The Nursing Math Thread

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A member pm'd me the following question highlighted below. We created this thread for you guys to talk about math, solve math problems, and post math websites that you have found helpful.

I was wondering, is there a sticky or a special site that can be coordinated for "math sufferers". Perhaps, beginning calculations or shall i say the basics..simple to complex...step by step on how to calculate. I'm a visual learner, numbers and I don't work well. I am trying, but I've got a block!

Google "self quiz math" and you will find lots of good sites that you can work with

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This is so helpful! Thank you.

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math tips

unit conversion

mass:

mcg → mg → g → kg ( ÷ by 1,000 )

mcg ← mg ← g ← kg ( x by 1,000 )

lb → kg ( ÷ by 2.2 )

lb ← kg ( x by 2.2 )

volume:

mcl → ml → l → kl ( ÷ by 1,000 )

mcl ← ml ← l ← kl ( x by 1,000 )

time:

min → hr ( ÷ by 60 )

min ← hr ( x by 60 )

example: convert 5,000 mcg to mg.

mcg → mg → g → kg ( ÷ by 1,000 )

5,000 mcg ÷ 1,000 = 5 mg

example: convert 44 lb to kg.

lb → kg ( ÷ by 2.2 )

44 lb ÷ 2.2 = 20 kg

example: convert 0.003 l to mcl.

mcl ← ml ← l ← kl ( x by 1,000 )

0.003 l x 1,000 = 3 ml

3 ml x 1,000 = 3,000 mcl

example: convert 5 hours to minutes.

min ← hr ( x by 60 )

5 hr x 60 = 300 min

mass for mass questions

given an amount of mass per tablet, how many tablets do you require?

formula:

ordered

have

= y (tablets required)

example: metroprolol (lopressor), 25 mg po, is ordered. metropolol is available as 50 mg tablets. how many tablets would the nurse administer?

ordered

have

= y (tablets required)

25 mg

50 mg

= 0.5 tablets

example: potassium chloride is available as 10 mg per tablet. potassium chloride (k-dur), 40 mg, is ordered. how many tablets would the nurse administer?

ordered

have

= y (tablets required)

40 mg

10 mg

= 4 tablets

mass/liquid for liquid questions

given an amount of mass per liquid, how much liquid do you require?

formula:

ordered

have

x volume per have

= y (liquid required)

example: phenytoin (dilantin), 0.1 g po, is ordered to be given through a nasogastric tube. phenytoin is available as 30 mg / 5 ml. how much would the nurse administer?

ordered

have

x volume per have

= y (liquid required)

convert 0.1 g to mg.

mcg ← mg ← g ← kg ( x by 1,000 )

0.1 g x 1,000 = 100 mg

100 mg

30 mg

x 5 ml

= 16.7 ml

example: ordered lasix 40 mg iv push now. available: 80 mg in 1 ml. how much will the nurse draw up?

ordered

have

x volume per have

= y (liquid required)

40 mg

80 mg

x 1 ml

= 0.5 ml

amount in iv fluid questions

given a volume of iv fluid and a dosage expressed in percent, what is the mass of a particular dosage?

formula:

concentration %

100

x volume (ml) = y (dosage amount in g)

example: calculate the amount of dextrose in 1000 ml d5w.

concentration %

100

x volume (ml) = y (dosage amount in g)

5%

100

x 1000 ml = 50 g

example: calculate the amount of sodium chloride in 2000 ml ns.

recall ns is 0.9% nacl (sodium chloride)

concentration %

100

x volume (ml) = y (dosage amount in g)

0.9%

100

x 2000 ml = 18 g

volume/time - iv ml rate questions

given a certain amount of liquid and a time period, what is the necessary iv flow rate in ml/hr? measurement used when iv regulated electronically by infusion pump.

formula:

volume (ml)

time (hr)

= y (flow rate in ml/hr)

example: infuse 250 ml over the next 120 minutes by infusion pump.

volume (ml)

time (hr)

= y (flow rate in ml/hr)

convert 120 minutes to hours.

min → hr ( ÷ by 60 )

120 min ÷ 60 = 2 hr

250 ml

2 hr

= 125 ml/hr

example: ordered 1000 ml d5w iv to infuse in 10 hours by infusion pump.

volume (ml)

time (hr)

= y (flow rate in ml/hr)

1000 ml

10 hr

= 100 ml/hr

volume/time - iv drop rate questions

given a certain amount of liquid, a time period, and a drop factor (gtts/ml), what is the necessary iv flow rate in gtts/min? measurement used when iv is regulated manually. because it is not possible to give a patient a fraction of a drop, it is typical to round answers for these problems up or down to the nearest whole number.

formula:

volume (ml)

time (min)

x drop factor (gtts/ml) = y (flow rate in gtts/min)

example: calculate the iv flow rate for 1200 ml of ns to be infused in 6 hours. the infusion set is calibrated for a drop factor of 15 gtts/ml.

volume (ml)

time (min)

x drop factor (gtts/ml) = y (flow rate in gtts/min)

convert 6 hours to minutes.

min ← hr ( x by 60 )

6 hr x 60 = 360 min

1200 ml

360 min

x 15 gtts/ml = 50 gtts/min

example: calculate the iv flow rate for 200 ml of 0.9% nacl iv over 120 minutes. infusion set has drop factor of 20 gtts/ml.

volume (ml)

time (min)

x drop factor (gtts/ml) = y (flow rate in gtts/min)

200 ml

120 min

x 20 gtts/ml = 33 gtts/min

fluid maintenance requirement questions

given the weight of a child or infant, calculate the necessary amount of fluid per day. different hospitals may have different policies, but for learning how to perform these pediatric dosage calculations, the following commonly used table of fluid requirements may be used.

weight range

required daily fluid

0-10 kg

100 ml per kg

10-20 kg

1,000 ml + 50 ml per each kg above 10 kg

20-70 kg

1,500 ml + 20 ml per each kg above 20 kg

over 70 kg

2,500 ml (adult requirement)

example: an infant weighs 4 kg. what is the required amount of fluid per day in ml?

0-10 kg

100 ml per kg

4 kg x 100 ml/kg = 400 ml

example: an infant weighs 30.8 lb. what is the required iv flow rate in ml/hr to maintain proper fluid levels?

convert 30.8 lb to kg.

lb → kg ( ÷ by 2.2 )

30.8 lb ÷ 2.2 = 14 kg

10-20 kg

1,000 ml + 50 ml per each kg above 10kg

14 kg - 10 kg = 4 kg (there are 4 kg over 10 kg).

1,000 ml + (50 ml/kg x 4 kg) = 1,200 ml/day

this is now an ordinary iv flow rate - ml rate question. the required volume is 1,200 ml and the time is one day.

volume (ml)

time (hr)

= y (flow rate in ml/hr)

there are 24 hours in one day.

1 day x 24 = 24 hr

1,200 ml

24 hr

= 50 ml/hr

dosage by weight questions

given the weight of a patient and a dosage specified in terms of weight, calculate the necessary dosage. these problems are a type of pediatric dosage calculations.

formula:

weight in kg * dosage per kg

= y (required dosage)

example: a doctor orders 200 mg of rocephin to be taken by a 15.4 lb infant every 8 hours. the medication label shows that 75-150 mg/kg per day is the appropriate dosage range. is this doctor's order within the desired range?

weight in kg * dosage per kg

= y (required dosage)

convert 15.4 lb to kg.

lb → kg ( ÷ by 2.2 )

15.4 lb ÷ 2.2 = 7 kg

7 kg * 75 mg/kg

= 525 mg (minimum desired dosage)

7 kg * 150 mg/kg

= 1,050 mg (maximum desired dosage)

24 hours in one day and the medication is ordered every 8 hours.

24 hrs / 8 hrs = 3 times per day doctor ordered medication

200 * 3 = 600 mg ordered per day

600 mg is within the desired range of 525-1,050 mg

yes doctor has ordered a dosage within the desired range.

example: solumedrol 1.5 mg/kg is ordered for a child weighing 74.8 lb. solumedrol is available as 125 mg / 2ml. how many ml must the nurse administer?

weight in kg * dosage per kg

= y (required dosage)

convert 74.8 lb to kg.

lb → kg ( ÷ by 2.2 )

74.8 lb ÷ 2.2 = 34 kg

34 kg * 1.5 mg/kg

= 51 mg

this is now an ordinary mass/liquid for liquid question. 51 mg is ordered and the medication is available as 125 mg / 2 ml.

ordered

have

x volume per have

= y (liquid required)

51 mg

125 mg

x 2 ml

= 0.82 ml

mass/time - iv ml rate questions

give an order in quantity of mass per time, determine the necessary iv flow rate in ml/hr based on the given mass per volume. these types of problems are often used in critical care nursing.

formula:

ordered per hour

have

x volume (ml)

= y (flow rate in ml/hr)

example: give patient 500 mg of dopamine in 250 ml of d5w to infuse at 20 mg/hr. calculate the flow rate in ml/hr.

ordered per hour

have

x volume (ml)

= y (flow rate in ml/hr)

20 mg/hr

500 mg

x 250 ml

= 10 ml/hr

example: aggrastat at 12.5 mg in 250 ml is prescribed to be infused at a rate of 6 mcg/kg/hr in a patient who weighs 100 kg. at what flow rate in ml/hr will you set the pump?

ordered per hour

have

x volume (ml)

= y (flow rate in ml/hr)

the first step is to convert the order per time to the amount required for this particular patient. this is a dosage by weight question. 100 kg is the weight in kg and 6 mcg/kg/hr is a dosage in terms of kg.

weight in kg * dosage per kg

= y (required dosage)

100 kg * 6 mcg/kg/hr

= 600 mcg/hr

convert 600 mcg/hr to mg/hr.

mcg → mg → g → kg ( ÷ by 1,000 )

600 ÷ 1,000 = 0.6 mg/hr

0.6 mg/hr

12.5 mg

x 250 ml

= 12 ml/hr

:dncgcpd::dncgcpd::dncgcpd:

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Awesome Unit Conversions sheet! It even has examples! Thank you for this as I'm starting nursing school in three weeks!

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You are so welcome....wish you the best of luck......

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hi, i am a first year rn student...i am an older lady and i have been out of school for a little while now lol...i have always had a problem with math. as far as basic math, no problem..i just get confused where and how to plug the numbers in at. and with word problems, i try to plug every number in whether it is relevant or not. can someone please help me with this nursing math problem. i have the answer due to the answer sheet, but i need to be shown step by step how to work this problem out. any help will be greatly appreciated. it may seem very easy to some people, but it just doesn't click with me...

the order is for 1000 ml of 5% dextrose in water to run at 250ml/hr. how many drops per minute should the iv infuse (60gtt/ml set)?

question is: do i set it up like this: 250ml/60minutes * 60gtt/ml? if so the 60 will cross each other out leaving 250 gtt/ml? i know this is totally wrong!! do you put the 1000 ml into the equation? i guess you can see now how very confused i am!

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Specializes in Psych.

actually it comes out to 250 gtt/min

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Specializes in Emergency, Critical Care (CEN, CCRN).
the order is for 1000 ml of 5% dextrose in water to run at 250ml/hr. how many drops per minute should the iv infuse (60gtt/ml set)?

question is: do i set it up like this: 250ml/60minutes * 60gtt/ml? if so the 60 will cross each other out leaving 250 gtt/ml? i know this is totally wrong!! do you put the 1000 ml into the equation? i guess you can see now how very confused i am!

don't worry about it, we're glad to help out. :)

all infusion-rate problems have a similar setup; the trick is picking out which numbers you need to plug in where. the common formula is: (vtbi x df) / t, where vtbi is volume to be infused (ml), df is drop factor (gtt/ml), and t is time (min). taking this example, since you're infusing 250 ml per hour, you've just about done it right: (250 x 60) / 60 = 250 gtt/min. the total volume is irrelevant in this case, since you already know volume per hour. (you'd only use total volume if you were told, say, to run 1000 ml over 4 hours.)

however, there is a shortcut, and you already hit upon it in your post. microdrop tubing always has a drop factor of 60 gtt/ml, and thus the infusion rate per hour will always be the same as the drops per minute (the 60s cancel out). handy little timesaver. ;)

hope this helps!

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"do not worry about your difficulties in mathematics. i can assure you mine are still greater."

albert einstein

general math help:

working with fractions:

algebra help:

for free unlimited practice problems in any of the math disciplines: http://www.interactmath.com/ - follow the directions to download the drivers you need to access the software and then choose a textbook of the type of math you want to work problems from

medication calculation help and practice problems you can work:

conversion charts:

dimensional analysis tutorials [keep in mind that dimensional analysis is usually done in chemistry and physics and nursing has only adapted it for use in medication calculation problems]:

statistics links can be found on post #46 of this thread.

ok that last link you posted took me to a demonstration on a*al sex. im not kidding.

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ok that last link you posted took me to a demonstration on A*al sex. im not kidding.

The original poster of this message past away last year, but I checked the link and it gave me a failure URL so hopefully it won't work anymore!:confused:

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im sorry about that :(

I clicked on it and it gave me a failure url with links under that for **** sex.

very strange.

But im sure it happens. URLs change all the time

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Specializes in Operating Room.

not sure if my answer is correct because i have been getting different ones everytime i calculate

a patient has an order for 1/2 strength pulmocare tube feedings, at 50 ml/hr through a peg tube. the nurse prepares the dilute formula and has a total volume of 475 ml. according to and has a total volume of 475 ml. according to hospital policy, only 4 hours of tube feeding formula can be hung at a time, to minimize bacterial growth. how many ml of the prepared 1/2-strength formula will the nurse use?

this is how i set up the problem

1/2 = 475 ml/x

(2 x 475) = x

950 ml = x

950-475 = 475 ml

the back of the book says 200 ml am i doing something wrong or not pulling out enough of the proper information. sometimes i tend to do that

here is another problem i am having

the nurse is instructing a patient to take diflucan 40 mg oral suspension at home. how many tsp will the nurse instruct the patient to take per dose?

the label reads 35 ml when reconstituted; 40 mg/ml; add 24 ml of distilled water or purified water to the bottle shake well; this package contains 1400 mg fluoconazole in a natural orange-flavored mixture

how would i go about solving this problem?

thank you

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