Calc

How to convert mg to ml (milligrams to milliliters)

Article Category: Units  |   


A common question I receive in my email inbox concerns the conversion of milligrams (mg) to milliliters (ml), so I thought we'd address this issue today. The questions tend to look a little like this:

Liquid volume conversion in milliliters - photo

Q: I would like to know how to convert mg to ml. Specifically, what is 15mg in liquid (IE: ml)?

Let's start with some explanation on why this type of conversion isn't as easy as it sounds. After that, we'll try an example conversion and then, at the bottom of the article, discuss how to convert an order when given a dosage label.

What is the difference between a milligram and a milliliter?

One milliliter (British spelling: millilitre) (ml) is 1/1000 of a liter and is a unit of volume. 1 milligram (mg) is 1/1000 of a gram and is a unit of mass/weight. This means that we require an extra piece of information in order to be able to convert the measurement across. That extra piece of information is a density or concentration of the substance you are using (the density of every substance is different).

Densities and concentrations

Let's look at an example. Pure water has a density of 1,000 kg/m3. Crude oil, however, has a density of around 870 kg/m3. Two very difference substances. So, you can see how important it is to ensure that you use the correct density figure for your substance in order to get an accurate conversion.

When it comes to drug calculations, every drug company manufactures their drugs in standard concentrations and you can find these on any container labeled appropriately for the particular drug in question. By law, pharmacies that dispense medications are required to have this info on the label.

Once you know the density/concentration of your substance, you can put calculus to work. Note that you need to ensure that the mass unit matches the unit used in the density. So, if the density is in g/cm3 (grams per cubic centimeter) you will need to ensure your mass figure is in grams. To convert from milligrams (mg) to grams (g) you divide by 1000.

At this point you can divide your mass figure by your density, which gives you your volume figure. That leaves the final step of converting your volume figure into milliliters. Let's try a couple of examples.

Converting mg to ml - example 1

A liquid has a concentration of 15mg/ml. Let's say we want to work out how many ml there are in 45mg of it.

This calculation is more straight forward because the concentration/density is given in mg/ml. It therefore allows us to do the following using dimensional analysis...

  1. Our calculation will be:
    45mg
    --------
    1

    x
    1ml
    --------
    15mg

  2. Multiplying these across, with the mg cancelling each other out, we get:
    45ml
    --------
    15

    This gives us our answer of 3ml.

Converting mg to ml - example 2

Should the density not be in mg/ml, we need to do a little more work.

Sunflower oil commonly has a density of 920kg/m3. If we want to convert 10mg of sunflower oil to ml then we would do the following:

  1. Let's convert the density figure to grams per cubic centimeter (g/cm3). You'll have noticed that the density in our example is kg/m3, so we need to divide that figure by 1000 to give us a g/cm3 figure. 920 / 1,000 = 0.92g/cm3.
  2. Next, we need to convert the unit figure from milligrams (mg) to grams (g). To do this, we divide by 1000. So, 10/1000 = 0.01g.
  3. Our conversion now looks like this:
    0.01g
    --------
    1

    x
    1cm3
    --------
    0.92g

  4. Multiplying these across, with the g cancelling each other out, we get:
    0.01cm3
    --------
    0.92

    Which gives us an answer of 0.010869565cm3
  5. The final step is to convert your volume into ml. As 1cm3 = 1ml it's a 1:1 conversion. So, we don't need to do anything and therefore have our answer. 10mg of sunflower oil is 0.010869565 ml.

Should you not want to attempt the conversion yourself, try the weight to volume calculator, which is included below.




Group digits?
 

Please note: At this point I would like to advise anyone trying to work out figures for medications to check your calculations carefully and note my disclaimer. Note that this article and converter are here purely as a service to you, please use them at your own risk and do not use calculations for anything where someone's health might be affected as a result of an inaccurate conversion.

Converting doses from mg to ml

When it comes to medication dosages, it's common to see a label with mg and mg/ml dosage information. This video explanation from Pennsylvania College Math Department explains how to convert an order when given a label. It covers all three methods of conversion: nursing formula, dimensional analysis, and proportion.

Should you be interested, we've covered the conversion of International units (IU) to mcg or mg in an article here.

Written by Alastair Hazell




Rate this article

Please rate this article using the star rater below. If there is anything missing from the article, or any information you would like to see included, please contact me.



Last update: 13 July 2016


Your comments


Featured article

The history of the calculator

Photo of abacus

From abacus to iPad, learn how the calculator came about and developed through the ages. Read our featured article.