This chapter covers basic math calculations that dialysis personnel may need to use while providing care to patients in a chronic or acute dialysis setting. Working with numbers and calculations can sometimes induce anxiety in even the most seasoned student or practitioner. Being able to convert numbers and perform math calculations is critical to safely administering the correct dosage of medication or determining a patient’s dialysis treatment prescription. It is imperative that you are able to correctly calculate medication dosages to ensure that your patient is appropriately treated. You will have the opportunity to review basic math skills and practice some problems to strengthen your skills and increase your comfort level in working with numbers and calculations.

**The metric system**

The metric system is the most widely used system of measurement in the world. In healthcare, it is the most commonly used system to measure medications. It is well suited for this purpose because it can be used to name very large numbers and, more importantly, very small numbers. The three base units used in the metric system are the meter, liter, and gram. The gram (g) is used to measure weight, the liter (L) is used to measure volume, and the meter (m) is used to measure length. You will most often use grams and liters to calculate medication dosages and meters to measure for height or size (__Boxes 25-1__ and __25-2__).

Box 25-1 Common Conversions Used in Healthcare

1 oz = 30 mL

1 L = 1000 mL

1 g = 1000 mg

1 mg = 1000 mcg

1 kg = 2.2 lb or 1000 mL

Box 25-2 Common Abbreviations Used in Healthcare

kg = kilogram

g = gram

mg = milligram

mcg = microgram

mL__*__ = milliliter

cc__*__ = cubic centimeter

__ ^{*}__ mL and cc are used interchangeably

You will use the metric system not only to calculate medication dosages, but also to calculate your patient’s treatment parameters. For example, a patient’s weight is always converted into kilograms when determining how much fluid the patient gained interdialytically, how much over “dry” weight the patient is, and how much fluid was removed intradialytically.

**How do you convert units within the metric system?**

It is easy to convert units within the metric system when you reference the metric line, which is illustrated on the next page. Make note of the base units in the center of the metric line: meter, gram, and liter. Everything to the left of the base unit gets larger and is represented by a whole number. Everything to the right of the base unit gets smaller and is represented by fractions of whole numbers. Prefixes are used with the base units to determine whether the units are larger or smaller than the base unit. The prefixes indicate the size of the unit in multiples of ten. The size of a base unit can be changed by multiplying or dividing by 10. When converting larger units to smaller units, multiply by ten, or move the decimal point to the right for each unit changed; when converting smaller units to larger units, divide by ten, or move the decimal point to the left for each unit changed. The prefixes in the metric line are based on powers of 10. When you make a conversion within the metric system, you multiply or divide by powers of 10. A move from one prefix to another is either 10 times larger or 10 times smaller.

1 meter is equal to 10 decimeters, 100 centimeters, and 1000 millimeters. For example, centimeters are 10 times larger than millimeters; therefore, 1 centimeter equals 10 millimeters. Because centimeters are larger than millimeters, it takes more millimeters to make up the same length.

For each “step” to the right along the metric line, you multiply by 10. For example, if you want to go from a base unit of liters (L) to centiliters (cL), use the following conversion:

If you want to go from a base unit of grams (g) to milligrams (mg), use the following conversion:

Convert 4 liters (L) to milliliters (mL)

Multiply 4 L by 1000

4 L × 1000 = 4000 mL

*or*

Move the decimal point three places to the right__*__ to give you 4000 mL

__ ^{*}__ You may need to fill in zeros to reach the new decimal point.

Convert 4000 milliliters (mL) to liters (L)

Divide 4000 mL by 1000

4000 mL ÷ 1000 = 4 L

*or*

Move the decimal point three places to the left to give you 4 L

In answers that contain only a decimal (e.g., .5 mg), place a zero to the left of the decimal point. This will prevent any errors from occurring should the decimal point go unrecognized. The difference between administering a 5 mg dose and a 0.5 mg dose is significant.

When you make a conversion within the metric system, you move the decimal point one place for each “step” that you move on the metric line. If you move to the right on the metric line, you move the decimal point to the right. If you move to the left on the metric line, you move the decimal point to the left.

An example of how to convert meters (m) to decimeters (dm), centimeters (cm), and millimeters (mm) follows:

Convert 5 m to dm

*or*

Convert 5 m to cm

*or*

Convert 5 m to mm

*or*

**Practice for metric units**

Convert the following measurements:

1. 135 lb = kg

2. 340 cc = mL

3. 658 kg = g

4. 4 L = mL

5. 51 mL = L

6. 1000 g = kg

7. 2.1 m = cm

8. 32 g = kg

9. 1 mg = mcg

10. 1 mm = cm

11. 1 g = mg

12. 6400 mL = L

13. 4.97 g = mg

14. 6.7 cm = mm

15. 600 m = km

16. 64 kg = lb

**Weight calculations**

In dialysis, patients are weighed most often in kilograms. Although a dialysis patient’s weight is variable, an accurate weight is critical so that neither too much fluid nor too little fluid is removed during the treatment. If your patient is weighed in pounds, then a conversion of pounds to kilograms would be needed.

The following are important definitions with regards to calculating weights and fluid removal in the dialysis patient.

*Pre-weight:* The patient’s weight upon arrival to the dialysis clinic for treatment.

*Gain:* The difference between the patient’s weight after the last treatment and the patient’s weight before the current treatment begins.

*Estimated dry weight (EDW):* The lowest weight a patient can tolerate without developing adverse symptoms or hypotension.

*Available weight (AW):* The amount of fluid the patient has available to remove; the difference between the patient’s pre-weight and EDW.

*Goal:* The goal for fluid removal during treatment; usually will include AW plus any fluids that might be administered to the patient during treatment, including any saline used for blood return, saline rinses, or medication.

*Lost:* The amount of fluid lost during a dialysis treatment; calculated by subtracting the patient’s pre-weight from the weight after the dialysis treatment, or post weight.

Example: Mrs. Jones arrives for her treatment on Friday and her pre-weight is 52 kg. Her weight after her last treatment was 49 kg. To calculate her gain, use the following equation:

Mrs. Jones’s EDW is 49.5 kg. To calculate her AW, use the following equation:

Mrs. Jones is receiving an antibiotic today that will be diluted with 150 mL of normal saline. To calculate her goal, use the following equation:

**Calculate the patient’s gain, available weight, and goal**

Anthony Smith arrived for his treatment today with a pre-weight of 74.5 kg. His ordered EDW is 72 kg. He left after his last treatment with a weight of 72.1 kg. He has brought with him a protein drink, which he will consume during his treatment. The protein drink is 8 oz. Anthony will be receiving vancomycin today, which will be reconstituted with 150 mL of normal saline. His rinseback when discontinuing treatment will be 350 mL.

1. Calculate gain

2. Calculate available weight

3. Calculate goal

**Practice for weight calculations**

Calculate the weights for the following patient situations.

Mrs. Renner arrives for her treatment on Monday with a pre-weight of 67.8 kg. Her last treatment was on Friday, and she left with a weight of 65.4 kg. Mrs. Renner’s EDW is 65.0 kg. She is ordered one unit (250 mL) of packed red blood cells to be given intradialytically. Her rinseback is 350 mL.

How much did Mrs. Renner gain between treatments?

What is her AW?

What is the goal for this treatment?

Mr. Whitmire arrives for his treatment with a pre-weight of 81.2 kg. His EDW is 77.0 kg. His rinseback will be 350 mL. What is the goal for this treatment?

**Calculating fluid removal**

Excess fluid is removed from the patient during a hemodialysis treatment by a process called ultrafiltration. Most dialysis equipment used today provides volumetric control, which allows for very precise fluid removal. The dialysis machine is programmed to calculate the ultrafiltration rate (UFR) based on the patient’s treatment goal and the number of hours he or she is scheduled to dialyze. The UFR can be calculated in mL/h or L/h. To calculate the UFR you need to know the goal and the length of treatment.

Example:

Treatment time: 4 hours

Pre-weight: 87.7 kg

EDW: 84.2 kg

AW: 87.7 − 84.2 = 3.5 kg

Rinseback: 300 mL

Goal: 3.5 × 1000 = 3500 + 300 = 3800 mL

UFR: 3800 mL ÷ 4 h = 950 mL/h or 0.95 L/h

**Ratios and proportions**

Ratios and proportions can be used to calculate the dosages for some medications used in dialysis. A ratio may be used to describe the quantity of a medication in proportion to the solution it is in. A proportion is two ratios that are equal. When using ratios and proportions to calculate dosages, you are actually solving for *x*. Heparin is one medication used in dialysis whose strength is measured by a ratio. Heparin is commonly found in dialysis units in the following strengths: 1:1000 or 1:5000. The 1:1000 strength means that there are 1000 units (U) of heparin per milliliter of solution. The 1:5000 strength means that there are 5000 U of heparin per milliliter of solution.

Example: The patient is ordered a loading dose of heparin of 8000 U. The heparin on hand is 1000 U/mL. How much heparin would you give?

Heparin on hand: 1000 U/mL

Ordered dose: 8000 U

1.

2. 1000 × *x* = 8000 × 1

3. 1000*x* = 8000

4. 8000 ÷ 1000 = 8 mL

Answer: 8000 U of 1:1000 heparin = 8 mL

Example: The patient is to receive 15,000 U of heparin. On hand is a vial containing 5000 U of heparin per milliliter. How many cubic centimeters (cc) would you administer?

1.

2. 5000 × *x* = 15,000 × 1

3. 5000*x* = 15,000

4. 15,000 ÷ 5000 = 3 cc

**Practice problems for heparin dosing**

Calculate the volume of heparin to administer for the following doses using a 1000 U/mL vial:

1. 6500 U = mL

2. 10,000 U = mL

3. 1500 U = mL

4. 14,000 U = mL

5. 3000 U = mL

Calculate the volume of heparin to administer for the following doses using a 5000 U/mL vial:

1. 6500 U = mL

2. 10,000 U = mL

3. 1500 U = mL

4. 14,000 U = mL

5. 3000 U = mL

**Solutions**

**Practice for metric units**

1. 135 lb = 61.36 kg(135 lb ÷ 2.2 = 61.36 kg)

2. 340 cc = 340 mL(cc and mL used interchangeably)

3. 658 kg = 658,000 g(658 kg × 1000 = 658,000 g)

4. 4 L = 4000 mL(4 L × 1000 = 4000 mL)

5. 51 mL = 0.051 L(51 mL ÷ 1000 = 0.051 L)

6. 1000 g = 1 kg(1000 g ÷ 1000 = 1 kg)

7. 2.1 m = 210 cm(2.1 m × 100 = 210 cm)

8. 32 g = 0.032 kg(32 g ÷ 1000 = 0.032 kg)

9. 1 mg = 1000 mcg(1 mg × 1000 = 1000 mcg)

10. 1 mm = 0.1 cm(1 mm ÷ 10 = 0.1 cm)

11. 1 g = 1000 mg(1 g × 1000 = 1000 mg)

12. 6400 mL = 6.4 L(6400 mL ÷ 1000 = 6.4 L)

13. 4.97 g = 4970 mg(4.97 g × 1000 = 4970 mg)

14. 6.7 cm = 67 mm(6.7 cm × 10 = 67 mm)

15. 600 m = 0.6 km(600 m ÷ 1000 = 0.6 km)

16. 64 kg = 140.8 lb(64 kg × 2.2 = 140.8 lb)

**Practice for weight calculations**

How much did Mrs. Renner gain between treatments?

What is her AW?

What is the goal for this treatment?

What is the goal for Mr. Whitmire’s treatment?

**Practice problems for heparin dosing**

Using a 1000 U/mL vial:

1. 6500 U = 6.5 mL(6500 U ÷ 1000 = 6.5 mL)

2. 10,000 U = 10 mL(10,000 U ÷ 1000 = 10 mL)

3. 1500 U = 1.5 mL(1500 U ÷ 1000 = 1.5 mL)

4. 14,000 U = 14 mL(14,000 U ÷ 1000 = 14 mL)

5. 3000 U = 3.0 mL(3000 U ÷ 1000 = 3.0 mL)

Using a 5000 U/mL vial:

1. 6500 U = 1.3 mL(6500 U ÷ 5000 = 1.3 mL)

2. 10,000 U = 2.0 mL(10,000 U ÷ 5000 = 2.0 mL)

3. 1500 U = 0.3 mL(1500 U ÷ 5000 = 0.3 mL)

4. 14,000 U = 2.8 mL(14,000 U ÷ 5000 = 2.8 mL)

5. 3000 U = 0.6 mL(3000 U ÷ 5000 = 0.6 mL)