Nursing Mathematics
PO AND IV CALCULATIONS
DOSAGE Calculations:
Desired Dose (mg)
Dose on Hand (mg)
x Volume Dose on Hand (mL) = Volume Desired Dose (mL)
Flow Rate (Drip Rate):
Drip rate (gtt/min) = Volume to be infused (mL) x Drop factor of tubing (gtt/mL)
Time (min)
Infusion Time:
Infusion time (hr) = Total Volume to be INFUSED (mL)
Infusion Rate(mL/hr)
Example One: The doctor’s order reads NaCl 750 mL over a 24-hr shift.
a) Calculate the mL/hr.
b) How much NaCl will the client receive in a 6-hr shift?
c) Calculate the drip rate using a drop factor of 15 gtt/mL.
Solution:
Part Set Up
Operation
a)
Rate (mL/hr) = Total Volume to be INFUSED (mL)
31.25 0
24)750.00
Time(min)
= 750 mL
- 72
24hr
30
- 24
60
- 48
120
- 120
0
b)
Volume (mL) = Rate (mL/hr) x Time (hr)
3125 
31.25
= 31.25 mL x 6 hr
x
6
x
6
hr
18750
187.50
Answer
The rate is 31.25 mL .
h
hr
The client will receive
187.5 mL of NaCl in a
6-hr shift.
c)
Drip rate(gtt/min)
= Volume to be infused (mL) x Tubing factor(gtt/mL)
Time (min)
= 31.25 mL x 15 (gtt/mL)
60 min
Step
One
3125
x 15
15625
+31250
46875
31.25
x 15
468.75
Step Two
The drip rate is
7.8175 gtt .
min
7.8125
0
60)468.7500
- 420
487
- 480
75
- 60
150
- 120
300
- 300
0
Example Two: An IV solution of 1044.6 mL at a flow rate of 30 gtt/min using a drop factor of 15 gtt/mL has
been ordered to be initiated at 1000.
a) Calculate the infusion time.
b) Calculate the completion time.
Solution:
Part Set Up
Operation & Answer
a)
Drip rate (gtt/min)
8.705
0
= Volume to be infused (mL) x Tubing factor(gtt/mL)
1200)10446.000
Time (min)
- 9600
30 (gtt/min) = Volume (mL) x15 (gtt/mL)
8460
Time (min)
- 8400
= Infusion Rate (mL/hr) x15 (gtt/mL)
600
- 0
Infusion Rate = 30 (gtt/min) ÷ 15 (gtt/mL) = 2 (mL/min)
6000
- 6000
120 (mL/hr) = 120 (mL/hr) ÷ 60 min =2 (mL/hr)
0
The infusion time is 8.705 hours.
b)
Infusion time (hr) = Total Volume to be INFUSED (mL)
Infusion Rate (mL/hr)
= 1044.6 mL
120 (mL/hr)
8.705 hr = 8 hr + 0.705 hr
0.705 hr x 60 min =
Completion time:
1000
+ 0843
705

0.705
x 60
x 60
42300
42.300
Thus, 8.705 hours = 8hours 43 min.
1000
+ 0843
1843
Thus, the completion time is 1843.
Practice (answers provided):
IT IS IN YOUR BEST INTEREST TO ATTEMPT THE QUESTIONS BY YOURSELF BEFORE CHECKING
THE ANSWERS.
1) Prepare an 8mg IV dosage from a vial labeled 50mg/10mL.
2) A dosage of 0.6 mg is ordered. The label reads 300 mcg/mL. How much will you administer?
3) To administer a dosage of fentanyl 0.01 mg from an ampule labeled Fentanyl 15 mcg in 2mL.
4) A. Calculate the correct dosage to be administered.
Cleocin Phosphate 0.12 g po bid
Source (for label): http://www.dailymedplus.com/monograph/view/setid/05a75685-0af5-407c-ac57e380c882b49d
B. How much Cleocin Phosphate will the patient intake in a day?
5) Doctor’s order: 360mg
Source (for label): http://www.cwladis.com/math104/lecture4.php
a. How much diluent should be added to the vial to reconstitute the medication?
.
b. What’s the final concentration after reconstitution?
c. How much of the reconstituted medication should be drawn up and added to the
minibag?
6) The doctor’s order: 1.5 L of NS to be infused in a 12-hr period. The drop factor is 60gtt/mL.
Calculate:
a. mL/hr
b. gtt/min
7) The doctor writes an IV order at 125mL/hr. At the beginning (1200) of your shift there is
450mL TBA. The drop factor is 10gtt/mL.
a. Calculate the drip rate.
b. What time (military time) will you change the bag?
8) Mr. Jane has an IV order at 120cc/hr. Calculate the drip rate with a drop factor of 10gtt/mL
9) Ordered: Pencillin G potassium 1 million units IV q2h
Amount of Sterile Water to be Final Dosage Strength
Pfizerpen®
Added (mL):
(units/mL):
Penicillin G Potassium
30
400,000
10,000,000 units
20
600,000
For Intravenous Infusion ONLY
8
1,000,000
For dosage information read the accompanying professional
information. After reconstitution, discard the unused portion
Caution: Federal law prohibits
after 24 hours.
dispensing without prescription.
Source: Math For Meds,6E from Curren, A.M. & Munday, L.D. Ch.12 Pg.130 (modified questions)
a. To make a solution with 600,000 units/mL strength, how much diluent should you add
to the vial?
b. If the medication in the vial is reconstituted with 8 mL of diluent, what solution
strength should you write on the label?
c. When reconstituted with 30 mL, how much solution should you administer?
d. If doctor’s IV order changes to 4,000,000 units of Penincillin G in 270mL of Sterile
Water and to infuse over 2 hours. The vial requires reconstitution with 8 mL of sterile
water. How much of the medication would you administer now?
e. If the drop factor is 10gtt/mL, what is the drip rate of Penincillin G IV?
ANSWER KEY
1) Desired Dose x Volume =
Dose on Hand
8 mg x 10 mL = 1.6 mL
50 mg
2) 0.6 mg = 600 mcg
Desired Dose x Volume =
Dose on Hand
600 mcg x 1 mL = 2 mL
300 mcg
3) 0.01 mg = 10 mcg
Desired Dose x Volume =
Dose on Hand
10 mcg x 2 mL = 1.33 mL
15 mcg
4)
A. 0.12 g = 120 mg
Desired Dose x Volume = 120 mg x 50 mL = 10 mL
Dose on Hand
600 mg
B.
bid  twice a day
10 mL x 2 times = 20 mL per
day
5)
a. 2 mL of sterile water must be added
c.
Desired Dose x Volume = 360 mg
Dose on Hand
225 mg
b. 225 mg/mL
x 1 mL = 1.6 mL
6)
a.
The answer must be in mL/hr. This indicates that we have to calculate the infusion rate.
Infusion Rate(mL/hr) = Volume (mL) = 1500 mL = 125 mL/hr
Time (hr)
12 hr
b.
The answer must be in gtt/min. We must calculate the flow rate/drip rate.
Two ways we can do this:
Method one: Drip rate (gtt/min) = Volume (mL) x Drop factor (gtt/mL) = 1500mL x 60 gtt/mL = 125
gtt/min
Time (min)
5 x 60 min
Method two: Drip rate (gtt/min) = Volume (mL) x Drop factor (gtt/mL) = 125mL x 60 gtt/mL = 125
gtt/min
Time (min)
60 min
7)
a. Drip rate (gtt/min) = Volume (mL) x Drop factor (gtt/mL) = 125mL x 10 gtt/mL = 20.83
gtt/min
Time (min)
60 min
b. Infusion time (hr) = Volume (mL) = 450 mL
= 3.6 hr
Rate(mL/hr)
125 mL/hr
3.6 hr = 3hr + 0.6 hr
0.6 x 60 min = 36 min  0.6 hr = 36 min
I will change the bag at: 1200+ 0336 = 1536
8) 1 cc = 1 mL
Drip rate (gtt/min) = Volume (mL) x Drop factor (gtt/mL) = 120 mL x 10 gtt/mL = 20 gtt/min
Time (min)
60 min
9)
a.
We should add 20 mL of sterile water.
b.
The solution strength will be 1,000,000 units/mL.
c.
When reconstituted with 30 mL, the dosage strength is 400,000 units/mL.
Desired Dose x Volume = 1,000,000 units x 1 mL = 2.5 mL
Dose on Hand
400,000 units
d.
When reconstituted with 8 mL, the dosage strength is 1,000,000 units/mL.
Desired Dose x Volume = 4,000,000 units x 1 mL = 4 mL
Dose on Hand
1,000,000 units
e.
Drip rate (gtt/min) = Volume (mL) x Drop factor (gtt/mL) = 270 mL x 10 gtt/mL
Time (min)
2 x 60 min
= 22.5 gtt/min