Medicines and mathematics: how to calculate the dose of medicine

Much of what you read below may seem strange and even offensive. After all, this “much” is studied in the first three grades of a regular secondary school. 

But nevertheless, reminders and primitive explanations can be useful, taking into account the fact that you will be engaged in calculations in a particularly nervous state due to a child’s illness … 

So, we will talk about how to correctly calculate the dose of a drug for a child.

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The dose of medicine prescribed for your child should be measured in some way, and the following can be used as units:

  • mass units (grams, milligrams, etc.);
  • volume units (liter, milliliter, drop, etc.);
  • special units (conventional, biological, etc.);
  • units of a specific dosage form (tablet, capsule, ampoule, etc.).

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicineThe main unit of mass measurement for the dosage of medicines is gram and its derivatives – milligrams and micrograms. Of course, we know that from the point of view of the international system of units (SI), the basic unit of mass is kilogram (kg), and the standard unit of volume is a cubic meter (m3), not a milliliter, but for clarity, we neglect conventions. 

Common abbreviations:

  • gram – g;
  • milligram – mg;
  • micrograms – mcg.

In 1 g – 1000 mg or 1,000,000 mcg. 
In 1 mg – 1000 mcg.

  • 1.0 is a gram;
  • 0.001 is a milligram;
  • 0.000001 is micrograms.

The basic unit for measuring volume is a milliliter . A liter, habitual in everyday life, is rarely used as a dose, but still it is sometimes used. For example, “the volume of fluid needed to conduct a cleansing enema is 1 liter” or “the daily volume of infusion therapy is 1.5 liters.” 
Common abbreviations:

  • liter – l;
  • milliliter – ml.

In 1 liter – 1000 ml. 

The unit of volume must be indicated! 

If it is not indicated, that is, 15.0 is simply written – it means that this is not volume, but mass – 15 grams. If we are talking about milliliters, then next to the number 15 should be written – ml: 15.0 ml. 

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicinePlease be careful: the most common parental mistake is when MG and ML get confused . 

We pay attention once again, since this moment is extremely relevant! 

Not to confuse mass units and volume units – this is very, very important! 

Whenever a drug is administered parenterallyin a certain amount of ml, we are talking about the fact that this volume will be measured by an injection syringe of the appropriate size or a bottle of the infusion solution having the appropriate volumetric labels will be used. 

Packages of modern (dosed in milliliters) medicines for oral administration without fail contain special measuring devices: caps, pipettes, syringes, glasses, measuring spoons. 

If there is nothing like this, but the medicine is still prescribed orally and in ml, then injection syringes or special graduated measuring cups sold in pharmacies should be used to measure the required volume. 

Precarious and inaccurate volume measuring unit is a drop. The drop volume is largely determined by the physical properties of the dosed liquid. 

So, for example, the volume of one drop of an alcoholic solution is on average 0.02 ml, and the volume of one drop of an aqueous solution can range from 0.03 to 0.05 ml. 

Pharmacists and doctors have long agreed that the standard pharmacy, medical measure of a drop is 0.05 ml . 

Thus, 1 ml = 20 drops. 

When a solution of a specific drug is prescribed to your child in drops and we are talking about a modern drug, the package usually contains a special pipette or the cap of the bottle is a special dropper.

If there is no pipette or dropper cap, then you can use a standard medical pipette sold at any pharmacy. If many drops are prescribed, it is quite possible to use a disposable syringe to measure the required volume of liquid. 

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicine10 drops are prescribed – this means 0.5 ml; 40 drops – 2 ml, respectively. 

You can even use the formula: 
number of ml = number of drops divided by 20.

The main thing to remember is that whenever a certain drug is prescribed in drops and you cannot figure out how to extract and measure these drops, it is clearly implied that the volume of one drop is 0.05 ml. And this means that having a 1 ml medical syringe in the house, you can easily and absolutely accurately determine the required volume of medicine: 2 drops – 0.1 ml, 3 drops – 0.15 ml, 5 drops – 0.25 ml etc. 

Even more non-standard (compared to drops) volume units are a variety of household spoons, which are sometimes (but less and less) used to dispense inactive and relatively safe medicines. 

Standard volume of spoons in ml:

  • tea spoon – 5 ml;
  • dessert spoon – approximately 10 ml (there is no single standard);
  • a tablespoon – in the CIS countries – 18 ml, in the USA, Canada – 15 ml, in Australia – 20 ml;

In some countries, a concept such as a baby spoon is used.

  • baby spoon – 10 ml.

To completely close the topic of kitchen accessories for measuring volume, let us recall the glass . Dosing with glasses is more common in cooking, but is sometimes used in medicine to measure the volume of infusions, decoctions, rinses, etc.

  • One glass – 200 ml.

The active substance is in a liquid drug in a certain concentration. The digital value of this concentration is reflected in such a seemingly obvious, but not always clear expression, as the percentage of solution . 

The expression “5% solution of ascorbic acid” does not look complicated and mysterious at all. But nevertheless, some clarifications should be given in order to finally dot the i. 

So, the concentration in pharmacology is usually displayed as the number of units of mass per unit volume . Thus, the expression “1% solution” means that in 100 ml of liquid is 1 g of the active substance. 

In the vast majority of cases, the volume of fluid assigned to a child is measured in milliliters. Therefore, we recount: 

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicine100 ml – 1 g;
10 ml – 0.1 g; 
1 ml is 0.01 g. 

0.01 g is 10 mg. It is a logical conclusion: 1 ml of a 1% solution contains 10 mg of the active substance . 

It turns out that it is not difficult to calculate the required amount of active substance per unit volume (in 1 ml): for this, it is only necessary to add a zero to the number of percent. 

We train:

  • in 1 ml of a 5% solution of ascorbic acid – 50 mg of ascorbic acid;
  • in 1 ml of a 50% solution of dipyrone – 500 mg of dipyrone;
  • in 1 ml of a 0.1% solution of loratadine – 1 mg of loratadine;
  • in 1 ml of a 66.7% solution of lactulose – 667 mg of lactulose;
  • in 1 ml of a 0.05% chlorhexidine solution – 0.5 mg of chlorhexidine …

Manufacturers of children’s dosage forms are very skeptical of the mathematical abilities of the parents of these very children. The instructions may well say “a solution of loratadine 0.1%”, but the packaging will be indicated in capital letters: “loratadine 1 mg / 1 ml” or “loratadine 5 mg / 5 ml”. 

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicineA huge amount of liquid medicines is available in different concentrations. In 1 ml of a suspension of paracetamol there may be 20, or maybe 50 mg: “120 mg / 5 ml” or “250 mg / 5 ml” will be written on the suspension box. A pharmacy worker will not be able to properly let go, and mom will not be able to properly give the child the paracetamol prescribed in a dose of “5 ml of suspension” – you need to know what concentration of the suspension is in question. Thus,always, when something is prescribed to your child, it is important to make sure that you know not only the name of the solution, but also its concentration! 

The situation when the doctor prescribes a solution, syrup, suspension, etc., but does not indicate the concentration, is nevertheless possible. 

So, almost all manufacturers produce lactulose syrups in the form of a 66.7% solution. And when the doctor wrote: “Lactulose syrup 5 ml in the morning before breakfast,” there is no mistake. 

Another option: we are talking about a drug prescribed under a specific trade name. 

An example of this purpose: “Nurofen for children, suspension, at a temperature above 39 ° C 10 ml inside”. A suspension called “nurofen for children” is available in only one concentration – 100 mg / 5 ml. Therefore, everything is written correctly, it is impossible to make a mistake. 

Another question is that the pharmacy can tell you something like this: “Now we do not have nurofen for children in suspension. We have another medicine, but in the composition of ibuprofen, as in nurofen, and this is different – only in 0.4 tablets. Everything else is in the regional center, a bus tomorrow morning … ” 

And then you will calculate: 
– 10 ml with a concentration of 100 mg / 5 ml – this means we were prescribed 200 mg. 
And in a tablet of 0.4 it is 400 mg. 
So, we will persuade Masha to swallow half a tablet …

Another fundamentally important point. Knowledge of the concentration is necessary not only when drugs are taken orally and are dosed in milliliters (ml). For topical application and dosing with drops, this is no less relevant. 

And if assigned “xylometazoline 2 drops in each nostril, 3 times a day” , then before the drip prenepremenno should clarify what kind of xylometazoline it – 0.1% or 0.05%? 

The concentration of the active substance in dermatological agents is also indicated by percentages, but there is no specificity here. Therefore, if it says “hydrocortisone ointment 1%”, then this means that 1 ml of this ointment contains 10 mg of hydrocortisone. But in the same way as with paracetamol suspension, you can’t just write “hydrocortisone ointment”, since this ointment is 0.5%, 1%, 2.5% …

Now about dosing using special units . Whenever it comes to certain dosage units, the number of these units is linked either to a unit of volume or to a specific package or dosage form Order-cs.com. And this relationship must be clarified! 

Those. it is imperative to know that a 1 ml insulin contains exactly 40 units or 100 units namely preparation. 

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicineYou must know that it is in this tablet with pancreatin thatcontains a dose equal to 10,000 units of lipase. Exactly 10 thousand, not 40 or 25. 

One must be aware that it is in this sterile bottle that 500,000 units of benzylpenicillin sodium salt are located .

Once again, I would like to emphasize that always, when something is assigned in units, it is imperative to clarify in what volume, in which bottle, in which capsule exactly this number of units is contained . 

With huge difficulties and many errors, the use of the name of a particular dosage form is associated with the dosage unit. 

In one tablet of the same pharmaceutical product may be a different amount of active substance. So, in one tablet of paracetamol can be 80, 120, 125, 200, 285, 325, 500 or 564 mg. Obviously, no one will be able to properly sell in the pharmacy or give the child the paracetamol prescribed in a dose of “1 tablet”.

Therefore, next to the name of the drug and the selected dosage form, the amount of active substance should be indicated in this particular dosage form prescribed for a particular patient. 

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicineExamples:

    • calcium gluconate, tablets of 0.5;
    • cephalexin, capsules of 0.25.

 

An indication of a certain tablet or capsule in the absence of information about the content of the active substance may in some cases be justified by the fact that there is no choice of tablets of this particular drug. 

This is possible if:

  • the drug is available in this dosage form only with a strictly defined amount of the active substance. For example, ornidazole is available in 0.5 tablets. There are no other tablets. You will not be mistaken;
  • the drug is prescribed under the trade name, and a specific manufacturer releases it only in such a dosage form – there is no choice. For example, one suprastin tablet always contains 0.025 chloropyramine . Therefore, if Suprastin is prescribed one tablet twice a day, you will not be mistaken;
  • the drug is a strictly defined combination of certain ingredients protected by the trade name. For example, decatylene , lozenges. There is no other decatylene. You will not be mistaken.

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We already know that the optimal way to dispense drugs to children is based on the relationship of dose with the weight of the child. 
Consider the intricacies of such dosing on the example of the most popular children’s antipyretic drugs – paracetamol . 
It is known that a single dose of paracetamol is 10-15 mg / kg. 
We have a child with a body weight of 15 kg. Thus, a single dose of the drug is from 150 (10 x 15) to 225 (15 x 15) mg. 
We bought a suspension of 120 mg / 5 ml. This means that in one ml – 24 mg. And we need from 150 to 225. So, our single dose is approximately 6.2–9.3 ml. 
We bought a suspension of 250 mg / 5 ml. This means that in one ml – 50 mg. And we need from 150 to 225. So, our single dose is 3-4 ml.
We bought 200 mg tablets. And we need from 150 to 225. So, our single dose is 1 tablet. 
We bought 325 mg tablets. And we need from 150 to 225. So, our single dose is half a tablet. 

Now let’s deal with the daily dose of the same paracetamol. If there is evidence, this medicine can be given again during the day, but no more than 4-5 times, and it is very important that the interval between doses should be at least 4 hours. 

All the same child – body weight 15 kg. The maximum daily dose of the drug should in no case exceed 60 mg / kg. This means that our baby can be no more than a day: 15 x 60 = 900 mg.
We bought a suspension of 120 mg / 5 ml. This means that in one ml – 24 mg. And we need no more than 900. Therefore, our maximum daily dose is 37.5 ml (900/24). 
We bought a suspension of 250 mg / 5 ml. This means that in one ml – 50 mg. And we need a maximum of 900 per day. Therefore, our daily dose should not exceed 18 ml (900/50). 
We bought 200 mg tablets. So, you can not have more than four tablets per day. 
We bought 325 mg tablets. So our maximum daily dose is 2 tablets and another three quarters of the tablet.

This listing of ours already shows that, knowing the weight and the necessary single / daily dose, it is quite easy to make a rational choice of the dosage form. Obviously, giving a child 3 ml of a suspension is in most cases much easier than 10 ml or a half tablet. Therefore, for a child weighing 15 kg, the optimal dosage form of paracetamol is, perhaps, a suspension of 250/5 ml.

In this aspect, the choice of the optimal dose of paracetamol for rectal administration is even more indicative. It is known that when using suppositories, a single dose of paracetamol is higher than when taken orally, and amounts to 20–25 mg / kg. Thus, a child weighing 10 kg should receive a candle containing from 200 to 250 mg. We go to the pharmacy, and it turns out that there are candles for sale with paracetamol containing the active substance in the amount of 50, 80, 100, 125, 150, 250, 300, 500, 600 and even 1000 mg. In our situation, it is most logical to buy candles at 250 mg and use them with a minimum load for the child’s psyche. But you can not know all this and mock a child by shoving two 100 mg candles into it, or scoff at yourself, trying to cut off half a candle from 500 mg.

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicineWe also draw attention to the fact that a careful study of the sheet with medical appointments in many cases will save you considerable money. 

Example prescriptions: “azithromycin suspension. 200 mg once a day half an hour before meals, 3 consecutive days . ” We go to the pharmacy, and there it turns out that the antibiotic azithromycin in suspension is sold in the following packages:

  • powder for suspension 100 mg / 5 ml, 20 ml vial;
  • powder for suspension 200 mg / 5 ml, 15 ml vial;
  • powder for suspension 200 mg / 5 ml, 30 ml vial;
  • powder for suspension 200 mg / 5 ml, 20 ml vial.

It is clear that the optimal choice in our situation – 200 mg / 5 ml, a bottle of 15 ml – this is just enough for the prescribed course of treatment. Any other packaging is not economically viable: either have to buy, or remain. 

Unfortunately, there is often a situation where the doctor simply does not have time to monitor the rapidly changing assortment of pharmacies. And in this case, such appointments are quite possible: “loratadine 5 mg 1 time per day for 2 weeks . ” This, of course, is wrong, but a very small parental intellectual effort can solve the problem. 

So, we come to the pharmacy for loratadine, 5 mg. 
It turns out that loratadine is in tablets of 10 mg, as well as in syrups or suspensions – 1 mg / 1 ml.
5 mg is half a tablet or 5 ml of syrup. We don’t want to share the pills, and swallowing pills has problems with our baby, so we get a liquid-tasty and give what the doctor prescribed … 

Knowledge is power !: Medicines and mathematics: how to calculate the dose of medicineBy the way, before buying, we make simple calculations: 5 ml per day, but for 2 weeks, it’s 5 x 14 – it turns out, for the course of treatment you need 70 ml. And how much is there in the bottle? We are interested in: it turns out that in one bottle of syrup or suspension of loratadine there can be 30, 50, 60, 100, 120 and 150 ml. Probably the most rational way to buy a bottle of 100 ml – please give … 

And the last thing I would like to draw your attention to. Whenever a doctor prescribes to divide the tablets, this is either indicated by the words (half, third, quarter), or by the fraction: 1/2, 1/3, 1/4.
And if it says “calcium gluconate 0.5” – it’s not half a tablet (!), It’s half a gram – 0.5 g. 
0.25 – it’s not a quarter tablet, it’s 0.25 g.