```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

for.
X =
ℎ
 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
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.

=
10 ×100
1 × 60
=
1000
60
= 16.6 =17/
 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

₌
60

×
50
20
=
3000
20
= 150/
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 _____
=
1800
24ℎ
= 75/ℎ
2. × ℎ =
2000
24ℎ
= 83.3 = 83/ℎ
1. ×

ℎ

3.  ℎ =

4. × ℎ =
5. ×

ℎ
=
500
12ℎ
= 41.6 = 42/ℎ
100
45
1500
24ℎ

750
16ℎ

30
6. × ℎ =
×
60
1ℎ
=
400
3
= 133mL/hr
= 62.5 = 63mL/hr
= 46.8 = 47 /ℎ
7. × ℎ = 20 ×
60
1ℎ
=
90
1
= 90/ℎ
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
1. ×

×
75
ℎ
=
60

×
30
ℎ
3. ×  =
15

×
125
1ℎ
2. ×

=
10

4. ×  =
×
×
×
1ℎ
60
1ℎ
60
=
=
60
2
750
60
=
= 12.5 =
13

30

1ℎ
1875
31
=
= 31.25 =
60

60
15
1000
1ℎ
×
×
= step 1: calculate mL/hr

6ℎ
60
15
167
1ℎ
2505
×
×
=
= 41.7 = 42/

1ℎ
60
60

60

15
1000
1ℎ
×
×
=  1:  /ℎ

16ℎ
60
15
63
1ℎ
63
×
×
=
= 15.75 = 16/

1ℎ
60
4
5. ×  =
6. ×  =
×
60
45
=
240
3
=
80

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

x
ℎ
×
=

1000
1
=
×
1000
1
2
500
×
×
2
500
60
1ℎ
×
=
60
60
240
1ℎ
=
= 240/ℎ
240
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?
×

×

ℎ
=
1000
1
×
100
500
=
1000
1
×
100
500
×
3
1ℎ
×
×
3
ℎ
1ℎ
60
=
=
600
ℎ
600
60
=
10

• 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 = 68.18 = 68.2
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

x
ℎ
=
250
400
×
1
1000
×
136.4
1
×
60
1ℎ
=
40,920
= 5 /ℎ
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
• 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?

ℎ
=
250
40
×
15
ℎ
=
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.

ℎ
=
20,000
1000
×
30
ℎ
=
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.

ℎ
Or
=
=
80

1000
25000

ℎ
=
×
×

2.2
1350
ℎ
1000
25000
×
=
18

x
165
1
1350
25
×
=
13200
= 6000   bolus
2.2
= 54ml/hr
75
ℎ
=
1350
25
= 54/ℎ
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
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
47. Pg 519 A client weighs 200 lb.
Order: Administer a bolus of heparin sodium IV at 80units/kg. how
= 80

×
1
2.2
×
200
1
= 7,272
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
```