The ultimate guide to calculations: how to do medical maths easily
Calculations are an essential part of our daily nursing life. But I’m well aware they are not the most fun topic to learn - in fact, they can be pretty headache-inducing!
Medical maths was not my strongest subject for most of my veterinary nursing journey. In fact, it’s only been the last few years where I’ve really felt comfortable with calculations. I’ve found my own ways to make the maths make sense to me, and I’m here to show you how to do the same.
Stay tuned as we walk through exactly how to perform all of the common calculations used in practice, so that you can do medical maths quickly, easily and without the headache in practice.
Medications
When it comes to drug calculations, there is a lot for the veterinary nurse to consider. We need to know how to calculate basic drug volumes, convert units, work with percentage solutions and reconstitute and dilute medications.
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.
Converting Units
What do we do if part of our calculation is in different units?
Well, if any part of our calculation (either the drug dose or the concentration) is in different units, we’ll need to convert them to perform the calculation. This is because the units either side of the equation must match to do the calculation correctly.
So how do we do this?
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.
You can then do the rest of your drug calculation as we discussed above.
Percentage Solutions
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, how do we convert a 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.
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 grams.
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.
Reconstituting Medications
Certain medications are not stable in a pre-prepared solution or have a very short shelf life once made up for use. Examples include cefuroxime (Zinacef), amoxicillin/clavulanic acid (Augmentin) and omeprazole vials.
So, with these medications, we need to add a diluent solution (such as water for injection or saline) to the vials before use. But how do we calculate how much diluent to add?
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.
Diluting Medications
There will be times where a ‘normal’ dose of medication is too small to accurately draw up and administer to a patient. This usually happens when you’re preparing medications in very small 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, so that our patient requires a higher volume, which is 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 - 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. You just minus the total volume required and the volume of neat drug to work out how much diluent (e.g. sterile water) you need to add to your syringe!
Constant Rate Infusions
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.
There are two ways to administer CRIs - either via a syringe driver or in combination with the patient’s intravenous fluid therapy.
To administer a CRI 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
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.
Intravenous Fluid Therapy Calculations
There are a few things we need to think about when we’re calculating fluid therapy requirements.
Firstly, we need to think about where the patient’s fluid losses have come from - are they dehydrated, or are they hypovolaemic?
To read more about classifying fluid deficits, check out my guide to fluid therapy post.
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.
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
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; the one used most commonly is:
Maintenance requirements (ml/day) = 50 x bodyweight (kg)
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.
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.
Calculating Fluid Rates
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.
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.
Resting Energy Requirements
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.
To calculate this, simply use the calculator app on your practice PCs (this can very easily be turned into a scientific calculator, or take your smartphone and tip it on its side to bring up a scientific calculator!
Then locate the 'x to the power of y' button. Type in the patient's bodyweight, then hit this button, then type in 0.75, then multiply your result by 70 to calculate the RER.
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. Now go out there and get calculating!
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