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Advanced Calculations
Nursing 201
Ms. Frasier
Summer 2014
Dimensional Analysis
 Simple technique with a fancy name
 Allows manipulation of units
 Also referred as factor label
method or the unit factor
method
 Less errors
 The advantage of dimensional analysis
is only one equation is needed
Review
 ml/hr
 gtt/min
Infusion of IV fluids with an IV pump
 Solve for mL/h
 The formula: x mL/h = Total volume in milliliters
Total time in hours
 On the left side of the equation, place what you are solving
𝑚𝑙
for.
X =
ℎ𝑟
 On the right side of the equation, place the available
information related to the measurement that was placed
on the left side of the equation. 1000ml
8h
 Answer 125mL/hr
Drops per minute (gtt/min)





Knowing the drop factor is the first step
The drop factor always appears on the IV package
Macrodrops are large and deliver 10, 15, 20 gtt/mL
Microdrops are small and deliver 60 gtt/mL
Drop factor = gtt/mL
Example: order: D5W to infuse at 100ml/hr. drop factor
10gtt/mL. at what rate in gtt/min should the IV be regulated?
1. You are calculating for gtt/min, so write gtt/min to the left of
the equation, (that is what you are looking for)
2. Extract the information that contains gtt/min from the
problem; drop factor is 10gtt/mL. add this factor into the
equation. X gtt = 10gtt
min
mL
 The next fraction is written so that the denominator matches
the previous fraction (what you are looking for). Looking back
at problem we are to infuse 100mL in 1 hr. enter the 1hr as
60min since we are looking for gtt/min.
𝑥𝑔𝑡𝑡
𝑚𝑖𝑛
=
10𝑔𝑡𝑡 ×100𝑚𝐿
1𝑚𝐿 × 60𝑚𝑖𝑛
=
1000
60
= 16.6 =17𝑔𝑡𝑡/𝑚𝑖𝑛
 Order: An IV medication of 50mL NS in 20 min. drop factor
(60gtt/mL). At what rate in gtt/min should the IV be
regulated?
 You are calculating gtt/min, so write gtt/min to the left of the
equation, followed by equals sign, label x, since that is what
you are looking for: extract the information that contains gtt
from the problem. Drop factor 60gtts/mL. numerators match
up
𝑥𝑔𝑡𝑡
𝑚𝑖𝑛
₌
60𝑔𝑡𝑡
𝑚𝐿
×
50𝑚𝐿
20
=
3000
20
= 150𝑔𝑡𝑡/𝑚𝑖𝑛
Practice Problems
Calculate the flow rate in mL/hr using dimensional analysis
1. 1,800 mL of D5W in 24 hr by infusion pump _____________
2. 2,000 mL D5W in 24 hr by infusion pump _______________
3. 500 mL RL in 12 hr by infusion pump __________________
4. 100 mL 0.45% NS in 45 min by infusion pump ___________
5. 1,500 mL D5LR in 24 hr by infusion pump _______________
6. 750mL D5W in 16 hr by infusion pump ________________
7. 30 mL of Ancef in 0.9% NS in 20min by infusion pump _____
Answers
=
1800𝑚𝑙
24ℎ𝑟
= 75𝑚𝐿/ℎ𝑟
2. × ℎ𝑟 =
2000𝑚𝑙
24ℎ𝑟
= 83.3 = 83𝑚𝐿/ℎ𝑟
1. ×
𝑚𝐿
ℎ𝑟
𝑚𝑙
𝑚𝐿
3. 𝑥 ℎ𝑟 =
𝑚𝐿
4. × ℎ𝑟 =
5. ×
𝑚𝐿
ℎ𝑟
=
500𝑚𝐿
12ℎ𝑟
= 41.6 = 42𝑚𝑙/ℎ𝑟
100𝑚𝐿
45𝑚𝑖𝑛
1500𝑚𝐿
24ℎ𝑟
𝑚𝐿
750𝑚𝐿
16ℎ𝑟
𝑚𝑙
30𝑚𝐿
6. × ℎ𝑟 =
×
60𝑚𝑖𝑛
1ℎ𝑟
=
400
3
= 133mL/hr
= 62.5 = 63mL/hr
= 46.8 = 47 𝑚𝐿/ℎ𝑟
7. × ℎ𝑟 = 20𝑚𝑖𝑛 ×
60𝑚𝑖𝑛
1ℎ𝑟
=
90
1
= 90𝑚𝐿/ℎ𝑟
Practice Problems
Calculate the flow rate in gtt / min using dimensional analysis
1. Administer D5LR at 75mL/hr. the drop factor is 10gtt/mL
2. Administer D5NS at 30mL/hr. the drop factor is a microdrop
3. Administer RL at 125mL/hr. the drop factor is 15gtt/mL
4. Administer 1000 mL D5NS in 6 hrs. the drop factor is 15gtt/mL
5. An IV medication in 60mL of NS is to be given in 45 min. the
drop factor is a microdrop
6. 1000 mL of LR is to infuse in 16 hr. the drop factor is 15gtt/mL
7. Infuse 150mL of D5W in 2hr. The drop factor is 20gtt/mL
Answers
1. ×
𝑔𝑡𝑡
𝑚𝑖𝑛
×
75𝑚𝐿
ℎ𝑟
=
60
𝑚𝐿
×
30𝑚𝐿
ℎ𝑟
3. × 𝑚𝑖𝑛 =
15
𝑚𝐿
×
125𝑚𝑙
1ℎ𝑟
2. ×
𝑔𝑡𝑡
𝑚𝑖𝑛
=
10𝑔𝑡𝑡
𝑚𝐿
𝑔𝑡𝑡
𝑔𝑡𝑡
4. × 𝑚𝑖𝑛 =
×
×
×
1ℎ𝑟
60𝑚𝑖𝑛
1ℎ𝑟
60𝑚𝑖𝑛
=
=
60
2
750
60
=
= 12.5 =
13𝑔𝑡𝑡
𝑚𝑖𝑛
30𝑔𝑡𝑡
𝑚𝑖𝑛
1ℎ𝑟
1875
31𝑔𝑡𝑡
=
= 31.25 =
60
𝑚𝑖𝑛
60𝑚𝑖𝑛
15𝑔𝑡𝑡
1000𝑚𝐿
1ℎ𝑟
×
×
= step 1: calculate mL/hr
𝑚𝐿
6ℎ𝑟
60𝑚𝑖𝑛
15𝑔𝑡𝑡
167𝑚𝐿
1ℎ𝑟
2505
×
×
=
= 41.7 = 42𝑔𝑡𝑡/𝑚𝑖𝑛
𝑚𝐿
1ℎ𝑟
60𝑚𝑖𝑛
60
𝑔𝑡𝑡
60𝑔𝑡𝑡
𝑚𝐿
𝑔𝑡𝑡
15𝑔𝑡𝑡
1000𝑚𝐿
1ℎ𝑟
×
×
= 𝑠𝑡𝑒𝑝 1: 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑚𝐿/ℎ𝑟
𝑚𝐿
16ℎ𝑟
60𝑚𝑖𝑛
15𝑔𝑡𝑡
63𝑚𝐿
1ℎ𝑟
63
×
×
=
= 15.75 = 16𝑔𝑡𝑡/𝑚𝑖𝑛
𝑚𝑙
1ℎ𝑟
60𝑚𝑖𝑛
4
5. × 𝑚𝑖𝑛 =
6. × 𝑚𝑖𝑛 =
×
60𝑚𝐿
45𝑚𝑖𝑛
=
240
3
=
80𝑔𝑡𝑡
𝑚𝑖𝑛
Critical Care Calculations
 Critically ill clients receive medications that are potent and
require close monitoring
 Titrated medications are added to a specific volume of fluid
and rate adjusted to desired effect; when a solution is
titrated, the lowest dosage of the med is set first and ↑ or ↓
as necessary
 The drugs that are titrated are potent antiarrhythmics,
vasopressor, and vasodilator medications
 Infusion pumps are used for titration
Critical Care Calculations
• Volume
• mL / hr
• Dosage
•
•
•
•
•
•
•
•
mg / min
mg / hr
mcg / min
mcg / hr
mcg / kg / min
mg / kg / min
mcg / kg / hr
mg / kg / hr
• mg / min
• mg / hr
A client is receiving Pronestyl 60mL/hr. the solution available is
pronestyl 2g in 500mL D5W . Calculate the mg/hr and the mg/min
the client will receive.
𝑚𝑔
x
ℎ𝑟
×
=
𝑚𝑔
𝑚𝑖𝑛
1000𝑚𝑔
1𝑔
=
×
1000𝑚𝑔
1𝑔
2𝑔
500𝑚𝐿
×
×
2𝑔
500𝑚𝐿
60𝑚𝐿
1ℎ𝑟
×
=
60𝑚𝑙
60𝑚𝑖𝑛
240𝑚𝑔
1ℎ𝑟
=
= 240𝑚𝑔/ℎ𝑟
240𝑚𝑔
60
=4 mg/min
 mcg / min
 mcg / hr
Order: a patient with heart failure has nitroglycerin infusing at
3mL/h. the nitroglycerin concentration is 100mg in 500 mL of
D5W. At what rate, in micrograms per minute, is the
nitroglycerin infusing?
×
𝑚𝑐𝑔
𝑚𝑖𝑛
×
𝑚𝑐𝑔
ℎ𝑟
=
1000𝑚𝑐𝑔
1𝑚𝑔
×
100𝑚𝑔
500𝑚𝐿
=
1000𝑚𝑐𝑔
1𝑚𝑔
×
100𝑚𝑔
500𝑚𝐿
×
3𝑚𝐿
1ℎ𝑟
×
×
3𝑚𝐿
ℎ𝑟
1ℎ𝑟
60𝑚𝑖𝑛
=
=
600𝑚𝑐𝑔
ℎ𝑟
600
60
=
10𝑚𝑐𝑔
𝑚𝑖𝑛
• mcg/kg/min
• mcg/kg/hr
Order: 400 mg of dopamine is added to 250ml. Of 0.9% NS. The
order is to begin the infusion at 2mcg/kg/min. the patient’s weight
is 150lb. The nurse needs to calculate the rate, in milliliters per
hours, at which to set the IV pump.
1. Convert client’s weight to kilograms:
150lb ÷2.2 = 68.18𝑘𝑔 = 68.2𝑘𝑔
2. Now that you have the client’s weight in kg, determine the
dosage per min.
68.2kg x 2mcg/kg/min = 136.4mcg/min
𝑚𝑙
x
ℎ𝑟
=
250𝑚𝑙
400𝑚𝑔
×
1𝑚𝑔
1000𝑚𝑐𝑔
×
136.4𝑚𝑐𝑔
1𝑚𝑖𝑛
×
60𝑚𝑖𝑛
1ℎ𝑟
=
40,920
= 5 𝑚𝑙/ℎ𝑟
8000
Practice Problems
1. A client weighing 50kg is to receive a Dobutrex solution of
250mg in 500ml D5W ordered to titrate between 2.5 and 5
mcg/kg/min.
a. Determine the flow rate setting for a volumetric pump.
b. If the IV flow rate is being maintained at 25mL/hr after
several titrations, what is the dosage infusing per minute?
2. Order: Epinephrine at 30mL/hr. The solution available is 2mg
of epinephrine in 250mL D5W. Calculate the following:
a. mg/hr
b. mcg/hr
c. mcg/min
3. Aminophylline 0.25g is added to 500mL D5W to infuse at
20mL/hr. Calculate the following:
a. mg/hr
4. Order: 3mcg/kg/min of Nipride:
Available: 50mg of Nipride in 250mL D5W . Client’s weight is 60
kg.
a. Calculate the flow rate in mL/hr that will deliver this dosage.
5. A nitroglycerin drip is infusing at 3mL/hr. The solution
available is 50mg of nitroglycerin in 250mL D5W. Calculate the
following:
a. mcg/hr
b. mcg/min
Heparin IV
• HIGH ALERT MEDICATION
• Heparin is a potent anticoagulant that prevents clot formation
and blood coagulation
• Expressed in units (no “U” abbreviation)
• The therapeutic range for heparin is determined individually
by monitoring the client’s blood clotting value (APTT –
activated partial thromboplastin time)
• Heparin is considered to be more therapeutic when based on
weight in kg.
• May be given SQ or IV. Never IM.
• Should always be on a pump…will be ordered either ml/hr or
units/hr
• Remember heparin comes in many different strengths. Make
sure you have the correct one.
Examples
• mL/hr – units/hr
Order: 15 units/hour. On hand you have 40units in 250ml of NS.
How many ml/hr will you administer?
𝑚𝑙
ℎ𝑟
=
250𝑚𝑙
40𝑢𝑛𝑖𝑡𝑠
×
15𝑢𝑛𝑖𝑡𝑠
ℎ𝑟
=
3750
40
= 94 ml/hr
Order: D5W 1000ml containing 20,000 units of heparin to infuse
at 30mL/hr. calculate the dosage of heparin the client is to receive
per hour.
𝑢𝑛𝑖𝑡𝑠
ℎ𝑟
=
20,000𝑢𝑛𝑖𝑡𝑠
1000𝑚𝐿
×
30𝑚𝐿
ℎ𝑟
=
600000
1000
= 600 units per hour
Calculating heparin dosages based on weight
A client weighs 165 lb.
Order: heparin 25,000 units in 1000ml 0.9% sodium chloride.
Bolus with heparin at 80units/kg, then initiate drip at
18units/kg/hr. calculate the initial bolus dosage, then calculate
the infusion rate at ml/hr.
𝑥 𝑢𝑛𝑖𝑡𝑠
𝑚𝑙
ℎ𝑟
Or
=
=
80𝑢𝑛𝑖𝑡𝑠
𝑘𝑔
1000𝑚𝐿
25000𝑢𝑛𝑖𝑡𝑠
𝑚𝑙
ℎ𝑟
=
×
×
𝑜𝑛𝑒 𝑘𝑔
2.2𝑙𝑏
1350𝑢𝑛𝑖𝑡𝑠
ℎ𝑟
1000𝑚𝑙
25000𝑢𝑛𝑖𝑡𝑠
×
=
18𝑢𝑛𝑖𝑡𝑠
𝑘𝑔
x
165𝑙𝑏
1
1350
25
×
=
13200
= 6000 𝑢𝑛𝑖𝑡𝑠 𝐼𝑉 bolus
2.2
= 54ml/hr
75𝑘𝑔
ℎ𝑟
=
1350 𝑚𝑙
25𝑢𝑛𝑖𝑡𝑠
= 54𝑚𝐿/ℎ𝑟
A client weighs 176 lb. Heparin infusion 20,000 units in 1000mL
0.9% sodium chloride.
Order: bolus with heparin sodium at 80units/kg, then initiate
drip at 18units/kg/hr. Calculate the following:
a. ___________ bolus dosage
b. ___________ infusion rate (initial)
c. ___________ mL/hr
Answers: 6400 units, 1440units/hr, 72mL/hr
46. pg.519 Order: Heparin drip at 18units/kg.
Available: 25,000units of heparin in 1,000mL of D5W. The client
weighs 80 kg. At what rate will you set the infusion pump?
First determine units/kg the client should receive.
18x80 = 1440units then mL/hr
Answer: 58 mL/hr
47. Pg 519 A client weighs 200 lb.
Order: Administer a bolus of heparin sodium IV at 80units/kg. how
many units will you administer:
𝑢𝑛𝑖𝑡𝑠 = 80𝑢𝑛𝑖𝑡𝑠
𝑥
𝑘𝑔
×
1𝑘𝑔
2.2 𝑙𝑏
×
200𝑙𝑏
1
= 7,272 𝑢𝑛𝑖𝑡𝑠
48. pg. 520 A client weight 210 lb.
Order: Heparin IV infusion: heparin sodium 25,000 units in 1,000
mL of 0.9% NS. Order is give a bolus with heparin sodium
80units/kg, then initiate drip at 18units/kg/hr.
Calculate the following:
a. Heparin bolus dosage ____________________
b. Infusion rate for the IV (initial) _____________
c. At what rate will you set the infusion pump? ___________
• Practice! Practice! Practice!
• Review Heparin Weight Based Protocol