# Math for Nursing School

## Formulas, Conversions, & Calculations for Drug Administration

# Med Math for Nursing School

**In This Section…**

- Weight: Pounds to Kilograms
- Height: Inches to Centimeters
- Temperature: Fahrenheit to Celsius
- Volume and Mass Calculations
- Time: Civilian to Military
- Decimal Use and Zeros
- Rounding
- Conversions Cheat Sheet
- IV Infusion Formulas
- Pediatric Nursing Math
- Public and Community Health Nursing Math
- Math Problem Strategies
- Math Charts

*Retractions: Corrections have been made to pounds to kilograms (one lb = 0.45 kg, NOT 2.2; rather, 1 kg = 2.2 lb), kilograms (which = 1,000 grams, NOT 10,000) and Celsius to Fahrenheit conversion. We have amended this and sincerely apologize for any confusion it caused.*-iStudentNurse Team

This page contains a variety of mathematical resources necessary for medication administration and documentation in nursing school. Find basic information on decimals, rounding, military time, and conversions for metric, US, and household units, followed by more involved formulas for IV pump and gravity drip calculations, maintenance fluid rate calculations, epidemiological formulas, and other math-related content. While nursing math is not complex, it’s crucial for nurses to perform calculations correctly each time; therefore, even if you consider yourself to be a “math genius,” it’s important for a nursing student to practice medication administrations consistently.

## Weight

**Converting Between Pounds and Kilograms**

- Medication administration generally relies upon a patient’s weight to be calculated in kilograms (kg) rather than pounds. Accordingly, nursing med math problems frequently require conversions between kilograms and pounds
- Converting between pounds and kilograms:
**1 kg = 2.2 lbs; 1 lb = 0.45 kg (approximately)** - The formula to convert a patient’s given weight from pounds to kilograms is:
**Known weight in pounds/2.2 kg/lb**. Example: 100 lb/ (2.2 kg/lb) = 45.5 kg

** 100 lb = 100 **~~lbs~~ = 45.5 kg

** 2.2 kg/lb ****2.2 kg/**~~lb~~

**2.2 kg/**~~lb~~

- The “lb” is canceled, leaving only the “kg”
- To simplify, the patient’s known weight in pounds can be divided by 2.2 with the unit of pounds replaced by the unit of kilograms; for example: 150 pounds/2.2 = 68.2 kg. (Note that some professors require their students to show all of their work, including how the actual units were converted)
- Take care to round your answer to the nearest 10th place, unless otherwise indicated in the math problem

## Height

**Height Calculations**

- The patient’s height is usually measured and documented in medical records as centimeters (cm)
- Nursing med math problems frequently require inches to be converted into centimeters
- 1 inch = 2.54 cm and 1 cm = 0.393701 inches
- Example: A patient who is 67 inches is 170.2 cm (67 x 2.54 = 170.18, rounded to 170.2)

## Temperature

**Temperature Calculations**

- In medical settings, temperature is usually referred in degrees (°) Celsius. Subsequently, nursing med math problems frequently require conversions between Fahrenheit and Celsius
- Celsius to Fahrenheit:
**°C x 9/5 + 32 = °F** - Fahrenheit to Celsius:
**(°F – 32) x 5/9 = °C**

**Celsius to Fahrenheit**

**37° Celsius x 9/5 + 32 = 98.6° **

**Fahrenheit to Celsius**

**98.8° Fahrenheit – 32 x 5/9 = 37.1° Celsius**

## Volume and Mass

**Volume and Mass Calculations**

Medication doses are often administered in units of milligrams (mg) and milliliters (mL). Nursing med math problems frequently require conversions between grams, milligrams, and micrograms, and liters and milliliters.

**Volume Versus Mass**

- Volume: Liters, milliliters, and microliters are used to express
**drug volume**for dosing - Mass: Grams, milligrams, and micrograms are used to
**drug mass**for dosing - In order to obtain the correct answer, determine the units that the question is asking for. Then set up your work in order to cancel out the units that are not included in the answer

## Time

**Time Calculations**

In healthcare settings, military time is generally used rather than civilian (standard or conventional) time units. This prevents confusion in the Medication Administration Record (MAR) and when documenting in the patient’s chart. Use of military time minimizes risk of drug administration errors that may result from mix-ups between a.m. and p.m. hours.

## Decimals

**Using Decimals and Zeros**

Out of all of the mathematical dilemmas, *improper decimal use the leading cause of preventable human error* pertaining to medication administration, both in nursing school* and* in professional practice.

In nursing, **trailing zeros are avoided** to in order to minimize the risk of mistaking the value for having an extra zero. For example, a prescription that is written as 13.0 mL rather than 13 mL poses the risk of being misinterpreted as 130 mL.

A trailing zero on a recorded medication order may lead to a misconception that an ordered dose is **10 times stronger than what is intended**. For example, a nurse can mistake 10 milligrams for 100 milligrams when someone writes “10.0 milligrams.”

To learn more about actor Dennis Quaid’s personal experience with medication errors and his twin babies, watch the video: **Quaid Family’s Story**

## Rounding

**The Importance of Correct Rounding**

Rounding errors are a *common source of missed questions* on nursing school exams. **Never become overly-comfortable with rounding**- always double check your work, both in nursing school and in clinical practice.

**Round to the 10th**

Medication administration calculations are *usually* rounded to the nearest 10′s place, but some test questions will ask for different rounding parameters. For example, if the drug is being administered in micrograms, the test question may ask you to round it to the nearest 100′s place.

**Rounding Exceptions**

There are also rounding exceptions that exist in standard clinical practice. Common exceptions to the 10ths place rounding standard include IV drip rates (in which the answer is rounded to the **nearest whole drop per minute**), and some pediatric and most neonatal medications doses (in which the dose is so small that it is **rounded to the 100ths place**)

## Conversions Cheat Sheet

Value | To | Value |
---|---|---|

1 gram | = | 1000 milligram |

1 milligram | = | 1,000 micrograms |

1 grain | = | 60 mg |

1 tablespoon | = | 3 teaspoons |

1 teaspoon | = | 5 milliliters |

1 tablespoon | = | 15 milliliters |

1 ounce | = | 30 milliliters (approximately) |

1 cup | = | 8 ounces |

1 pound | = | 2.2 kilograms |

1 inch | = | 2.54 centimeters |

1 ºFahrenheit | = | 5/9 ºCelsius |

1 quart | = | 32 ounces |

1 pint | = | 16 ounces |

4 quarts | = | 8 pints |

1 gallon | = | 128 ounces |

1 quart | = | 2 pints |

## Fahrenheit & Celsius Temperature Chart

Conversion | Formula |
---|---|

Fahrenheit to Celsius | (°F - 32) x 5/9 = °C |

Celsius to Fahrenheit | °C x 9/5 + 32 = °F |

## Metric Unit Mnemonic Chart: Weight, Volume, & Length

KING | HARRY | DIED | MONDAY | DRINKIN' | COLD | MILKY | MOCAS |
---|---|---|---|---|---|---|---|

1,000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 | 0.000,001 |

Kilogram | Hectogram | Dekagram | Gram | Deci | Centigram | Milligram | Microgram |

Kiloliter | Hectoliter | Dekaliter | Liter | Deciliter | Centiliter | Milliliter | Microliter |

Kilometer | Hectometer | Decameter | Meter | Decimeter | Centimeter | Millimeter | Micrometer |

## US to Metric Conversions Chart

US Unit | to | Metric Unit |
---|---|---|

1 inch | = | 2.54 centimeter |

1 pound | = | 0.45 kilogram |

1 teaspoon | = | 5 milliliters |

1 tablespoon | = | 15 milliliters |

1 ounce | = | 30 milliliters |

## Length, Capacity, and Weight Chart

Length | Capacity | Weight |
---|---|---|

1 in = 2.54 cm | 1 Tbsp = 3 tsp | 1 lb = 2.2 kg |

1 ft = 12 in | 1 fl oz = 2 tbsp | 1 kg = 0.45 lb |

3 ft = 1 yd | 1 c = 8 fl oz | lb = kg |

1 yd = 36 in | 1 pt = 2 c | 1 T = 2000 lb |

1 mi = 5280 ft | 1 qt = 2 pt | 1 gm = 1000 mg |

1 mi = 1760 ft | 1 gal = 4 qts | 1 mg = 1000 mcg |

## Standard to Military Time Conversion

Standard | To | Military |
---|---|---|

12:00 am | = | 1200 |

01:00 am | = | 0100 |

02:00 am | = | 0200 |

03:00 am | = | 0300 |

04:00 am | = | 0400 |

05:00 am | = | 0500 |

06:00 am | = | 0600 |

07:00 am | = | 0700 |

08:00 am | = | 0800 |

09:00 am | = | 0900 |

10:00 am | = | 1000 |

11:00 am | = | 1100 |

12:00 pm | = | 1200 |

01:00 pm | = | 1300 |

02:00 pm | = | 1400 |

03:00 pm | = | 1500 |

04:00 pm | = | 1600 |

05:00 pm | = | 1700 |

06:00 pm | = | 1800 |

07:00 pm | = | 1900 |

08:00 pm | = | 2000 |

09:00 pm | = | 2100 |

10:00 pm | = | 2200 |

11:00 pm | = | 2300 |

## IV Infusion Formulas

**Flow Rate Calculation**

- Involves the use or a volumetric pump (or another electronic device) or a manual gravity pump
- Flow rates are expressed in volume over time
- For electronic devices, the flow rate is expressed in milliliters per hour; in gravity pumps, the flow rate is expressed in drops per minutes
- Converting between flow rates is possible by understanding that
**one hour equals 60 minutes**and that knowing**how many milliliters are contained within one drop**(the “drip factor”)

**IV Pump: Milliliters per Hour**

- Stated in the format of milliliters per hour, or mL/hour (mL/hr, or mL/h)
- Milliliters per hour are usually rounded to the nearest 10ths Place
- An volumetric pump or other electronic infusion device is the most commonly used equipment for the infusion of intravenous medications in clinical practice
- The flow rate is typed in the electronic pump (for example: 60 mL/hr)

**IV Gravity Drip: Drops per Minute**

- Gravity drips involve the use of a manual, or non-electronic pump that relies upon gravity rather pump technology (it’s actually a simple process but may trip a student out the first time it’s seen in clinical practice. An experienced nurse will find this to be amusing)
- The drops per minute refers to the drops that enter the drip chamber per minute
- Due to the advancement of technology, gravity drips are rarely used in American medical settings; however, knowledge of gravity pumps are a required component of nursing school curriculum (after all, nurses must be proficient in the event that the electricity goes out or if practicing in rural or foreign areas. Even in a modern ER, a RN may choose to use this method)
- Stated in the format of drops per minute. Drops per minute can also be stated as gtt/minute (or gtt/min)
- Drops per minute are rounded to the nearest whole number (think of it this way: it’s impractical to aim for a fraction of a drop per minute)
- Requires a drip factor: unless stated otherwise, the standard drip factor is 20 gtt/minute for adults (a “macrodrip”) and 60 gtt/minute for pediatrics (a “microdrip”)
- There are three sizes for macrodrips: 10 gtt/mL, 15 gtt/mL, and 20 gtt/mL

## Intravenous Nursing Formulas Calculation Chart

IV Formula | & | Calculation |
---|---|---|

Drops per Minute | = | (Total volume x drip factor) ÷ time in minutes |

Milliliters per Hour | = | Total volume in mL ÷ number of hours |

Infusion Time | = | Total volume to be infused ÷ mL per hour to be infused |

Adult Drip Factor | = | 20 gtts/minute (or drops per minute) |

Pediatric Drip Factor | = | 60 gtts/minute (or drops per minute) |

## Pediatric Math

**Comprehending Maintenance Fluid Rate**

- To calculate the maintenance fluid rate, the patient’s weight must be known in kilograms (kg)
- This may require conversion if the patient’s weight is only given in pounds
- To convert, divide the patient’s weight in pounds by 2.2 [ _ lbs x 1 kg / (2.2 lbs)]

**Convert Pounds to Kilograms**

**(40 lbs x 1 kg)/2.2 lbs = 18.2 kg**

**Maintenance Fluid Rate**

- 1
^{st}10 kg: 100 mL x kg - 2
^{nd}10 kg: 50 mL x kg - 3
^{rd}for every additional kg: 20 mL x kg - The sum of theses values (adding the results of each) determine the maintenance fluid rate per day
- To determine the fluid maintenance per hour, the value of the maintenance fluid rate per day is divided by 24 hours

**Fluid Maintenance Rate for a 18.2 Kg Patient**

**1st 10 kg: 10 kg x 100 mL/kg = 1,000 mL**

**Remaining 8.2 kg: 8.2 x 50 mL/kg = 410 mL**

**Daily Fluid Maintenance Rate: 1,000 mL + 410 mL = 1,410 mL/day**

**Hourly Fluid Maintenance Rate: 1,410 mL/24 hours = 58.75 mL/hr (or 58.8 mL/hr)**

## Fluid Maintenance Requirements Chart

Step | = | Calculation |
---|---|---|

1st 10 kg | = | 100 mL x kg |

2nd 10 kg | = | 50 mL x kg |

3rd: Additional kg | = | 20 mL x kg |

Daily Requirement | = | Sum of Steps 1, 2, and 3 |

## Fluid Maintenance Total: Milliliters/Day & Milliliters/Hour

Calculation | = | Totals |
---|---|---|

Daily Fluid Needs | = | The sum of steps 1-3 (expressed as mL/day) |

Fluid Needs per Hour | = | Divide the daily fluid needs value by 24 (expressed as mL/hr) |

## Public Health

**Epidemiology in Public and Community Health Care**

- Epidemiology is the occurrence of a disease or a condition within a population or group of people
- “Condition’ is included in epidemiological analysis as the variable of focus is not always a disease (for example, it could be violence)
- When referring to the occurrences of disease in populations, epidemiological equations are used

## Epidemiological Nursing Formula Chart

Value | = | Formula |
---|---|---|

Rate and Ratio | = | (Number of health events in a specified period ÷ Population in same area in the same time period) x (k) |

Incidence Rate | = | (Number of new cases or events occurring in the population within a specified time frame ÷ Population at risk during same specified period) x (k) |

Prevalence Rate | = | (Number of total cases or events occurring in the population within a specified time frame ÷ Population at risk during same specified period) x (k) |

Crude Death Rate | = | [Number of deaths within a given year ÷ Estimated population as of mid-year (July 1st)] x (1,000) |

Crude Birth Rate | = | [Number of live births within a given year ÷ Estimated population as of mid-year (July 1st)] x (1,000) |

## Math Problem Strategies

**Approaching Math Problems**

- Determine the method that works the best for you, such as
*Desired over Have*,*Ratio and Proportion*, or*Dimensional Analysis* - Become familiar with the types of math questions that you find to be the most challenging, such as gtts/min (drops per minute)
- Write out the units that the problem is asking for; for example: ml/hr, before beginning the calculations
- Use a highlighter to extract the important data from the questions
- Double-check your work during tests, if time permits
- If math brings you anxiety, start with these problems first on lecture tests, while your mind is the most fresh and less prone to avoidable errors

## Math Charts for Nursing School

# Visual Med Math Charts

I believe your Metric Unit Mnemonic Chart – Weight, Volume and Length is incorrect.

Under Kilo should be 1,000 not 10,000. Hecto should be 100 not 1000. Please revise.

Thanks!

The correction has been made- thank you for pointing it out.

Hello, thank you, for the information, but it is in need of a correction: ggts does not mean drops, gtts does. I checked several resources and could not find those letters to be indicative of drops.

Sincerely,

Tamiia

Tamila: Yes, the article had “ggts” rather than “gtts” listed in a couple of areas. Thank you for looking into this and bringing it to our attention. It has been amended.

Your conversion for Fahrenheit to Celsius is incorrect. Its supposed to be:

C = (F – 32)*(5/9)

not

C = (F – 32)*(9/5)

C = (F – 32)*(1.8)

We had that mixed up in the chart. Thank you for informing us Shaira.

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