Need To Know Math Formulas

Need to Know Math Formulas Ratioproportion

dosage on hand amount on hand

=

dosage desired (X) amount desired

Cross Multiply: dosage on hand x (X) = amount on hand x dosage desired

Ex:

Order – 3 mg On hand – 2 mg/5 mL

2 mg = X = 3 mg x 5 mL 5 mL

3 mg

Cross Multiply:

2mg x

X mL 2X

Solve for X

= 15

Check your work: insert answer into formula for X

Solve for X:

2X =15

X = 7.5 mL 2

IV Flow Rates **Always round to nearest whole number! Drop Factor Short Cut 60 gtts/mL = 1 20 gtts/mL = 3 15 gtts/mL = 4 10 gtts/mL = 6 IV Infusion Time

Total mL Total hours Total mL Total min. mL/h drop factor

=

mL/h

x 60 min/h

Ex: 1000 mL in 8 hours

= mL/h

= gtts/min

Drop factor x gtts/min = mL/h Total volume = time in hours mL/h

1000 mL = 125 mL/h 8h Ex: 100 mL in 45 min

**

100 mL x 60 min/h = 600 = 133 mL/h 45 min 45 Ex: 90 mL/h using 20 gtt/mL tubing (drop factor 3) 90 = 30 gtt/min ** 3 Ex: 15 gtts/mL (drop factor 4) x 25 gtts/min = 100 mL/h ** Ex: 1000 mL 60 min/h = 18 75 mL/h

=

13.3 h

0.3 h x 13

hours, 18 min Dosing by weight

Amount x weight

= dose

* Be sure weight is calculated as specified: either pounds or kilograms Dosing by

Amount range x weight = safe dose range

Ex: 1.5 mg / kg q 4 h

pt weighs 22 pounds

22 pounds ÷ 2.2 = 10 kg 1.5 mg x 10 kg = 15 mg q 4 h Ex: 10 – 15 mg / kg q 4 hr pt weighs 12 kg

weight using range Weight-based Heparin Drips

Weight-based Heparin Bolus

IV medication ordered per minute

Pt’s weight in kg (rounded to nearest 10 kg) Standard Heparin drip concentration is 250,000 units/250 mL of ½ NS (which is equivalent to 100 units/mL) Calculate x units/kg/h

Pts’s weight in kg (rounded to nearest 10 kg) Standard Heparin bolus concentration is 1000 units/mL Calculate x units/kg

D x Q = R (mL/min) H D = dosage desired H = dosage you have available Q = quantity of available solution

1 g = 1,000 mg = 1,000,000 mcg 0.001 g = 1 mg = 1,000 mcg 0.000001 g = 0.001 mg = 1 mcg 1 kg = 1000 g 1 L = 1000 mL 0.001 L = 1 mL 1 mL = 1 cc

10 mg x 12 kg = 120 (low limit of range) 15 mg x 12 kg = 180 ( high limit of range) Safe dose falls between 120 – 180 mg q 4 h Ex: pt weighs 160 pounds 160 ÷ 2.2 = 72.7 kg or 70 kg Order: 18 units/kg/h 18 units x 70 kg/h = 1260 units/h (remember 100 units/mL) 1260 ÷ 100 = 12.6 Begin infusion of Heparin 250,000 units/250 mL ½ NS at 12.6 mL/h Ex: 160 pound pt = 70 kg (see above) Order: 75 units/kg bolus 75 units x 70 = 5250 units (remember 1000 units/mL) 5250 ÷ 1000 = 5.25 Administer 5.25 mL bolus of Heparin 1000 units/mL Ex: Lidocaine 2 g IV in 500 mL D5W at 2 mg/min (remember 2 g = 2000 mg) 2 mg/min 2000 mg

x 500 mL = R (mL/min)

1000 = ½ or 0.5 mL/min 2000 Common Equivalents and Abbreviations 3t=1T gr i = 60 mg gtts – drops 2 T = 1 fl oz gr ¼ = 15 mg g – gram 1 cup = 8 fl oz gr ss = 30 mg mg – milligram 1 t = 5 mL mcg – microgram 1 T = 15 mL 1 kg = 2.2 lb kg – kilogram 1 fl oz = 30 mL 1 in = 2.5 cm L – liter 1 cup = 240 mL mL – milliliter

lb – pound in – inch oz – ounce t – teaspoon T – Tablespoon gr – grain i – one v – five ss – ½

• • • • •

Rules for Math Notation Always include a leading zero: 0.4 mg NOT .4 mg Never include a trailing zero: 16 mL NOT 16.0 mL Answers must include unit of measurement: 4 mL, 60 gtts/min, 100 mg etc. NOT 4, 60, 100. IV flow rates and drip rates must be rounded to nearest whole number Basic Rounding Rule: volumes less than 1 mL – round to nearest hundredth (2 decimal places); volumes greater than 1 mL – round to nearest tenth (1 decimal place)