 # Volume Conversions Chemistry Tutorial

## Key Concepts

• The unit of volume derived from SI units(1) is the cubic meter, m3.
• Chemists in a laboratory usually deal with much smaller volumes than cubic meters and the metric but non-SI units of liter or litre (L) and milliliter or millilitre (mL or ml) are in common use.
• In 1964 the litre was redefined as being equal to exactly 1 cubic decimetre:
1 L = 1 dm3

So 1 milliltre = 1 cubic centimetre

1 mL = 1 cm3 (= 1cc)

• Other metric units of measuring volume are given in the table below:

   name symbol volume (L) large volume → → → → → → → → → → small volume teralitre gigalitre megalitre kilolitre hectolitre decalitre decilitre centilitre millilitre microlitre nanolitre picolitre femtolitre attolitre TL GL ML kL hL daL dL cL mL µL nL pL fL aL 1012 L 109 L 106 L 103 L 102 L 101 L 10-1 L 10-2 L 10-3 L 10-6 L 10-9 L 10-12 L 10-15 L 10-18 L

• Non-metric units of volume can still be found in use around the world, for example, gallons of gas in the USA and a pint of beer in the UK.

Conversion factors for some US units are given below:

1 US liquid gallon = 231 cubic inches = 3.785411784 L

1 US fluid ounce = 1/128 US gallon = 0.0295735295625 L = 29.5735295625 mL

1 US pint = 1/8 US gallon = 16 US fluid ounces = 473.1764729984 mL

1 US quart = 1/4 US gallon = 32 US fluid ounces = 946.3529459968 mL

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## Converting Metric and SI Units of Volume

Litres (L) and millilitres (mL) are common units for measuring volume in many countries that have adopted the metric system such as Australia.
For example you can buy 1 litre (1 L) of milk or 2 litres (2 L) of milk to take home and put in the fridge. But if you want a drink right now you will buy a smaller amount, for example a 375 millilitre (375 mL) bottle or a 250 millilitre (250 mL) popper of juice. Clearly 1 millilitre (1 mL) is a much smaller volume than 1 litre (1 L).

The prefix "milli" refers to a thousandth (1/1000) and is given the symbol m.
1 millilitre (1 mL) is therefore one thousandth of a litre (L).
1 mL = 1/1000 L
If we divide 1 by 1000 we can convert the fraction (1/1000) to a decimal:
1 mL = 0.001 L
and we can express the decimal number in scientific notation:
1 mL = 1 × 10-3 L

So, if we want to convert the volume of our 375 mL bottle of juice to a volume in litres
we know that 1 mL = 1/1000 L
so 375 mL = 375 × 1 mL = 375 × 1/1000 L
and 375 × 1/1000 L = 375 × 0.001 L = 0.375 L
which we can express in scientific notation as 375 × 10-3 L = 3.75 × 10-1 L

If you look around at the glassware in the laboratory designed to contain liquids and solutions you will find small pieces labelled in milliltres (mL) and large pieces labelled in litres (L).
For example you might see 10 mL, 50 mL, 100 mL, 250 mL and 500 mL beakers, and a big 1 L beaker. Small volumetric flasks might be 25 mL, 50 mL and 100 mL, larger flasks are 250 mL and 500 mL, but the biggest flask is probably 1 L.

When you make up a solution in the laboratory you will probably measure the volume in milliltres (mL), but when you perform calculations you will probably need to convert those volumes in mL to volumes in litres (L).
The reverse is also true, you might calculate a volume of solution needed in litres (L) but you will need to use glassware graduated in milliltres (mL) to measure out the volume in the lab.

Let's say you need to measure out 0.018 L of water using a measuring cylinder that is graduated in milliltres (mL).
How many milliltres are in 0.018 L ?
we know that 1 mL = 1/1000 L
so if we multiply both sides of the equation by 1000 to clear the fraction we arrive at:
1000 × 1 mL = 1000 × 1/1000 L
so 1000 mL = 1 L
which is the same as writing 1 L = 1000 mL
Multiply both sides of the equation by 0.018 gives us:
0.018 × 1 L = 0.018 × 1000 mL
0.018 L = 18 mL
and now we can use the graduated measuring cylinder to get a volume of 18 mL (or 0.018 L) of water for our experiment.

Other prefixes before "litres" you might encounter are:

• micro (μ) = 1/1000000 ( 1 millionth)
• deci (d) = 1/10 (1 tenth)
• kilo (k) = 1000
• mega (M) = 1 000 000
• giga (G) = 1 000 000 000

Water stored in dams is often reported in units of gigalitres (GL), billions of litres.
A liquid active ingredient in a medicine, however, might be given as a volume in microlitres (μL), millionths of a litre.

The name, symbol, and conversion factors for some prefixes is given in the table below:

   factors prefix symbol large → → → → → → → → → → → → small 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto T G M k h da d c m µ n p f a

This means that:

 1 kilolitre (1 kL) = 103 litres (1000 L) 1 litre (1 L) = 1 ÷ 103 kilolitres = 0.001 kL 1 millilitre (1 mL) = 10-3 litres (0.001 L) 1 litre (1 g) = 1 ÷ 10-3 millilitre = 1,000 mL 1 microlitre (1 µL) = 10-6 litres (0.000001 L) 1 litre (1 L) = 1 ÷ 10-6 microlitres = 106 µL

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## Worked Examples of Volume Conversions Using Metric Units

Question 1: Convert 1 litre to decilitres

Solution:

From the table above we see that deci = 10-1 = 0.1

1 dL = 0.1 L

Divide both sides of the equation by 0.1

1 dL ÷ 0.1 = 0.1 L ÷ 0.1

10 dL = 1 L

Question 2: Convert 2.5 L to millilitres

Solution:

From the table above we see that milli = 10-3

1 mL = 10-3 L

Divide both sides of the equation by 10-3

1 mL ÷ 10-3 = 10-3 L ÷ 10-3

103 mL = 1 L

which we can also write as

1 L = 1,000 mL

Multiply both sides of the equation by 2.5

2.5 × 1 L = 2.5 × 1,000 mL

2.5 L = 2,500 mL (or 2.5 × 103 mL)

Question 3: Convert 5 millilitres to litres

Solution:

From the table above we see that milli = 10-3

1 mL = 10-3 L

Multiply both sides of the equation by 5:

5 × 1 mL = 5 × 10-3 L

5 mL = 0.005 L

Question 4: Convert 0.250 L to microlitres

Solution:

From the table above we see that "micro" means 10-6

1 µL = 10-6 L

Divide both sides of the equation by 10-6

1 μL ÷ 10-6 = 10-6 L ÷ 10-6

106 μL = 1 L

which is the same as writing 1 L = 106 μL

Multiply both sides of the equation by 0.250

0.250 × 1 L = 0.250 × 106 μL

0.250 L = 2.50 × 105 μL = 250,000 μL

Question 5: Convert 25 µL to millitres

Solution:

First convert 25 μL to L

From the table above we see that μ is the symbol for "micro", that is 10-6

1 μL = 10-6 L

so 25 μL is

25 × 1 μL = 25 × 10-6 L = 2.5 × 10-5 L

Next, convert 2.5 × 10-5 L to mL

From the table above we see that "milli" refers to 10-3

1 mL = 10-3 L

divide both sides of the equation by 10-3

1 mL ÷ 10-3 = 10-3 L ÷ 10-3

103 mL = 1 L

which we can write as 1 L = 1,000 mL

multiply both sides of the equation by 2.5 × 10-5

2.5 × 10-5 × 1 L = 2.5 × 10-5 × 1,000 mL

2.5 × 10-5 L = 2.5 × 10-2 mL = 0.025 mL

Write the final answer

25 μL = 0.025 mL

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## Converting Non-metric Units of Volume to Metric Units

The scientific community generally uses SI units of measurement, the SI unit of volume is the cubic metre, m3.
Chemists most often use metric units of volume such as litres (L) and millilitres (mL).
But if you live in a country like the USA you probably don't regularly use metric or SI units for measuring volume, so we have included the conversion factors between commonly used non-metric units of volume and metric units below:

• 1 US liquid gallon = 231 cubic inches = 3.785411784 litres
• 1 US fluid ounce = 1/128 US gallon = 0.0295735295625 L = 29.5735295625 mL
• 1 US pint = 1/8 US gallon = 16 US fluid ounces = 473.1764729984 mL
• 1 US quart = 1/4 US gallon = 32 US fluid ounces = 946.3529459968 mL

## Worked Examples of Converting Between Non-metric Units of Volume and Metric Units of Volume

Question 1: Convert 10 US gallons to millilitres

Solution:

Use the information above to convert 10 gallons to litres (L)

1 gallon = 3.7854 L

Multiply both sides of the equation by 10

10 × 1 gallon = 10 × 3.7854 L

10 gallons = 37.854 L

Convert 37.854 L to mL

1 mL = 10-3 L ("milli" = 10-3)

divide by sides of the equation by 10-3

1 mL ÷ 10-3 = 10-3 L ÷ 10-3

103 mL = 1 L

Multiply both sides of the equation by 37.854

37.854 × 103 mL = 37.854 × 1 L

37,854 mL = 37.854 L

10 gallons = 37,854 mL

Question 2: Convert 2.5 US fluid ounces to millilitres

Solution:

Use the information above to convert 1 fluid ounce (fl oz) to millilitres (mL):

1 fl oz = 29.5735 mL

Multiply both sides of the equation by 2.5

2.5 × 1 fl oz = 2.5 × 29.5735 mL

2.5 fl oz = 73.9338 mL

Question 3: Convert 200 litres to US gallons

Solution:

Use the information above to convert 1 L to gallons

1 gallon = 3.7854 L

Divide both sides of the equation by 3.7854

1 gallon ÷ 3.7854 L = 3.7854 L ÷ 3.7854

0.2642 gallon = 1 L

Multiply both sides of the equation by 200

200 × 0.2642 gallon = 200 × 1 L

52.8346 gallon = 200 L

Question 4: Convert 150 millilitres to US fluid ounces

Solution:

Use the information above to convert 1 mL to fl oz

1 fl oz = 29.57353 mL

Divide both sides of the equation by 29.57353

1 fl oz ÷ 29.57353 = 29.57353 mL ÷ 29.57353

0.03381 fl oz = 1 mL

Multiply both sides of the equation by 150

150 × 0.03381 fl oz = 150 × 1 mL

5.072 fl oz = 150 mL

Question 5: Convert 500 millilitres to US quarts.

Solution:

Use the information above to convert 1 mL to quarts

1 quart = 946.353 mL

Divide both sides of the equation by 946.353

1 quart ÷ 946.353 = 946.353 mL ÷ 946.353

0.00106 quart = 1 mL

Multiply both sides of the equation by 500

500 × 0.00106 quart = 500 × 1 mL

0.528 quart = 500 mL

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Footnotes:

(1) SI is the abbreviation for Système Internationale d'Unités. It is a unified version of the metric system agreed upon by the General Conference of Weights and Measures in 1960 and is used world-wide.