Math for Nurses

  Sample IV problems for nurses

IV Problems 
Calculating drip rate:

Drip rate is the number of drops per minute to be infused (gtt/min).
Drip factor of the tubing is found on the manufacturer's packaging. (expressed as gtt/ml)
If the problem states microdrops (microgtts), then the drip factor of the tubing is 60 gtt/ml.
total # of milliliters (volume)
   total # of minutes (time)  x drip factor = gtt/min


The physician orders IV fluids to hydrate a client. The order is written as "D5NS 4 Liters over 24 hours."  Looking at the package indicates the drip factor of the tubing is 15 gtt/ml.  What is the drip rate?
Critical information:
Volume = 4000 ml
Time = 24 hours
Drip factor of tubing = 15 gtt/ml.
How many minutes is the ordered time period?
24 (hr) x 60 (minutes) = 1440 minutes
4000 ml
1440 minutes  X 15 gtt
 1 ml
4000 x 15 = 60000
60000 / 1440 = 41.66

Answer:  41.66 gtt/min or 42 (if your instructor wants you to "round").

Order: Run current IV fluids at 175 ml/hr for 2 hours.
Critical information:
Volume = 175 ml
Time = 1 hr
(What is the drip factor of the tubing?  Assume 15 gtt/ml unless otherwise indicated.  Exception would be: If on infusion pump or problem states microgtts, use 60 gtt/ml)
Extraneous information for calculating:
2 hours (but important in carrying out the order).
175 ml
60 min  x 15 gtt
1 ml
175 x 15 = 2625
2625 / 60 = 43.75

Answer: 43.75 gtt/min or 44 (if your instructor wants you to "round").


Shortcut method when you know the ordered ml/hr: 15 gtt/ml: divide the ml/hr by 4
10 gtt/ml (typically blood products): divide ml/hr by 6
20 gtt/ml: divide ml/hr by 3

Shortcut method
175 / 4 = 43.75 gtt/min
175 / 6 = 29.16 gtt/min
175 / 3 = 58.33 gtt/min

(Most nurses can calculate this way "in their head" at the bedside.)


Sometimes the nurse will need to administer an intravenous med at a prescribed concentration.

The client's K+ is 2.0 mEq/dl and the physician orders a potassium bolus of 40 mEq of KCl in 200 ml of NS to be delivered at a rate of 10 mEq/hr.  What is the drip rate in microdrops? (Ideal, deliver on a pump.)
Critical information:
How many ml is needed to provide 10 mEq?
Flow rate = 10 mEq
Drip factor = 60 gtt/ml
This is a two-part problem.
Calculate the concentration of the KCl in the NS using ratio and proportion.
40 mEq
200 ml  = 10 mEq
x ml
40x = 2000
x  =  50

Now you can use the IV formula.
50 ml
60 min  x 60 gtt
1 cc
50 x 60  = 3000
3000 / 60  = 50

Answer: 50 (microgtts/min)
You could have canceled out the 60s.
50 ml
60 min x 60 gtt
1 ml
x  =  50
This technique can be used to calculate drip rate of many continuos infusions of IV meds.

(Baxter IV Pump)
 Calculating flow rate:

Flow rate refers to number of ml of fluid to be infused over one hour (ml/hr).
total # of milliliters (volume)
total # of hours  = X ml/hr
Order: 500 ml NS bolus over 3 hours
Critical information:
Volume = 500 ml
Time = 3 hours
500 ml
3 hrs = ?  or 500 ml 3 hrs
 = x ml 1 hr
500 / 3 = 166.67 3x = 500

Answer:  166.67 ml/hr or 167 (if your instructor wants you to "round").
    Calculating time if given the flow rate:
The nurse needs to know how long a volume of fluid in the IV bag at the current flow rate will last, i.e.., When will a new bag need to be hung?
Flow rate = (Infusion) time

The nurse makes rounds and notes that the current IV bag contains approximately 450 ml. The IV flow rate is 150 ml/hr.  How long will it be before the nurse must hang a new bag?
Critical information:
Volume = 450 ml
Flow rate = 150 ml/hr
450 ml
150 ml/hr  = .
450 / 150 = 3 hr

Calculating time if given the drip rate:

Sometimes exam problems provide you with the volume to be given and the drip rate of the IV and you must calculate how long (time) it will take to infuse.

Critical information for calculation:

Must be given volume to be infused

Must be given drip rate (gtt/min)

Must know drip factor (gtt/ml)

Time is constant (1 hr = 60 minutes)

drip rate  volume  drip factor  time constant  time
1 min
x gtt  x
 x  x gtt
1 ml  x  1 hr
60 min  =  x hr

Order:  Administer 1000 cc at 50 gtt/min.

Critical information:

Volume = 1000 ml
Drip rate =  50 gtt/min
Known = time constant (1 hr = 60 min)
Missing = drip factor of tubing (You would use what is available or standard protocol for the unit you are working in.  Assume 15 gtt/ml unless otherwise indicated.)
1 min
50gtt/min  x  1000 ml  x  15 gtt
1 ml  x  1 hr
60 min  =  x hr

1 x 1000 x 15 x 1
50 x 1 x 60  =
3000  =

Answer =  5 hr
You can use the principle of reducing to minimize the number you will have to deal with.  
    Administering fluids/medications via an infusion pump

How do I use the pump to deliver the right dose?
Each brand of infusion pump has specific tubing, filling volumes, filters and other accessories.
A problem indicates that a medication or fluid is to be given via an infusion pump.    Even though the problem may state the tubing that is specific to the particular pump has a "drip factor of 15 gtts/ml or 20 gtts/ml", it will still be delivered the equivalent to 60 gtts/ml if it is placed on the pump.  Remember when the physician orders x ml/hr or you calculate x ml per hour, that is essentially what you dial into the IV pump.
John is to receive Cleocin 150 mg IV q 8 hours. The nurse dilutes the medication to a total volume of 30 ml and plans to deliver it via an infusion pump over thirty minutes.  What would be the flow rate?
Critical information:
Volume = 30 ml
Use of an infusion pump (equivalent of drip factor of tubing) = 60 gtts/ml
Time = 30 minutes
Extraneous information for calculation:
Cleocin 150 mg IV q 8 hours.
30 (cc)  x  60 (gtt / ml)
30 ( min)
30  x  2
flow rate =  60

Numbers to be dialed into the pump = 60

Hint:  Use the principle of reducing fractions to reduce 60/30 to 2.

Note this is 30 multiplied by 2, not 30x which then is set up as the divisor.
The doctor writes an order for D5 NS to run at 90 cc/hr.  The packaging for the IV tubing indicates that the drip factor of the tubing is 15 gtt/cc.  Hospital policy states that all fluids are placed on a pump.  How will the nurse set the infusion pump?
Critical information:
Doctor's order of 90 ml/hr
Use of an infusion pump.
Extraneous information for calculation:
Drip factor of the tubing.
Answer:  Set the pump for 90.