To minimise the number of errors caused by miscalculating dose, volume or rate of administration nurses must be familiar with and apply a number of mathematical formulae
(Trim, 2004).
Many organisations’ policies stipulate that two practitioners must check drugs, particularly those administered intravenously. The NMC (2002) also stipulates that two practitioners should be involved in complex calculations and it is considered good practice for two to be involved in all but the most basic drug calculations.
The use of calculators in applying mathematical formulae is inevitable, particularly for more complex calculations. However, it is important to take extra care when using a calculator to prevent operator or machine error.
→Unit conversions
Many calculations require different volumes or weights to be converted into the same unit or value. To convert larger units to smaller the larger is multiplied:
Kilograms (kg) to grams (g) = kg x 1,000;
Grams to milligrams (mg) = g x 1,000;
Milligrams to micrograms (mcg) = mg x 1,000;
Micrograms to nanograms (ng) = mcg x 1,000;
Litres (L) to millilitres (ml) = L x 1,000.
To convert smaller units to larger the smaller is divided:
Grams to kilograms = g/1,000;
Milligrams to grams = mg/1,000;
Micrograms to milligrams = mcg/1,000;
Nanograms to micrograms = ng/1,000;
Millilitres to litres = ml/1000.
Large infusion rates
To administer fluid volumes over a specified time a gravitational flow administration set may be used, which requires the infusion rate to be administered as ‘drops per minute’. To calculate this the number of drops per ml for the specific set must be ascertained - this is usually identified on its packaging. Generally, crystalloid administration sets operate at 20 drops per millilitre (d/ml) and blood (large-bore) sets operate at 15d/ml.
TO CALCULATE THE INFUSION RATE IN DROPS PER MINUTE THE FOLLOWING FORMULA IS APPLIED (FIG 1):
Vol required / Duration (hr)
x
Set value (d/ml) / Minutes (60)
Fluid infusions are often administered via volumetric pumps, many of which run in a millilitre per hour (ml/hr) rate.
TO CALCULATE ML/HR THE FOLLOWING FORMULA IS APPLIED (FIG 2):
Volume to be infused / Duration of infusion,
Nurses must ensure they have received specific training in the use of the particular infusion device before operating it.
Required drug volume from stock strength
This is a common calculation as many prescribed doses are smaller than the available preparation. In some drugs the stock concentration may depend on the volume of diluent. This is often the case in reconstituting antibiotics.
THE FOLLOWING FORMULA IS APPLIED (FIG 3):
Amount required / Stock strength
x Stock volume
Or more simply
What you want / What you have got
x Volume
→Calculating weight-related doses
Occasionally, and particularly in paediatrics, drugs are prescribed based on the patient’s body weight. The prescription may be expressed as millilitres per kilogram (ml/kg) or milligrams per kilogram (mg/kg).
THE FOLLOWING FORMULA IS APPLIED (FIG 4):
Prescribed volume x Body weight
or
Prescribed dose x Body weight
→Concentrations (mg/ml) from solutions
Some drugs are presented in a percentage concentration (for example, lidocaine, calcium chloride and dextrose in solution).
The expression refers to grams per 100ml, so a one per cent solution would be 1g per 100ml and a 50 per cent solution would be 50g per 100ml. The volume always remains constant (Fig 5).
Concentrations from weight to volume ratios
Some drugs are expressed as a weight to volume ratio (such as adrenaline and noradrenaline). These could be expressed as 1:1,000 or 1:10,000.
The expression is similar to a percentage except that the weight remains constant (1g) and the volume differs. The volume is in millilitres. Therefore:
Adrenaline 1:10,000 = 1g in 10,000ml;
Noradrenaline 1:1,000 = 1g in 1,000ml.
Once a mg/ml concentration has been calculated, further formulae such as dose or stock strength x volume may be necessary to calculate the volume required (Fig 6).
→ Iv Drips Formulas
To calculate rate using minutes:
(volume x calibration) /minutes
= gtt/min
To calculate rate using hours:
(volume x calibration) /hours x 60
= gtt/min
Examples
1) Give a 50cc IVPB over 30 minutes using IV tubing with a calibration of 10. How many drops per minute should this IVPB be set for? See the example below.
select "x = minutes"
x = 30
volume = 50
calibration = 10
Actual formula:
(50 /30 ) × 10
= 16.7 or 17 gtt/min
Example Only! Calculator does not work.
2) Using IV tubing alone (calibrated at 60), prepare an IV to infuse 1 liter over 8 hours. How many drops per minute should the IV be set for? See the example below.
select "x = hours"
x = 8
volume = 1000
calibration = 60
Actual formula:
(1000ml x 60 )/ 8 x 60
= 125 gtt/min
Example Only! Does not work!
Note, when using microdrip tubing (calibration = 60), the drip rate will be the same as mL/hr. This will save you the time of calculating the drip rate if asked to give the rate in mL/hr.
3) The doctor orders an IV to infuse at 125cc/hr. Calculate the flow rate using 10 drop/min IV tubing.
select "x = milliters/hour"
x = 125
calibration = 10
Actual formula:
125cc x 10
60 = 20.8 or 21 gtt/min
Example Only! Calculator does not work.
→Iv doses calculator Formula
(dose ordered / dose available) x volume available
Actually this is the same formula used in the "PO dosage calculator."
Examples
1) Dr. Smith has ordered a heparin infusion of 1000 units/hour for John Doe in bed 7. The infusion is to be mixed as 25,000 units in 500 mL .9% NS. What rate will the IV pump be set to?
In this example,
1000 units/hr = dose ordered
25,000 units = dose available
500 mL = volume available
(1,000units /25,000units) x 500mL
which = 20 mL
So the volume to give, an infusion, = 20 mL/hour
See the example below.
Doesn't work, just an example
2) Give 40mg of Lasix® (furosemide) IVP. The vial of furosemide contains 100 mg per 10 mL. In the example,
40 mg = dose ordered
100 mg = dose available
10 mL = volume available
(40mg /100mg) x 10mL
which = 4 mL
So the volume to give, a 1x dose, = 4 mL
Doesn't work, just an example
Note
It doesn't matter what type of units are used in this calculator. You can figure out how many grams to give or how many milligrams to give, micrograms, units, grains, etc. Remember to be consistent (i.e. don't mix milligrams with grams).
You may be wondering why a second answer is displayed in the calculator. The first answer displays the number of drops per minute. The second answer displays how many drops fall in 15 seconds. Sometimes the IV rate is set by counting for 15 seconds instead of a full minute.
→ infusion doses formula
Example
You have received a patient from another hospital on a dopamine drip except no information was given about it. The bag is labeled with the concentration of 800 mg in 500cc of D5W. The IV pump is infusing at 53 cc/hr and the patient weighs 70kg. How much dopamine is this patient receiving? Use the example below to see how this problem was solved.
rate = 53mL/hr
weight = 70kg
dose available = 800
ml available = 500
Using the calculator, we know the patient is receiving 20 mcg/kg/min of dopamine.
Formula
Using the example above, first determine how many milligrams/hour is being delivered by the IV pump. The rate of the IV (cc/hr) is divided by the volume of the IV bag (mL available), then multiply this result by the total amount of medication (mg) in the IV bag.
( rate/mL available )x dose available
becomes
( 53mL/hr /500mL )x 800mg
which = 84.8 mg/hr
Next, after the milligrams/hour has been determined, use the next formula to convert from milligrams/hour to mcg/kg/min.
( mg /60min) x 1000 / kg
becomes
(84.8mg/60min) x 1000 / 70
which = 20.2 mcg/kg/min
PROFESSIONAL RESPONSIBILITIES
All nurses who administer medication must have undertaken a programme of education and demonstrated competence under supervision.
The practitioner is responsible for ensuring that her or his practice is compliant with Nursing guidelines. The practitioner should also ensure that she or he is familiar with local trust policies.
10 R' practice
1) right patients
2) right drug
3) right route
4) right time
5) right dose
6) right to refuse
7) right health education
8) right assessment
9) right evaluation
10) right documentation
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