meaning” and “exponential notation” columns are especially useful for creating conversion factors, also called unit equalities.

---

Conversion Factors

A conversion factor is a ratio that expresses the relationship between two units. Because conversion factors represent equal quantities, they can be written in multiple ways.

Examples:

• 1 mm = 0.001 m (10⁻³ m)

• 1 m = 1,000 mm (10³ mm)

• 1 km = 1,000 m (10³ m)

• 1 m = 0.001 km (10⁻³ km)

Conversion factors are the foundation of dimensional analysis.

Dimensional Analysis: Setting Up Conversions

Dimensional analysis is a problem-solving strategy that uses units to guide calculations. Units behave like algebraic variables: they can be multiplied, divided, and canceled.

If the same unit appears in both the numerator and denominator, it cancels out.

Dimensional Analysis Setup Rules

1. Write the given value and unit

2. Multiply by a conversion factor written as a fraction

3. Place the unit you want to eliminate in the denominator

4. Check that unwanted units cancel

5. Perform the math and write the final unit

If your units cancel correctly, your setup is correct, even before doing the math.

Example 1: Converting Kilograms to Grams

Convert 30 kg to grams

Conversion factor:

• 1 kg = 1,000 g

Set up the problem so kilograms cancel:

• 30 kg × (1,000 g / 1 kg)

The kilograms cancel, leaving grams:

• 30 kg × (1,000 g / 1 kg) = 30,000 g

Example 2: Multi-Step Conversion

Convert 250 cm to km

Step 1: Convert centimeters to meters

• 250 cm × (1 m / 100 cm) = 0.25 m

Step 2: Convert meters to kilometers

• 0.25 m x (1 km / 1,000 m) = 0.0025 km

Steps 1 and 2 can be combined to one dimensional analysis formula

• 250 cm × (1 m / 100 cm) × (1 km / 1,000 m)

Both centimeters and meters cancel, leaving kilometers:

• = 0.0025 km

---

Final Thoughts

Dimensional analysis is not about memorizing steps; it is about using units to think through a problem. When set up correctly, the units guide the solution and reduce errors.

Mastering SI units and conversions is a foundational skill that supports success in chemistry, physics, and other scientific disciplines.