## 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.

## 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, Maths, etc.

We will try to understand the conversion of units in chemistry and physics through a numerical example:

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 (ex: kg to gram), first, we will check the number of smaller units needed to make one larger unit. Then multiply that number by the larger units.

Again to change a smaller unit to a larger unit (ex: gram to kg), divide it by the number of smaller units which we are needed to make 1 larger unit.

For example :

1 kg = 1000 gm = 10^{3} gm

1 gm = 10^{–3} kg

## 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,

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 ×= ML^{2}T^{–2}

So, 1 Joule = 1 kg. (1m)^{2} (1sec)^{–2}

1 erg = (1g) (1 cm)^{2} (1 sec)^{–2}

= 10^{3} × 10^{4} = 10^{7}

1 Joule = 10^{7} erg

## How to do conversion of units: Quick tables

### Conversion of units of “Pressure”

1 Psi = 6.89 kPa

1 Bar = 14.5 Psi = 100 kPa

1 Pa = 1 N/m^{2}

1 Psi = 6,891 Pa

1 Bar = 10^{5} N/m^{2} = 100 kpa1 atm

1 Tor = 1 mm of Hg 1 kPa

1 atm = 101.3 kPa = 760 mm of Hg = 14.70 Psi

### Conversion of units of “Weight”

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”

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 centimeter

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”

Celsius to Kelvin K = C + 273.15

Kelvin to Celcius C = K – 273.15

Fahrenheit to Celsius C = (F – 32) ×

Celcius to Fahrenheit F = C + 32

Fahrenheit to Kelvin K = (F – 32) × + 273.15

Kelvin to Fahrenheit F = (K – 273.15) × + 32

### Conversion of units of “Volume”

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 point = 2 cups = 473.176 milliliters = 473 milliliters

1 quart = 2 points = 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 points = 16 cups = 128 fluid ounces

1 ml = 1 cc = 10^{–6} m^{3}

### Conversion of units of “Time”

60 seconds = 1 minutes

3,600 seconds = 1 hour

86,400 seconds = 1 day

60 minutes = 1 hour

1,440 minutes = 1 day

24 hour = 1 day

168 hours = 1week

7 days = 1 week

30 days = one month

365 days = 1 year

4 weeks = 1 month

52 weeks = 1 year

12 months = 1 year

10 years = 1 decade

100 years = 1 century

1,000 years = 1 millennium

### Conversion of units of “Energy”

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 m^{3} natural gas = 31736 kJ = 7580 kcal = 8.816 kwh

1 kgoe = 41868 kJ = 1000 kcal = 1163 kwh

1000 J = 1000 W_{s} = 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 m^{3}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 = 10^{7 }erg

### Conversion of units of “Area”

1 m^{2} = 10.76 ft^{2}

1 ft^{2} = 929 cm^{2}

1 mi ^{2} = 640 acres

1 acre = 4046.85 m^{2}

1 acre = 100 m^{2} = 10 m ×10 m

1 (hectare) = 0.01 km^{2} = 10.000 m^{2}

1 hectare = 2.471 acre

1 km^{2} = 100 hectare = 10^{6} m^{2}

1 acre = 66 feet × 660 feet = 43560 ft^{2}

### Conversion of unit of “Mass”

1 kilogram = 0.0011 ton

1 kilogram = 2.2046 pounds(lb)

1 gram = 0.035 ounce

1 milligram = 0.000035 ounce

1 ounce = 28350 milligram

1 Pound = 0.454 kilogram

1 ton = 907.19 kilogram

1 amu = 1.6606 × 10^{24} grams

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Related: Significant figures

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