Conversion of Units Explained: Methods, Formulas, and Quick Reference Tables
- Unit conversion uses multiplicative factors to express the same quantity in different units.
- Dimensional analysis is a reliable method for converting between unit systems like SI and CGS.
- To convert larger units to smaller, multiply; to convert smaller to larger, divide.
- Pressure, temperature, energy, and length each have distinct conversion formulas and factors.
What is a Conversion of Units?
Conversion of units is the conversion between different units of measurements for the same physical quantity primarily through multiplicative conversion factors. Unit conversion is a foundational skill in thermodynamics, physics, chemistry, and engineering, where quantities must be expressed consistently across different measurement systems.
What is the Purpose of a Unit Conversion?
A unit conversion represents the same property as a different unit of measurement.
For example, length can be expressed in centimetres instead of meters. A conversion factor is a numeric expression that enables a centimetre to be changed to a meter.
Ex: Anyone wants to know how many seconds are in 2 hours and 20 minutes.
Ans. We will change 2 hours and 20 minutes to the same units.
We can write 2 hours as:
2 hour = 2 × 60 minutes = 2 × 60 × 60 sec.
⇒ 2 hour = 7200 sec.
and 20 minutes = 20 × 60 sec = 1200 sec.
Hence, 2 hours 20 minutes = (7200 + 1200) sec = 8400 sec.
Conversion of Units in Chemistry, Physics, and Maths
We will try to understand the conversion of units in chemistry and physics through a numerical example. Problems in fluid mechanics and related engineering disciplines regularly require switching between unit systems, making this skill essential.
Suppose an HCl molecule has a dipole moment of 3.4 × 10–30 C.m. Assuming that equal and opposite charges lie on the two atoms to form a dipole. What is the magnitude of this charge? The separation between two atoms of HCl is 1Å.
Here in the above example, the separation between two atoms is in angstrom. We can convert angstrom into the meter as:
1Å = 10–10 m.
So, we can write:
P = qd ⇒ 3.4 × 10–30 = q × 10–10
q = 3.4 × 10–20 coulomb
In mathematics, to change a larger unit to a smaller unit (e.g. kg to gram), first check the number of smaller units needed to make one larger unit. Then multiply that number by the larger units.
To change a smaller unit to a larger unit (e.g. gram to kg), divide it by the number of smaller units needed to make 1 larger unit.
For example:
1 kg = 1000 gm = 103 gm
1 gm = 10–3 kg
Students working through transport phenomena — momentum, heat, and mass problems will encounter these conversions frequently when reconciling SI and CGS values.
How to Do Conversion of Units: Step by Step
Starting with a simple example: convert 2 km into meters. For this purpose, we will follow a system.
- Express the conversion as a fraction that equals 1.
- Multiplying it out (learning all units in the answer.)
- Cancel any units that are both numerator side and denominator side.
Example: Convert 1 km/hour to meter/sec.
We can write:
$1frac{{km}}{h} = frac{{1,km}}{h} times frac{{1000,m}}{{1,km}} times frac{{1,h}}{{3600,sec }}$
$Rightarrow 1frac{{km}}{h} = frac{{1000}}{{3600}}frac{m}{sec}$
$1frac{{km}}{h} = frac{5}{{18}},m/s$
We can also convert units with the help of dimensional analysis.
Example: The SI and CGS units of energy are joule and erg, respectively. How many ergs are equal to 1 joule?
Ans. Dimensionally, Energy = mass × (velocity)2 = mass × ${left( {frac{{length}}{{time}}} right)^2}$ = ML2T–2
So, 1 Joule = 1 kg. (1m)2 (1sec)–2
1 erg = (1g) (1 cm)2 (1 sec)–2
$frac{{1,Joule}}{{1,erg}} = left( {frac{{1,kg}}{{1,g}}} right){left( {frac{{1,m}}{{1,cm}}} right)^2}{left( {frac{{1,sec }}{{1,sec }}} right)^{-2}} = left( {frac{{1000,g}}{g}} right){left( {frac{{100,cm}}{{cm}}} right)^2}$
= 103 × 104 = 107
1 Joule = 107 erg
Dimensional analysis is also widely applied in computer science contexts, such as when converting data storage units or timing values in algorithm analysis. Understanding the underlying method — not just the tables — is what allows students to handle unfamiliar conversions confidently.
How to Do Conversion of Units: Quick Tables
Conversion of Units of Pressure
| Unit | Equivalent |
|---|---|
| 1 Psi | 6.89 kPa |
| 1 Bar | 14.5 Psi = 100 kPa |
| 1 Pa | 1 N/m2 |
| 1 Psi | 6,891 Pa |
| 1 Bar | 105 N/m2 = 100 kPa |
| 1 Torr | 1 mm of Hg |
| 1 atm | 101.3 kPa = 760 mm of Hg = 14.70 Psi |
Conversion of Units of Weight
| Unit | Equivalent |
|---|---|
| 1 ounce (Oz) | 28.35 gm |
| 1 pound (lb) | 453.592 gm |
| 1 kilogram (kg) | 1000 gm |
| 1 ton metric (t) | 2204.623 pound |
| 1 ton | 0.907 metric ton |
Conversion of Units of Length
| Unit | Equivalent |
|---|---|
| 1 centimeter | 10 millimeters |
| 1 meter | 100 cm |
| 1 kilometer | 1000 meter |
| 1 foot | 12 inch |
| 1 yard | 3 feet |
| 1 mile | 1760 yards |
| 1 inch | 2.54 centimeters |
| 1 foot | 30.48 centimeters |
| 1 yard | 91.44 centimeters |
| 1 mile | 1609.344 meters |
| 1 mile | 1.609344 kilometers |
| 1 Å | 10–10 meter |
Conversion of Units of Temperature
| Conversion | Formula |
|---|---|
| Celsius to Kelvin | K = C + 273.15 |
| Kelvin to Celsius | C = K – 273.15 |
| Fahrenheit to Celsius | C = (F – 32) × 5/9 |
| Celsius to Fahrenheit | F = C × (9/5) + 32 |
| Fahrenheit to Kelvin | K = (F – 32) × 5/9 + 273.15 |
| Kelvin to Fahrenheit | F = (K – 273.15) × 9/5 + 32 |
Conversion of Units of Volume
| Unit | Equivalent |
|---|---|
| 1 tablespoon | 2 teaspoons = 14.78677 milliliters ≈ 15 milliliters |
| 1 fluid ounce | 2 tablespoons = 29.573 milliliters ≈ 30 milliliters |
| 1 cup | 8 fluid ounces = 236.588 milliliters ≈ 237 milliliters |
| 1 pint | 2 cups = 473.176 milliliters ≈ 473 milliliters |
| 1 quart | 2 pints = 946.352 milliliters ≈ 946 milliliters |
| 1 gallon | 4 quarts = 3.7854 liters ≈ 3.8 liters |
| 1 gallon | 128 fluid ounces = 3.7854 liters ≈ 3.8 liters |
| 1 gallon | 4 quarts = 8 pints = 16 cups = 128 fluid ounces |
| 1 ml | 1 cc = 10–6 m3 |
Conversion of Units of Time
| Unit | Equivalent |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 3,600 seconds |
| 1 day | 86,400 seconds |
| 1 hour | 60 minutes |
| 1 day | 1,440 minutes |
| 1 day | 24 hours |
| 1 week | 168 hours |
| 1 week | 7 days |
| 1 month | 30 days |
| 1 year | 365 days |
| 1 month | 4 weeks |
| 1 year | 52 weeks |
| 1 year | 12 months |
| 1 decade | 10 years |
| 1 century | 100 years |
| 1 millennium | 1,000 years |
Conversion of Units of Energy
| Unit | Equivalent |
|---|---|
| 1 kJ | 0.2388 kcal = 0.000278 kWh |
| 1 kcal | 4.1868 kJ = 0.001163 kWh |
| 1 kWh | 3600 kJ = 860 kcal |
| 1 kg SKE | 29308 kJ = 7000 kcal = 814 kWh |
| 1 m3 natural gas | 31736 kJ = 7580 kcal = 8.816 kWh |
| 1 kgoe | 41868 kJ = 1000 kcal = 1163 kWh |
| 1000 J | 1000 Ws = 1 kJ |
| 1000 cal | 1 kcal = 4186 kJ |
| 1 Wh | 3.6 kJ |
| 1 kg SKE | 29308 kJ |
| 1 kg ROE | 41868 kJ |
| 1 (kg) oe | 41868 kJ |
| 1 m3 Erdgas | 31736 kJ |
| 1 BTU | 0.000293071 kWh = 1.05506 kJ |
| 1 kpm | 2.72 × 10–6 kWh = 0.00980665 kJ |
| 1 erg | 2.78 × 10–14 kWh = 1 × 10–10 kJ |
| 1 eV | 1.60217733 × 10–19 J = 1.60217733 × 10–22 kJ |
| 1 J | 107 erg |
Conversion of Units of Area
| Unit | Equivalent |
|---|---|
| 1 m2 | 10.76 ft2 |
| 1 ft2 | 929 cm2 |
| 1 mi2 | 640 acres |
| 1 acre | 4046.85 m2 |
| 1 are | 100 m2 = 10 m × 10 m |
| 1 hectare | 0.01 km2 = 10,000 m2 |
| 1 hectare | 2.471 acres |
| 1 km2 | 100 hectares = 106 m2 |
| 1 acre | 66 feet × 660 feet = 43,560 ft2 |
Conversion of Units of Mass
| Unit | Equivalent |
|---|---|
| 1 kilogram | 0.0011 ton |
| 1 kilogram | 2.2046 pounds (lb) |
| 1 gram | 0.035 ounce |
| 1 milligram | 0.000035 ounce |
| 1 ounce | 28350 milligrams |
| 1 pound | 0.454 kilogram |
| 1 ton | 907.19 kilogram |
| 1 amu | 1.6606 × 1024 grams |
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Trigonometry is another area where unit conversion matters — angles can be expressed in degrees or radians, and knowing how to switch between them is essential. Students who need support with angle-based calculations can work with an online trigonometry tutor to build that fluency.
Related: Significant figures | Mastering Physics homework help | Physics Homework Help | Physics Tutor Online
For students navigating interdisciplinary coursework, understanding how unit conversion connects to broader academic skills can be valuable. See how mechatronics education addresses multi-domain engineering challenges for a practical example of how measurement systems interact across fields.
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