Units are standards for measurement of physical quantities that need clear definitions to be useful. Without them, measurements would not make sense.
For example, "the object weighs 170" is meaningless. Perhaps it is a paper box that weighs 170 grams. But it could also be metal cube that weighs 170 kilograms. A predetermined unit needs to be placed after the number to make the measurement meaningful.
Fundamental units
There are many possible systems of measurement that have been developed. In science, we use the International System of units (SI).
The fundamental or base units in SI are presented in the table below:
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Mass | Kilogram | kg |
| Length | Meter | m |
| Time | Second | s |
| Electric Current | Ampere | A |
| Amount of Substance | Mole | mol |
| Temperature | Kelvin | K |
| Luminous Intensity | Candela | cd |
Note: You do not need to memorize the formal scientific definitions of these units to apply them correctly.
3. Derived Units
All other measurements are Derived Units, created by combining the seven fundamental units.
Example — Speed: Speed is Distance ÷ Time. Therefore, the unit for speed is m/s or m · s-1.
Special Names: For convenience, common combinations are given unique names.
| SI Derived Unit | SI Base Equivalent | Alternative Form |
|---|---|---|
| Newton (N) | kg · m · s-2 | — |
| Pascal (Pa) | kg · m-1 · s-2 | N · m-2 |
| Watt (W) | kg · m2 · s-3 | J · s-1 |
| Ohm (Ω) | kg · m2 · s-3 · A-2 | V · A-1 |
4. SI Prefixes
Prefixes help manage very large or very small numbers. Use them to keep your data readable, but be careful when using them in calculations.
| Symbol | Prefix Name | Factor | Example |
|---|---|---|---|
| G | giga | 109 | Gigahertz (GHz) |
| M | mega | 106 | Megawatt (MW) |
| k | kilo | 103 | Kilometer (km) |
| m | milli | 10-3 | Milliliter (mL) |
| μ | micro | 10-6 | Microgram (μg) |
| n | nano | 10-9 | Nanometer (nm) |
5. Unit Conversions
Conversions are essential when measurements are given in a format different from the one required for a final answer.
Internal System Conversions
When converting area or volume, remember that the conversion factor must also be squared or cubed.
Example: A cube with a side length (a) of 1m:
- a = 1m = 100cm
- Surface Area (A): 6a2 = 6(100cm)2 = 60,000cm2
- Volume (V): a3 = (1m)3 = 1m3 = (100cm)3 = 1,000,000cm3
Inter-System & Specialty Conversions
1m3 = 1000L
1dm3 = 1L
1cm3 = 1mL
1 AU: ≈ 1.5 × 108 km
1 ly: ≈ 9.5 × 1012 km
1 pc: ≈ 3.1 × 1013 km
💡 Success Tips
- Track Your Units: Writing units throughout your calculations helps ensure your final result is logically correct.
- Use Ratios: Treat conversion factors as fractions (e.g., 1km / 1000m) to cancel out units easily.
- Calculator Use: Some calculators handle these automatically, but always verify if your specific model is allowed in your exam or competition.