The ultimate guide to calculations: how to do medical maths easily
We all know that calculations are an essential part of our daily life as veterinary nurses and technicians. And yes, I am well aware they are not the most fun topic to learn (unless you’re a maths nerd like me!!)- and, in fact, they can be pretty headache-inducing!
Medical maths was not my strongest subject for most of my earlier years as a vet nurse. I also didn’t get the opportunity to really practice them for many years, either - everything was either a pre-calculated dose from a chart on the wall, or a vet giving you doses already (or worse, a CRI bag already made up, and instructions just to start at Xml/hour!).
You might be thinking, “but Laura, that sounds great! All of the nursing with none of the maths?! Why are you moaning?“
And if you are - then I understand. But let me put it to you this way: If you’re not being given the chance to practice calculations like this, you’re not being given the chance to learn, develop your skills, get confident with calculations, and ultimately, help your patients.
You know what else? If you’re not being given drug doses in mg/kg, or being asked to calculate them, then you’re also missing out on understanding exactly what each dose means for your patient.
Because how do you know if 0.1ml of methadone is going to be enough analgesia?! Without doing backwards maths - which none of us want - you don’t.
But 0.1mg/kg? That’s a different story. You know that’s a relatively low dose, so to be on the lookout for signs your patient might need more - or that they might be comfortable enough to stop it. So (as I step off of my soapbox…) if your vets aren’t getting you to calculate doses for them - now’s the time to ask them.
You don’t get comfortable with calculations by ignoring them (or not being given the chance to practice them).
I wasn’t always comfortable with calculations. In fact, it’s only been the last few years that I’ve really felt comfortable with calculations. I’ve found my own way to make the maths make sense to me, and I’m here to show you how to do the same.
So, in this post, I’m bringing you a bumper blog on all things medical maths. Stay tuned as we walk through exactly how to perform all of the common calculations used in practice, so that you can do them quickly and easily, and focus on giving even better care to your patients.
Starting with - calculating medications
When it comes to drug calculations, there is a lot for us to consider as nurses and technicians. We need to know how to calculate basic drug volumes, convert units, work with percentage solutions and reconstitute and dilute medications - which is what we’ll start with now.
First up, let’s look at how to calculate standard drug doses
To calculate a dose of liquid medication (either via injection or an oral solution), simply multiply the dose (in mg/kg) by the patient's body weight (in kg), then divide by the concentration of the drug (in mg/ml).
This will give you the volume of medication required for each dose.
When calculating tablets, the maths looks a little different. Here we multiply the dose (in mg/kg) by the patient's weight (in kg), then divide by the tablet size (in mg). This gives us the number of tablets required for the patient's dose (in reality, this often needs a little rounding to accommodate for tablet size, and how easy it is to divide the tablets).
Once we've got our dose, we need to calculate the number of tablets needed for the patient's medication course. We do this by multiplying the tablets needed at each dose by the dose per day (e.g. 2 if it's a BID medication), and then multiplying this by the number of days required.
But not all of our maths is easy, and the first stumbling block is usually converting units
If you’ve ever had to work with a dose in mcg/kg or g/kg, you’ll know this pain.
For a drug calculation to work, our units on either side (aka the dose and the concentration) must match. If they differ, we’ll need to convert them to perform the calculation correctly.
The way we do this depends on what your units are - and what you want to convert them to. Usually, most of our drug doses and concentrations are in mg/kg, so I’ll use that as a ‘standard’ - since this is likely the same scenario you’ll encounter in practice.
If you're working with a dose in grams/kg (g/kg) or a concentration in grams/ml, you need to multiply this by 1000 to get a dose in mg/kg. This is because there are 1000 milligrams in a gram.
If you're working with a dose in micrograms/kg (mcg/kg) or a concentration in micrograms/ml, you need to divide this by 1000 to get a dose in mg/kg. This is because a milligram is made up of 1000 micrograms.
Now that your units are converted, you can do the rest of your drug calculation, just like we talked about above.
What if you’ve got a drug that isn’t in mg/ml? What if you’ve got a percentage?!
Let me tell you - I HATED percentage solutions for SO long. I had no idea how to convert them, and any calculation with a percentage solution in it hurt my brain immediately.
I had no idea how to convert a percentage to mg/ml for ages. 2% lidocaine?! Might as well be in a foreign language - I spent more time annoyed with drug companies for not using mg/ml than I spent trying to calculate them, to be honest!
But it’s actually pretty easy to convert - especially when I share my cheat rule with you (in a second, you’ve got to cover the ‘real’ calculation first).
A percentage solution is defined as the weight of the solute (in grams) per 100ml volume of drug (aka weight divided by volume or w/v).
For example, a 2% lidocaine injection is made up of 2 grams of lidocaine dissolved in 100ml of carrier solution. 50% glucose contains 50g of glucose in 100ml and 10% mannitol contains 10g of mannitol in 100ml of carrier solution.
So now we know this, we can convert our percentage to a mg/ml concentration.
To convert a % solution to mg/ml, you take the weight of the drug (in grams) and multiply it by 1000 to convert it to mg. You then divide it by the volume (100ml) to get the concentration in mg/ml.
As I previously mentioned, there is also a sneaky shortcut for converting percentage solutions. This works for nearly all medications - but not for things like potassium, magnesium and calcium injections, as these are expressed in mmol, not milligrams. So don’t use it for electrolyte solutions, but go ahead and use it for all other drugs!
In general, you can add 1 decimal place to the percentage of the medication - so every 1% is 10mg/ml. For example, 2% lidocaine becomes 20mg/ml, 50% glucose becomes 500mg/ml and 10% mannitol becomes 100mg/ml. So if you’re stuck, just multiply the percentage by 10!
What about reconstituting medications? How do we handle that?
Most of the calculations we perform rely on us knowing the concentration of our drug. But what about when we get to CHOOSE the concentration?!
Crtain medications are not stable in a pre-prepared solution or have a very short shelf life once made up for use, so they come powdered - ready for us to reconstitute. Examples of these drugs include cefuroxime (Zinacef), amoxicillin/clavulanic acid (Augmentin) and omeprazole vials, where we’ll add a diluent solution (such as water for injection or saline) to the vials before use.
To work out how much diluent to add, you first need to know the desired concentration you want to achieve. Once you have this, simply divide the total number of milligrams of drug in the vial by the desired concentration (mg/ml). This will give you the total number of mls of diluent you need to add to the vial.
For example, to make your 40mg omeprazole vial into a 10mg/ml solution:
40mg / 10 = 4, so add 4ml of water for injection to your vial!
So that’s reconstituting medications - and the last drug calculation we need to look at is dilution.
There will be times when a ‘normal’ dose of medication is too small to draw up and administer to a patient accurately. This usually happens when you’re preparing medicines in tiny doses or for very small patients, or when the medication is only available in a higher concentration.
In these cases, we need to reduce the concentration of the drug by diluting it. This way, our patient will require a higher volume, making it much easier to draw up and administer.
The calculation for diluting medications can be a little confusing, but stick with me for this 3-part calculation:
Divide the stock concentration (the volume of drug ‘neat’ from the bottle) by the desired concentration (the concentration you want to achieve). This gives you a dilution factor - aka how much you’ll need to dilute your drug by.
Take your total diluted drug volume (this is the total volume of your new, diluted drug that you’ll need, which you’ll calculate just by performing a normal drug calculation) and divide this by the dilution factor (the answer to part 1). This tells you the amount of neat drug you need to add to your syringe.
Now you know how much volume you need in total, and how much of it is made up of the neat drug. Simply subtract the total volume required and the volume of neat drug to determine how much diluent (e.g., sterile water) you need to add to your syringe.
Need an example?
Let’s make up a 10ml syringe of ketamine for a patient’s CRI. Our ‘neat’ ketamine concentration is 100mg/ml, but we want to make it 5mg/ml.
100mg/ml divided by 5mg/ml = 20
10ml syringe / 20 = 0.5
10ml syringe = 0.5 = 9.5
To make up our syringe, we’ll add 9.5ml of saline to 0.5ml of 100mg/ml ketamine injection, for an overall concentration of 5mg/ml!
What about administering constant rate infusions? How do we do that correctly?
CRIs administer medications at a low rate, continually. They are commonly used for things like analgesia and can be really useful, as they eliminate the peaks and troughs associated with intermittent dosing. But, they can also be headache-inducing - especially if you’re the one asked to calculate and prepare them.
There are two ways to administer CRIs - either via a syringe driver or in combination with the patient’s intravenous fluid therapy - and the calculation varies a little, depending on how you plan to administer your patient’s infusion.
To administer a CRI via a syringe driver
To calculate a CRI for administration via a syringe driver, take the patient's dose (in mg/kg/hour) and multiply it by their weight (in kg). Then divide this by the drug concentration (in mg/ml) to get their rate in ml/hour.
But what about if you're working with a dose in different units?
Quite often, our CRI doses may be in mg/kg/day, or mcg/kg/hour, or mcg/kg/minute, rather than in mg/kg/hour. If any of these units are different to mg/kg/hour, you'll need to convert these before doing the rest of the calculation:
To convert doses /day to /hour, divide by 24
To convert doses /minute to /hour, multiply by 60
To convert doses in g/kg to mg/kg, multiply by 1000
To convert doses in mcg/kg to mg/kg, divide by 1000
To administer a CRI via your patient’s fluid therapy
When administering CRIs via the patient’s fluid therapy, we need to take into account not only the patient’s drug dose but also their fluid therapy rate, to determine how much drug to add to their fluid bag.
To calculate the volume of the drug to add to the patient's fluid bag:
Calculate the rate of the drug needed in ml/hour (dose x weight / concentration, remembering to convert your units as necessary)
Calculate the number of hours the patient's fluid bag will last (total volume of fluid in bag / fluid rate per hour = number of hours)
Multiply the drug rate (ml/hr) by the number of hours the bag will last. This will equal the volume of the drug (in ml) you need to add to the fluid bag.
Ok, so that’s drug calculations. What about Intravenous Fluid Therapy?
There are a few things we need to think about when we’re calculating fluid therapy requirements - and the first is where the patient’s fluid losses have come from.
Is your patient dehydrated, or are they hypovolaemic? Both of these require very different rates, and different calculations - so understanding the difference is key. To read more about classifying fluid deficits, check out my guide to fluid therapy post.
How to correct hypovolaemia
Patients with hypovolaemia or perfusion deficits require rapid fluid rates over short periods – this is known as a fluid bolus. A set fluid volume (typically 5-20ml/kg depending on the species or patient) is administered over a 10-30-minute period, and after this has been administered the patient is re-assessed. This volume can then be repeated if needed, based on the patient assessment, until their perfusion parameters return to normal.
To calculate and administer a fluid bolus to a hypovolaemic patient:
Calculate the total bolus volume required (e.g. 10ml/kg x 4kg = 40ml)
Calculate how many boluses fit into 1 hour (e.g if you’re giving the bolus over 15 minutes, 60 minutes / 15 minutes = 4)
Multiply the bolus volume by the number of boluses that ‘fit’ into 1 hour to get your ml/hour rate for your infusion pump (e.g. 40ml x 4 = 160ml/hour)
Set your infusion pump as follows:
Drip rate: 160ml/hour
Volume to be infused: 40ml
Time: 15 minutes
After the bolus has been given, re-examine your patient, see if their vitals have changed, discuss with the veterinary surgeon and repeat the bolus as required under veterinary direction.
How to spot and correct dehydration
Patients with dehydration have alterations to their bodyweight, skin elasticity, mucous membrane tackiness/dryness and eye position. We can assess their percentage dehydration based on the severity of these signs:
% Dehydration
0-4: No examination findings
4-6: Tacky mucous membranes
6-8: Loss of skin turgor, dry mucous membranes
8-10: Loss of skin turgor, dry mucous membranes, retracted globe position/’sunken eyes’
10-12: Persistent skin tent, dry mucous membranes, dull corneas/corneal dryness, retracted globes
>12: Persistent skin tent, dry mucous membranes, retracted globes, dull corneas, evidence of perfusion deficits/hypovolaemia
Once the percentage dehydration has been calculated, we can determine the fluid volume required.
This is calculated by multiplying the patient’s body weight by their % dehydration, by 10.
Fluid volume required (ml) = % dehydration x body weight (kg) x 10
This gives us the total volume of fluid needed to rehydrate our patient - now we just divide this by the number of hours you’re correcting the dehydration over, to get your ml/hour rate!
However, in addition to the volume required to correct the patient’s dehydration, we also need to incorporate daily maintenance requirements and any ongoing fluid losses.
Maintenance requirements are the volumes of fluid required each day to replace normal daily losses (through normal urination, defecation and respiration). A healthy patient would drink this amount per day, but in many unwell patients, it needs to be given via intravenous fluid therapy. Several calculations can be used to determine maintenance requirements; these include 2ml/kg/hour, 50ml/kg/day, and calculations similar to our patient’s RER.
Ongoing losses include fluid losses through vomiting and/or diarrhoea, polyuria or increased fluid losses through wounds and drains. These should be estimated as closely as possible by weighing dressings, bedding or litter trays, collecting urine passed in a jug or via a urinary catheter and collection system where appropriate, and measuring output from drains.
(Quick PSA from me: these ongoing losses are ON TOP of maintenance! They don’t include normal urination, normal defecation, etc - we’re already covering these by meeting our patient’s regular maintenance fluid requirements.)
The fluids out should be calculated (in ml/kg/hour) and compared with the fluid in (in ml/kg/hour) at regular intervals, to ensure the patient’s fluid therapy rates match (or slightly exceed) their fluid output.
Ok, we know how much fluid our patient needs. Where do we go from here?
Once we know how much fluid our patient needs, we need to turn this into a fluid rate. If you have access to syringe drivers or infusion pumps, this is simple as we only need to calculate a rate in ml/hour. But if you are administering your fluids via the gravity drop method, it gets a little more complicated. Let’s take a look:
Calculate your rate in ml/day (eg. 50ml/kg)
Calculate your rate in ml/hour (by dividing your rate in ml/day by 24)
Calculate your rate in ml/minute (by dividing your rate in ml/hr by 60)
Now we need to convert our rate in ml to a rate in drops. To do this, we need to know the drip factor of the giving set we're using. This is usually 20 for a standard/spiral line, 60 for a burette or paediatric line, or 10 for a high-flow line.
4. Convert your ml/minute to drops/minute (by multiplying the rate in ml/minute by the drip factor)
5. Divide 60 seconds (1 minute) by the drops/minute to give you the number of seconds between each drop of fluid.
Ok, so that’s drugs and fluids down. Let’s talk about nutritional calculations!
Nutrition is one of the most important aspects of inpatient care, and a key area for veterinary nurses to get involved in. It’s often up to us to perform nutritional assessments, create nutritional plans and calculate energy requirements and food volumes for our patients - and to do that, we first need to understand how much our patients SHOULD eat.
We’ll start by determining their resting energy requirement or RER.
The resting energy requirement is the calories required to maintain normal body processes at rest each day.
We should ideally be calculating resting energy requirements routinely in all of our hospitalised patients, especially our unwell patients!
There are several different calculations which can be used, but the allometric formula RER = 70 x (bodyweight^0.75) is considered most accurate, especially in very small or very large patients - some of our other formulas, such as 30 x bodyweight + 70, can overestimate calories.
Once you’ve got your patient’s RER, we’ll turn this into a feeding plan.
To turn this into a nutritional plan, divide the RER by the calorific density of the food to calculate the mls or grams of food needed each day.
Then, simply divide this by the number of meals being fed (or by 24 hours if you're administering a constant rate infusion of food through a feeding tube), to get your volume to feed per meal.
So there you have it! Some of the most common (and a few of the most complicated) calculations we veterinary nurses need to perform in practice, broken down simply - so you can calculate to your heart’s content without the headache, and spend less time doing maths, and more time on patient care.
Remember, you only get confident with calculations by doing them. So next time there’s the opportunity to calculate your patient’s fluid rate (instead of ‘twice maintenance’), or you’ve got a patient you’re tempting to eat and you want to make sure you’re meeting their calorie needs, don’t wait for the vet to ask you - go ahead and calculate it out, then take them the information!
And if you want a helping hand putting all of these calculations into practice, I’ve got a workshop you’ll find REALLY useful. Join me for ‘Making Maths Easy’ - an instant-access workshop where we work through all of these calculations (and more) together, with examples, to make them really stick. You’ll also get a bonus calculations guide to use in practice so you don’t need to remember all of the sums off the top of your head!
