The proper administration of medication requires the ability to calculate the medication doses accurately and measure medication correctly. Any errors in the calculation may cause a fatal error. The health care industry uses Metric, Apothecaries, Household system and solutions. Three systems of measurement are used. The metric system, the apothecaries system, and the household system which is similar to apothecaries system.
1. Metric system: The metric system is logically arranged in to units of 10; it is decimal system. Basic units can be multiplied or divided by 10 to form secondary units. Multiples are calculated by moving the decimal points to the right, and the division is accomplished by moving the decimal point to the left.
· Basic units of measurement are the meter, the litre and the gram.
· Prefixes derived from the Latin designate subdivisions of the basic unit: deci (1/10 or 0.1) centi (1/100 or 0.01) and milli (1/1000 or 0.001).
· Multiples of the basic units are designated by prefixes derived from greek: deka (10) hecto (100) and kilo (1000)
· Only the measurements of volume (the litre) and of weight (gram) are the measures used in medication administration. In nursing practice kilogram (kg) is the only multiple of the gram (gm.) used and milligram (mg) and microgram (mcg or Ug) are subdivisions.
· Fractional part of the liter are usually expressed in millilitres (mL) Multiples of the liter are usually expressed in liters or milliliters for example 2.5 liters or 2500ml.
· The basic units of measurement in metric system are the meter (length). liter (volume), and gram (weight).
Designation of units:
Gram

g or Gm

Liter

l or L

Milligram

mg

Milliliter

ml

Greek prefix designate the multiples of the basic units
Deka

10

Hexa

100

Kilo

1000

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Apothecaries’ system
· The basic unit of the weight in apothecaries system is grains (gr) likened to grain of the Wheat and the basic unit of volume IS minim, a volume of water equal in weight to a grain of a wheat. The word minim means \”the least\”.
· In ascending order the other units of weight are the scruple, the dram, the ounce, and the pound,
· The units of volume are in ascending order the fluid dram, the fluid ounce, the pint, the quart and the gallon
· The roman letters follows rather than procedes the units of measure. For e.g., 2 ounces are written as 3 II.
· Quantities less than I are expressed as fraction form e.g. Gr 1/6.
· This system is not used much.
Household system
Household measures may be used when more accurate systems of measure are not required. Included in household measures are drops, teaspoons, tablespoons, cups, and glasses. Although pints and quarts are often found in home, they are defined as apothecaries measures.
Metric

Apothecary

Household

1 ml

1516 minims

15 drops

5 ml

1 drams

1 tablespoon

15 ml

4 drams

1 tablespoon

30 ml

1 ounce

2 tablespoon

240 ml

8 ounce

1 cup

480 ml

1 pint

1 pint

960 ml

1 quart

1 quart

3840 ml

1 gallon

1 gallon

Unit

Approximate value


1 dram

60 minims

60 grains

4 grams

4 ml (1 teaspoonful)

1 ounce

8 tsf

480 grains

30 grams

30 ml

1 liter

40 ounces

2 pints

1 quart

1000 ml

1 gram

15 grains

1000 mg


1 grain

60 mgms


1 cc

15 minims

1 ml


1 minim

1 drop


1 pint

20 ounces

500 ml


1 pound

16 ounces

480 grams


1 kg

2.2 lb

1000 grams


1 mgm

1000 mcg


1 gallon

4000 ml

4 quarts


1 tsf

4 to 5 ml

60 drops


1 tablespoon

15 ml

4 drams

4 tsf


1 tea cupful

150 ml

6 ounces


1 glassful

200 ml

8 ounces


1 cm

10 mm


1 km

1000 m


1 mile

1.6 km


1 foot

12 inches

30 cm


1 inch

2.5cm

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3. Household measurements
Household measurements are familiar to most people as it is used in the home set up for measurement. The main disadvantage is its inaccuracy and the .variation in the size and shape of the utensils. Household measures include Drops, Teaspoon, Tablespoon and cups for volume and Pints and quarter for weight.
4. Solutions
Solutions of various concentrations are used for injections, irritations and infusions. A solution is a given mass of solid substance dissolved in a known volume of liquid.
The concentration is in units of mass per units of volume. E.g. g/ml, g/ l, mg/ml.
We can also express a concentration of solution in percentage.
e.g.: 10% solution = I0 g solid dissolved in 1000 ml of liquid.
1/1000 solution = 1 g of solid in 1000ml of liquid
OR
1 ml of liquid in 1000ml of liquid.
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System of Measurement
Household: tsp., gtt, T, c
Apothecary: gr, dr, oz
Metric: ml, mg, g, I
Converting weights within metric system.
Only three metric units of weight are used for drug dosages, the gram (gm.) milligram (mg) and microgram (mcg or Ug) 1000mg or l, 00,000 mcg, equals 1 gm. Equalents are computed by dividing or multiplying; for e.g. to change milligrams to grams divide the number of milligrams by 1000, simplest way to divide by 1000 is to move the decimal point three places to the left.
E.g.; 500mg=? gm
Move the decimal point three places to the left.
Answer is 0.5 gm
Conversely, to convert grams to milligrams, multiply the number of grams by 1,000, or move the decimal point three places to the right: 0.006 g = ? mg. Move the decimal point three places to the tight:
Answer = 6 mg
Converting units of volume
Approximate volume equivalents:
I ml = 15 minims / 15 drops
15 ml = 4 fluid drams / I tablespoon
30ml = I fluid ounce/ I ounce
500ml = 1 pint (pt)
1000ml= Iquart (qt)
4000ml = 1 gallon (gal)
· ml dosages need to be fractionalized. The nurse can fractionalize ml dosages by remembering that I ml contain 15 drops or minims.
· Fluid drams and ounces are commonly used in prescribing liquid medications, such as cough syrups, laxatives, antacids, and antibiotics for children.
· The fluid ounce is usually converted to ml when measuring a client’s fluid intake or output.
· Liters and milliliters are the volumes commonly used in preparing solutions for enemas, irrigating solutions for bladder irrigations, and solutions for cleaning open wounds.
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Calculating units of weight
The units of weight commonly used in nursing practice are the gram, milligram and kilogram, and the gain and the pound.
1 mg 1/60 grain
60 mg= 1 grain
1 g = 15 grains
4 g = 1 dram
30gm = 1 ounce
500gm= 1.1 pound (1b)
1000 gm = 2.2 lb
· Converting milligrams to grains and vice versa, for example, when preparing medications
· Converting pounds to kilograms and vice versa, for example, a person’s weight
· When converting units of weight from the metric system to the apothecaries’ system, the nurse should keep in mind that a milligram is smaller than a grain
· Small units (mg) to large units conversion ( grains) = smaller number
· large units ( grains) to Small units (mg) to conversion= larger number
3000mg
—————– = 50 grains
60
50 grains x 60 = 3000mg
When converting pounds to kg pound is smaller unit than the kg
2.2 lb = 1 kg
1 10 lb = x kg
110 x 1
X = ————— = 50 kg
2.2
50 kg = x lb
2.2 x 50
X = ————— = 110 lb
1
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Calculating dosages
Several formulas can be used to calculate the drug dosage.
Amount to administer (X) = desired dose x quantity on hand
——————————————–
Dose on hand
E.g. Erythromycin 500 mg is ordered. It is supplied in a liquid form containing 250 mg in 5m to calculate the dosage
500 x 5ml
—————— = 10 ml
250
Dose ordered: Amount of medication prepared.
Dose on hand: weight or volume of medication available in units supplied from pharmacy.
Amount on hands: Is the basic unit or quantity of the medication that contains the dose on hands.
Amount to administer: Is the actual amount of available medication that will administer.
The amount to administer is always expressed in the same unit as the amount on hands.
E.g. the dose ordered is Inj Heparin 5000 units. It is supplied in a liquid form containing 10,000 units per ml.
5000 units x I ml
———————— = ½ ml = 0.5 ml
10000 units
Tab Lanoxin 0.125 mg is ordered. It is supplied is 0.25 mg tablets
0.125 x I
————— = ½ tablet
0.25
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2. Conversion between systems
Frequently you will determine the correct dose of medication by converting weight or volume from one system to another. e.g.: Metric units are converted in to equalent household measures for ease administration at home.
To convert from one measurement system to other, it is mandatory to use equalent measurement. E.g. A health care provider orders 30ml of Robittusin for your patient. To provide 9roper instruction to the client, you will convert ‘ml’ to common household measurement. From the table, determine that 30ml = 2 tablespoon. Therefore instruct to take 2 table spoon of Robittusin.
Dosages for children
Although dosage is stated in the medication order, nurses must understand something about the safe dosage for children. Body size significantly affect dosage for children.
Body surface area is determined by using a nomogram and the child’s height and weight. This is considered to be the most accurate method of calculating a child’s dose.
Child’s dose = surface area of child (m2)
————————————– X normal adult dox
1.7 m2
For example, a child who weighs 10 kg and is 50 cm tall has a body surface area of 0.4 m2. Therefore, the child’s dose of tetracycline corresponding to an adult dose of 250 mg would be as follows:
Child’s dose = 0 4 m2 X 250 mg
= 0.23 X 250 = 58.82 mg
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Dimensional Analysis
Given Quantity: the beginning point of the problem
Conversion Factors Equivalents necessary to convert between systems of measurement and to allow unwanted units to be cancelled from the problem
Unit Path: the series of conversions necessary to achieve the Wanted Quantity
Wanted Quantity: the answer to the problem
Drip Rates
You have started an IV of 0.9% Sodium Chloride and a physician request that you give 150 mL/ hr. You are using a 20gtt tubing set. How many drops/ minute will you give?
· 50drops / minute
· (mL * drop factor) / minutes
· Example: 500 ml, using 15 gtt set over I hour.
· (500 x 15) / 60 = 125 drops/min