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CALCULATIONS

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Terms & Concepts What is the IV flow rate? The speed at which intravenous fluid infuses into the body What is the drop factor? The number of drops (abbreviated “gtt”) required to deliver 1mL of fluid What determines gtt/mL? The size of the IV administration set (tubing) What are the tubing sizes? 10, 15, or 20 gtt/mL (Macrodrip tubing) 60 gtt/mL (Microdrip tubing) How do you calculate the IV flow rate? Using the IV flow rate formula

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IV Flow Rate Formula IV Flow Rate Formula is used when calculating an infusion by gravity (without an IV pump). Volume to be Infused (in mL) x Drop Factor = Flow Rate Total Infusion Time (in minutes) (in gtt/min) Electronic Flow Rate Formula is used when calculating an infusion by IV pump (electronic infusion device, or EID). Volume to be Infused (in mL) = Flow Rate Total Infusion Time (in hours) (in mL/h) *Round all rates to the nearest whole number

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Dosage Calculations Complete necessary conversions (i.e. dosage per weight, mass, volume, etc) prior to using either of the two previous flow rate formulas. Conversions may be calculated using: Ratio/Proportion Dimensional Analysis Whatever method you are most comfortable with and use consistently/correctly

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800mL ÷ 10 hours = 80mL/h Volume to be Infused (in mL) = Flow Rate Total Infusion Time (in hours) (in mL/h) Order: Infuse 800mL of NS in 10 hours. This is a straight-forward IV flow rate calculation, in which no conversion is required. We know we will be using the Electronic Flow Rate Formula because we were not given the tubing size or drop factor, which would be required to calculate a gravity flow rate. The correct formula is: #1

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150mL x 20gtt/mL ÷ 30 minutes = 100gtt/min Order: Infuse 150mL of D5W in 30 minutes using an administration set with a drop factor of 20gtt/mL. This is also a straight-forward IV flow rate calculation, in which no conversion is required. We know we will be using the IV Flow Rate Formula because we were given the drop factor. The correct formula is: #2 Volume to be Infused (in mL) x Drop Factor = Flow Rate Total Infusion Time (in minutes) (in gtt/min)

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Order: Infuse 100mL of LR by IV pump in 20 minutes. We know we will be using the Electronic Flow Rate Formula because we were directed to use an IV pump, and because we were not given the tubing size or drop factor. Before using our flow rate formula, we must complete the necessary conversion(s). To use our Electronic Flow Rate Formula, we need the total volume to be infused in mL (which we know), and the total infusion time in hours (which we don’t know). We must convert minutes to hours using our chosen dosage calculation method. #3

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Order: Infuse 100mL of LR by IV pump in 20 minutes. Our calculation method of choice is ratio/proportion, which involves a 3-part process: 1) Set up ratio, 2) Cross-multiply, 3) Isolate X by dividing its value by itself Step 120 min = X hour 60 min 1hour Step 260( X ) = 20(1) or 60 X = 20 Step 360 X = 20 so X = CONTINUED

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Order: Infuse 100mL of LR by IV pump in 20 minutes. Now that we have converted minutes to hours (20 minutes = 0.33 hours), we can use our Electronic Flow Rate Formula to solve our IV dosage calculation problem. (The IV pump would be programmed for 303 mL per hour in order to infuse the desired 100 mL in 20 minutes.) 100mL ÷ 0.33 hours = 303mL/h CONTINUED

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Order: Infuse 200mL of D5W in 4 hours using a Microdrip tubing. We know we will be using the IV Flow Rate Formula because we were given a tubing size (remember that a Microdrip administration set delivers 60gtt/mL). Before using our flow rate formula, we must complete the necessary conversion(s). To use our IV Flow Rate Formula, we need the total volume to be infused in mL (which we know), the drop factor (which we also know), and the total infusion time in hours (which we don’t know). We must convert hours to minutes using our chosen dosage calculation method. #4

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Order: Infuse 200mL of D5W in 4 hours using a Microdrip tubing. Complete the conversion calculation. Step 14 hours = X minutes 1 hour 60 minutes Step 21( X ) = 4(60) or 1 X = 240 Step 31 X = 240 so X = CONTINUED

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Order: Infuse 200mL of D5W in 4 hours using a Microdrip tubing. Now that we have converted hours to minutes (4 hours = 240 minutes), we can use our IV Flow Rate Formula to solve our IV dosage calculation problem. (The roller clamp on the IV tubing would be manually regulated to deliver 50 drops per minute.) 200mL x 60gtt/mL ÷ 240 minutes = 50gtt/min CONTINUED

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Reminders When preparing to tackle any type of IV flow rate calculation, be sure to determine what, if any, conversions need to take place first. Once you have completed all necessary conversions, you are ready to calculate the IV flow rate using one of the two IV flow rate formulas we’ve discussed in this tutorial. Remember, it is always best to be consistent with the dosage calculation method you choose to use when completing this type of problem.

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Order: Give 500mg of dopamine in 250mL of D5W to infuse at 20mg/h. Calculate the flow rate in mL/h. *In order to know how many mL we need to infuse in 1 hour per the IV pump, we need to convert our dosage needed (20mg) into its equivalence in mL. *Set up ratio, and then cross-multiply: 500mg = 250mL so 500 X = 250(20) 20mg X mL *Isolate X and solve: 500 X = 5000 so X = 10mL *There are 20mg of dopamine in 10mL of solution, so we will program our IV pump at 10mL/h.

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Your patient has an order to receive 800U of heparin per hour by continuous intravenous infusion. If the pharmacy mixes the IV bag to contain a total of 5,000U of heparin in 500mL of D5W, how many mL per hour should the patient receive? *In order to calculate mL/hour, we need to convert our dosage needed (800U) into its equivalence in mL. *Set up ratio, and then cross-multiply: 5000U = 500mL so 5000 X = 500(800) 800U X mL *Isolate X and solve: 5000 X = 400,000 so X = 80mL *There are 800U of heparin in 80mL of solution, so we will program our IV pump at 80mL/h.

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Order: 21.7mg of dopamine in 105mL of D5W to be infused at a rate of 9mg/h. Calculate the flow rate in mL/h. *In order to calculate mL/hour, we need to convert our dosage needed (9mg) into its equivalence in mL. *Set up ratio, and then cross-multiply: 21.7mg = 105mL so 21.7 X = 9(105) 9mg X mL *Isolate X and solve: 21.7 X = 945 so X = 43.55mL *There are 9mg of dopamine in 43.55mL of solution, so we will program our IV pump at 44mL/h.

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Order: Aggrastat at 12.5mg in 250mL to be infused at a rate of 6 mcg/kg/hr in a patient who weighs 100kg. At what flow rate will you set the IV pump? *For problems that include a weight/mass, do that conversion 1 st : 6mcg per kg = 6mcg x 100kg = 600mcg/hr *Since our ordered dose is in mg, we need to convert mcg to mg: 600mcg ÷ 1000 = 0.6mg/hr *In order to calculate mL/hour, we need to convert our dosage needed (0.6mg) into its equivalence in mL. *Set up ratio, and then cross-multiply: 12.5mg = 250mL so 12.5 X = 0.6(250) 0.6mg X mL *Isolate X and solve: 12.5 X = 150 so X = 12mL *There are 0.6mg of Aggrastat in 12mL of solution, so we will program our IV pump at 12mL/h.

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A 1000cc solution of D5NS with 20,000U of heparin is infusing at 20mL/h. The IV set delivers 60gtt/mL. How many units of heparin is the patient receiving each hour? *This is a reverse calculation, as we already know the electronic flow rate (mL/h). We will use our dosage calculation method to work through the problem. *Set up ratio, and then cross-multiply: 20,000U = 1000mL so 1000 X = 20(20,000) X U 20mL *Isolate X and solve: 1000 X = 400,000 so X = 400U *There are 400U of heparin in 20mL of solution, which means the patient is receiving 400U of heparin per hour. The drop factor is simply a distracter, and is not used in this problem.

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The physician orders an IV infusion of D5W 1000mL to be infused over the next 8 hours. The IV tubing you are using delivers 15gtt/mL. What is the correct rate of flow? *In order to use the IV Flow Rate Formula, we need to know time in minutes instead of hours, which is the only conversion we will need to do to solve this problem. *We can eliminate the extra steps of a time conversion by incorporating it into our formula: 1000mL x 15gtt/mL = 15,000 = h x 60 min 480 *Remember our “mL” labels are cancelled out during the calculation process, and we must round all flow rates, leaving us with 31gtt/min as the correct rate of flow.

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Your patient has an order to infuse 10mEq of KCl in 100mL of D5½NS over the next 30 minutes. The set calibration is 10gtt/mL. What is the correct rate of flow? *We will be using the IV Flow Rate Formula, and no conversion calculation is needed: 100mL x 10gtt/mL = 1000 ÷ 30 = min *The correct rate of flow is 33gtt/min. *Do not be confused by extra numbers, such as are used in the name of a solution (i.e. D 5 W or ½ NS). These have no bearing on your dosage calculation. *Be careful in determining which value(s) are pertinent in solving your problem. In this example, the 10mEq of KCl is not a necessary component in terms of calculating the correct rate of flow, so ignore it!

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The 0900 medications scheduled for your patient include Keflex 1.5g in 50mL of a 5% dextrose solution. According to the pharmacy, this preparation should be administered in 30 minutes. The IV tubing on your unit delivers 15gtt/mL. What is the correct rate of flow in gtt/min? *We will be using the IV Flow Rate Formula, and no conversion calculation is needed: 50mL x 15gtt/mL = 750 ÷ 30 = min *The correct rate of flow is 25gtt/min. *Again, remember the 5% dextrose is just describing the type of solution, and the Keflex 1.5g does not have anything to do with calculating the flow rate for this problem.

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On Wednesday afternoon, your patient returns from surgery with an IV fluid order for 1000mL every 8 hours. On Thursday morning at 0800, you note that 600mL of a 1L bag has been infused. The physician orders the remainder of the bag to infuse over the next 6 hours. The IV tubing used by your unit delivers 10gtt/mL. What is the correct rate of flow? *There are 400mL remaining in the IV bag, which needs to be infused in 6 hours. *We need to know time in minutes instead of hours, which can be incorporated into our IV Flow Rate Formula calculation: 400mL x 10gtt/mL = 4000 ÷ 360 = h x 60 min *The correct rate of flow is 11gtt/min.

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The physician orders 1.5L of Lactated Ringers solution to be administered intravenously to your patient over the next 12 hours. Calculate the rate of flow if the IV tubing delivers 20gtt/mL. *In order to utilize the IV Flow Rate Formula, we must convert liters to milliliters and hours to minutes, both of which can be completed as part of the formula calculation: (1.5L x 1000) x 20gtt/mL = 30,000 ÷ 720 = h x 60 min *The correct rate of flow is 42gtt/min.

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Miscellaneous Dosage

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#1:The physician orders 200mg of Rocephin to be taken by a 15.4 lb infant every 8 hours. The medication label shows that mg/kg/day is the appropriate dosage range for this medication. Is the order within the desired range?

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Convert weight (lbs to kg) : 15.4 lbs ÷ 2.2 = 7kg Calculate minimum and maximum dosage : 75mg x 7kg = 525mg (minimum daily therapeutic dose) 150mg x 7kg = 1050mg (maximum daily therapeutic dose) Determine if the order is within range : 200mg every 8 hours (or 200mg x 3 times per day) = 600mg Solve the problem : Yes, 600mg/day of Rocephin is within the desired daily range of 525mg and 1050mg for this patient.

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#2:Solumedrol 1.5mg/kg is ordered for a child weighing 34 kg. This medication is available as 125mg/2mL. How many mL will you administer?

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Calculate mg according to weight : 1.5mg/kg x 34 kg = 51mg Convert mg to mL using your chosen dosage calculation method : 125mg = 2mL so 125 X = 51(2) 51 mg X mL 125 X = 102 so X =.82mL Solve the problem : You will administer 0.82mL of Solumedrol to this patient.

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#3:You are to infuse 800mL of Lactated Ringers over 20 hours using an IV administration set that delivers 20gtt/mL. What is the drip rate?

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Solve using the IV Flow Rate Formula : 800mL x 20gtt/mL = 16,000gtt = 13gtt/min 20 h x 60 min 1200 min

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Calculate the mL/h of the following orders via IV pump: #4.Administer 1500mL of 0.9 NS in 24 hours. #5.Administer 750mL of LR in 16 hours. #6.Administer 500mL of D5W in 12 hours. #7.Administer 2000mL of D5W in 24 hours.

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Solve the previous calculations using the Electronic Flow Rate Formula : 1500mL ÷ 24 hours = 63mL/h 750mL ÷ 16 hours = 47mL/h 500mL ÷ 12 hours = 42mL/h 2000mL ÷ 24 hours = 83mL/h

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#8Order: Administer 30mL of Ancef in 0.9 NS over 20 minutes via intravenous infusion pump.

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Convert minutes to hours : 20 minutes = X hours so 60 X = 20(1) 60 minutes 1 hour 60 X = 20 so X = 0.33∞ hours Solve using the Electronic Flow Rate Formula : 30mL ÷ 0.33∞ hours = 90mL/h

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#9Order: Administer 100mL of ½NS in 45 minutes.

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Convert minutes to hours : 45 minutes = X hours so 60 X = 45(1) 60 minutes 1 hour 60 X = 45 so X = 0.75 hours Solve using the Electronic Flow Rate Formula : 100mL ÷ 0.75 hours = 133mL/h

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#10Order: Administer 150mL of D5W in 30 minutes.

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Convert minutes to hours : 30 minutes = X hours so 60 X = 30(1) 60 minutes 1 hour 60 X = 30 so X = 0.5 hours Solve using the Electronic Flow Rate Formula : 150mL ÷ 0.5 hours = 300mL/h

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#11Your patient is to receive 2000mL of D5W with a flow rate of 160mL/h. How long will this order take to infuse?

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Solve using your chosen dosage calculation formula : 2000mL = X hours so 160 X = 2000(1) 160mL 1 hour 160 X = 2000 so X = 12.5 hours *It will take 12 ½ hours to infuse 2000mL of D5W to your patient under this order.

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#12Your patient has been prescribed 1L of NS. The IV pump is set at 150mL/h. How long will this order take to infuse?

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Solve using your chosen dosage calculation formula : 1L x 1000 = 1000mL 1000mL = X hours so 150 X = 1000(1) 150mL 1 hour 150 X = 1000 so X = 6.7 hours *It will take just under 7 hours to infuse 1000mL of NS to your patient under this order.

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#13The physician orders D5W IV at 125mL/h. The infusion set is calibrated for a drop factor of 10gtt/mL. Calculate the IV flow rate in gtt/min.

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Solve using the IV Flow Rate Formula : 125mL x 10gtt/mL = 1250gtt = 21gtt/min 1 h x 60 min 60 min

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#14Order: 150mL Lactated Ringers solution to infuse in 30 minutes. The drop factor is 15gtt/mL.

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Solve using the IV Flow Rate Formula : 150mL x 15gtt/mL = 75gtt/min 30 min

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#15Order: Cefazolin 0.5g in 100mL D5W IV piggyback to run over 30 minutes. The drop factor is 20gtt/mL. What is the drip rate?

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Solve using the IV Flow Rate Formula : 100mL x 20gtt/mL = 67gtt/min 30 min

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#16Order: Ampicillan 500mg IV in 100mL of NS to infuse over 45 minutes. How will you program the infusion pump?

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Convert minutes to hours : 45 minutes = X hours so 60 X = 45(1) 60 minutes 1 hour 60 X = 45 so X = 0.75 hours Solve using the Electronic Flow Rate Formula : 100mL ÷ 0.75 hours = 133mL/h

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#17Order: Bactrim 500mg IV in 50mL D5½NS in 30 minutes by IV pump. What is the mL/h?

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Convert minutes to hours : 30 minutes = X hours so 60 X = 30(1) 60 minutes 1 hour 60 X = 30 so X = 0.5 hours Solve using the Electronic Flow Rate Formula : 50mL ÷ 0.5 hours = 100mL/h

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#18Order: NS 1800mL IV to infuse in 15 hours by infusion pump. Calculate the flow rate.

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Solve using the Electronic Flow Rate Formula : 1800mL ÷ 15 hours = 120mL/h

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#19You receive a physician’s order for D5W 250mL IV over the next 2 hours by infusion pump. What is the mL/h?

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Solve using the Electronic Flow Rate Formula : 250mL ÷ 2 hours = 125mL/h

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#20You receive an order for D5W 500mL with heparin 25,000U IV at 850U per hour. Calculate the flow rate in mL/h.

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Convert U/h to mL/h to solve this problem : 25,000U = 500mL so 25,000 X = 850(500) 850U X mL 25,000 X = 425,000 so X = 17mL/h 25,000 25,000 *The flow rate is 17mL/h.

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#21You receive an order for D5W 1000mL IV to infuse at 50mL/h to begin at At what time will this IV be complete?

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Solve using your chosen dosage calculation formula : 1000mL = X hours so 50 X = 1000(1) 50mL 1 hour 50 X = 1000 so X = 20 hours *This IV will be complete at 0200 the following morning.

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#22You receive an order for LR solution 1000mL IV to run at 125mL/h. How long will this IV last?

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Solve using your chosen dosage calculation formula : 1000mL = X hours so 125 X = 1000(1) 125mL 1 hour 125 X = 1000 so X = 8 hours *This IV will last for 8 hours.

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#23Order: Dobutamine 250mg in 250mL D5W per IV to infuse at 5mcg/kg/min. The client’s weight is 80 kg. Calculate the flow rate using an infusion pump.

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Calculate mcg according to weight : 5mcg/kg x 80 kg = 400mcg/min Convert mcg/min to mg/min: 400mcg ÷ 1000 = 0.4mg/min Convert mg/min to mg/hour: 0.4mg x 60 minutes = 24mg/h Convert mg to mL based on dosage on hand : 250mg = 250mL so 250 X = 24(250) 24mg X mL 250 X = 6000 so X = 24mL Solve using the Electronic Flow Rate Formula : 24mL/h via IV pump

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#24Order: Lidocaine 2g in 500mL D5W IV to run at 4 mg/min. What is the flow rate per IV pump?

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Convert g to mg: 2g x 1000 = 2000mg Convert mg/min to mL/min based on dosage on hand : 2000mg = 500mL so 2000 X = 4(500) 4mg X mL 2000 X = 2000 so X = 1mL/min Convert mL/min to mL/h to solve the problem : 1mL x 60 minutes = 60mL/h

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#25Order: Ancef 1g in 100mL D5W IV piggyback to be infused over 45 minutes. You are using a Microdrip tubing. What is the flow rate in gtt/min?

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Solve using the IV Flow Rate Formula : 100mL x 60gtt/mL = 133gtt/min 45 min

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#26Order: 50mL Zofran solution IV piggyback to infuse over 30 minutes. The drop factor is 60gtt/mL. What is the flow rate in gtt/min?

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Solve using the IV Flow Rate Formula : 50mL x 60gtt/mL = 100gtt/min 30 min

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#27Order: 1000mL D5W IV q 24 hours. The drop factor is 60gtt/mL. What is the flow rate in gtt/min?

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Convert hours to minutes and solve using the IV Flow Rate Formula : 1000mL x 60gtt/mL = 60,000 = 42gtt/min 24 hours x 60 minutes 1440

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#28A dose strength of gr ¼ of an IV push medication is ordered. The available dosage is 15mg/mL. How many mL will you administer?

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Convert gr to mg : 1grain = 60mg so 1 X = ¼(60) ¼ grain X mg 1 X = 15 so X = 15mg 11 Solve the problem : 15mg = 1mL, so you will administer 1mL.

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#29You have an order for epinephrine to be infused at 30mL/h. The solution available is 2mg of epinephrine in 250mL D5W. Calculate the mcg/min.

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Convert mL/h to mg/h based on dosage on hand : 2mg = 250mL so 250 X = 2(30) X mg 30mL 250 X = 60 so X = 0.24mg/h Convert mg/h to mcg/h : 0.24mg x 1000 = 240mcg/h Convert mcg/h to mcg/min to solve the problem: 240mcg ÷ 60 minutes = 4mcg/min

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#30Aminophyline 0.25g is added to 500mL D5W to infuse in 8 hours. Calculate the mg/h.

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Use the Electronic Flow Rate Formula to determine mL/h : 500mL ÷ 8h = 62.5mL/h Convert mL/h to g/h based on dosage on hand: 0.25g = 500mL so 500 X = 0.25(62.5) X g 62.5mL 500 X = 15.6 so X = 0.03g/h Convert g/h to mg/h to solve the problem : 0.03g x 1000 = 30mg/h

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#31You receive an order to infuse 500mL ½NS with 30,000U heparin at 600U/h. The drop factor is 60gtt/mL. What is the gtt/min?

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Convert U/h to mL/h per on dosage on hand : 30,000U = 500mL so 30,000 X = 500(600) 600U X mL 30,000 X = 300,000 so X = 10mL/h 30,000 30,000 Convert hours to minutes and solve using the IV Flow Rate Formula : 10mL x 60gtt/mL = 10gtt/min 1 hour x 60 minutes

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#32A patient is to receive Pitocin at 15microgtt/min. The solution contains 10U Pitocin in 1000mL D5W. Calculate the number of units of Pitocin the patient is receiving per hour.

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Convert m gtt/min to m gtt/h : 15mgtt x 60 minutes = 900mgtt/h Convert m gtt/h to mL/h (*remember Microdrip tubing delivers 60 drops in 1mL): 60mgtt = 1mL so 60 X = 900(1) 900mgtt X mL 60 X = 900 so X = 15mL/h *Continued on next slide

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Convert mL/h to U/h : 10U = 1000mL so 1000 X = 10(15) X U 15mL 1000 X = 150 so X = 0.15U Solve the problem: The patient is receiving 0.15U/hour of Pitocin.

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#33You have an order for 3 mcg/kg/min of Nipride. You have available 50mg of Nipride in 250mL D5W. The client’s weight is 60 kg. Calculate the flow rate in mL/h that will deliver the correct dose.

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Calculate mcg according to weight : 3mcg/kg x 60 kg = 180mcg/min Convert mcg/min to mg/min: 180mcg ÷ 1000 = 0.18mg/min Convert mg/min to mg/hour: 0.18mg x 60 minutes = 10.8mg/h Convert mg to mL based on dosage on hand : 50mg = 250mL so 50 X = 10.8(250) 10.8mg X mL 50 X = 2700 so X = 54mL Solve using the Electronic Flow Rate Formula : 54mL/h via IV pump

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#34A 50mg nitroglycerin drip in 250mL D5W is infusing at 3mL/h. Calculate the mcg/min of nitroglycerin this patient is receiving.

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Convert mL/h to mg/h based on dosage on hand : 50mg = 250mL so 250 X = 50(3) X mg 3mL 250 X = 150 so X = 0.6mg/h Convert mg/h to mcg/h : 0.6mg x 1000 = 600mcg/h Convert mcg/h to mcg/min to solve the problem: 600mcg ÷ 60 minutes = 10mcg/min

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#35A dose strength of 0.3g of a medication has been ordered to infuse over 20 minutes. The available dosage is 0.4g in 1.5mL of solution. Calculate the mL/h.

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Convert g to mL based on dosage on hand : 0.4g = 1.5mL so 0.4 X = 0.3(1.5) 0.3g X mL 0.4 X = 0.45 so X = 1.125mL Convert minutes to hours : 20 minutes = X hours so 60 X = 20(1) 60 minutes 1 hour 60 X = 20 so X = 0.33∞ hours Use the Electronic Flow Rate Formula to solve: 1.125mL ÷ 0.33∞ hours = 3mL/h

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