A Step-by-Step Guide to Dimensional Analysis

Step 1:  Identify the unit of measure needed in the answer.

Example:	gtt
	min

Step 2:  From known information, select the ratio that has the same unit of measure in its numerator as in the numerator of “Step 1”.

Example:	10 gtt
	1 mL

Step 3:  From known information, select a ratio by which to multiply the previous ratio.  (The ratio should be selected so that its unit of measure is the same as the unit of measure in the previous ratio’s denominator; this allows the unwanted unit of measure to be eliminated when we multiply.)

Example:	10 gtt	x	115 mL
	1 mL		1 hr

Step 4: Repeat “Step 3” until the unit of measure remaining in the denominator matches the unit of measure in the denominator of “Step 1”.

Example:	10 gtt	x	115 mL	x	1 hr
	1 mL		1 hr		60 min

Step 5: As appropriate, multiply/divide the numbers in the equation to get the answer.

Example:	10 gtt	x	115 mL	x	1 hr	=	19.1666	gtt	=	19	gtt
	1 mL		1 hr		60 min			min			min

Notes:

(1)  For the sake of reducing errors by improving organization and clarity, numerators and denominators of all numbers are lined-up by expressing each as a ratio; a fraction.  For example, if we had “125 mL” the equivalent expression of “125 mL/1” should be used.  In this case we are simply dividing by a number “1” that has no unit of measure.  Remember, division or multiplication by “1” doesn’t change the value of an expression.

(2)  Ratios express a relationship between the value in the numerator and the value in the denominator.  The validity of the relationship does not change if the reciprocal of the ratio is used.  For example, “10 gtt/1 mL” expresses the same relationship as “1 mL / 10 gtt”.  In other words, if there are 10 drops per 1 mL, then it is also valid to say there is 1 mL per 10 drops.

Problem #1: A suspension is labeled to contain 250 mg of amoxicillin per 5 mL of product.  If a patient’s dose is 150 mg, what volume of suspension should the patient receive?

Step 1:  Identify the unit of measure needed in the answer.

mL

Step 2:  From known information, select the ratio that has the same unit of measure in the numerator as in the numerator of “Step 1”.

5 mL

250 mg

Step 3:  From known information, select a ratio by which to multiply the previous ratio.

5 mL	x	150 mg
250 mg		1

Step 4: Repeat “Step 3” until the unit of measure remaining in the denominator matches the unit of measure in the denominator of “Step 1”.

There is no 4^th step for this problem because the answer doesn’t have a unit of measure in its denominator.

Step 5: As appropriate, multiply/divide the numbers in the equation to get the answer.

5 mL	x	150 mg	=	3 mL
250 mg		1

Problem #2: Administer 2000 mL NS intravenous at 115 mL/hr.  The available drip chamber drop factor is 10 gtt/mL.  Calculate the infusion rate in gtt/min

Step 1:  Identify the unit of measure needed in the answer.

gtt

min

Step 2:  From known information, select the ratio that has the same unit of measure in the numerator as in the numerator of “Step 1”.

10 gtt

1 mL

Step 3:  From known information, select a ratio by which to multiply the previous ratio.

10 gtt	x	115 mL
1 mL		1 hr

Step 4: Repeat “Step 3” until the unit of measure remaining in the denominator matches the unit of measure in the denominator of “Step 1”.

10 gtt	x	115 mL	x	1 hr
1 mL		1 hr		60 min

Step 5: As appropriate, multiply/divide the numbers in the equation to get the answer.

10 gtt	x	115 mL	x	1 hr	=	19.1666	gtt	=	19	gtt
1 mL		1 hr		60 min			min			min

Problem #3: A 55 pound patient is prescribed 5 mg/kg/day of diphenhydramine HCl.  The daily dose it to be divided into 4 doses, each administered 6 hours apart.  Available medication is a 12.5 mg/5 mL solution.  How many teaspoons need to be given to the child at one time.

Step 1:  Identify the unit of measure needed in the answer.

tsp

“6 hour interval”

Step 2:  From known information, select the ratio that has the same unit of measure in the numerator as in the numerator of “Step 1”.

1 tsp

5 mL

Step 3:  From known information, select a ratio by which to multiply the previous ratio.

1 tsp	x	5 mL
5 mL		12.5 mg

Step 4: Repeat “Step 3” until the unit of measure remaining in the denominator matches the unit of measure in the denominator of “Step 1”.

1 tsp	x	5 mL	x	5 mg
5 mL		12.5 mg		1 kg ∙ day

1 tsp	x	5 mL	x	5 mg	x	1 kg
5 mL		12.5 mg		1 kg ∙ day		2.2 lb

1 tsp	x	5 mL	x	5 mg	x	1 kg	x	55 lb
5 mL		12.5 mg		1 kg ∙ day		2.2 lb		1

1 tsp	x	5 mL	x	5 mg	x	1 kg	x	55 lb	x	1 day
5 mL		12.5 mg		1 kg ∙ day		2.2 lb		1		4 “6 hr interval”

Step 5: As appropriate, multiply/divide the numbers in the equation to get the answer.

1 tsp

x

5 mL

x

5 mg

x

1 kg

x

55 lb

x

1 day

=

2.5

tsp

5 mL

12.5 mg

1 kg ∙ day

2.2 lb

1

4 “6 hr interval”

“6 hr interval”