Comprehensive Nursing Math Review

Method: D/H x Q (basic tablet calculation)

$\text{Tablets} = \frac{50 \text{ mg}}{25 \text{ mg}} \times 1 = 2 \text{ tablets}$

Answer: Administer 2 tablets per dose.

Reasonableness: The ordered dose is exactly double the available strength, so 2 tablets makes sense. No splitting required.

Review if missed: Three Calculation Methods

Method: mL/hr flow rate formula

$\text{mL/hr} = \frac{1{,}000 \text{ mL}}{8 \text{ hr}} = 125 \text{ mL/hr}$

Answer: Set the pump to 125 mL/hr.

Reasonableness: A 1-liter bag over 8 hours is a common maintenance rate. 125 mL/hr is a typical value — not too fast, not unreasonably slow.

Review if missed: IV Drip Rate Calculations

Method: Weight-based dosing + D/H x Q

Step 1: Convert weight to kg.

$\frac{44}{2.2} = 20 \text{ kg}$

Step 2: Calculate total daily dose.

$40 \times 20 = 800 \text{ mg/day}$

Step 3: Divide into individual doses. The order says “divided TID,” meaning the total daily dose is split into 3 equal parts.

$\frac{800}{3} \approx 266.7 \text{ mg per dose}$

Step 4: Calculate volume using D/H x Q.

$\frac{266.7 \text{ mg}}{250 \text{ mg}} \times 5 \text{ mL} \approx 5.3 \text{ mL}$

Answer: Administer 5.3 mL per dose, three times daily.

Reasonableness: A 20 kg child receiving 40 mg/kg/day is getting 800 mg total. Each dose of roughly 267 mg from a 250 mg/5 mL suspension should be just over 5 mL. This checks out.

Important distinction — TID vs. “divided TID”: TID means “three times a day” and refers to frequency, not division. An order of “50 mg TID” means give 50 mg each time, three times a day (150 mg total daily). By contrast, “divided TID” (as in this problem) means the stated total daily dose is split into 3 equal parts. Here, 800 mg/day divided TID = 266.7 mg per dose. Confusing the two can cause a three-fold dosing error.

Review if missed: Weight-Based Dosing

Method: Critical care mcg/kg/min to mL/hr

Step 1: Convert concentration to mcg/mL.

$\frac{400 \text{ mg}}{250 \text{ mL}} = 1.6 \text{ mg/mL} = 1{,}600 \text{ mcg/mL}$

Step 2: Apply the formula.

$\text{mL/hr} = \frac{5 \times 80 \times 60}{1{,}600} = \frac{24{,}000}{1{,}600} = 15 \text{ mL/hr}$

Answer: Set the pump to 15 mL/hr.

Reasonableness: Dopamine at 5 mcg/kg/min is a moderate (cardiac) dose. For an 80 kg patient with a standard 400 mg/250 mL concentration, pump rates of 10 to 20 mL/hr are typical. 15 mL/hr falls right in that range.

Clinical note: Older references classify low-dose dopamine (1-3 mcg/kg/min) as a “renal dose” that was once thought to protect kidney perfusion. Current evidence (including KDIGO and Surviving Sepsis Campaign guidelines) does not support low-dose dopamine for renal protection, and “renal dose dopamine” is considered a historical concept. Dopamine dosing is now described by its hemodynamic effects: low dose (1-5 mcg/kg/min) primarily stimulates dopaminergic receptors, moderate dose (5-10 mcg/kg/min) adds beta-1 (inotropic) effects, and high dose (greater than 10 mcg/kg/min) adds alpha-1 (vasopressor) effects.

Review if missed: Critical Care Drip Calculations

Method: MAP formula

$\text{MAP} = \frac{96 + (2 \times 62)}{3} = \frac{96 + 124}{3} = \frac{220}{3} \approx 73.3 \text{ mmHg}$

Answer: MAP is approximately 73 mmHg — this is above the ICU target of 65 mmHg.

Reasonableness: MAP should fall between the systolic and diastolic values, closer to diastolic. A value of 73 is between 62 and 96 and is weighted toward the diastolic, which is correct.

Review if missed: Hemodynamic Calculations

Method: gtts/min formula

Step 1: Convert time to minutes.

$6 \text{ hours} \times 60 = 360 \text{ minutes}$

Step 2: Apply the drip rate formula.

$\text{gtts/min} = \frac{500 \times 15}{360} = \frac{7{,}500}{360} \approx 20.8 \approx 21 \text{ gtts/min}$

Answer: Set the drip rate to approximately 21 gtts/min.

Reasonableness: For a 500 mL bag over 6 hours with standard 15 gtts/mL tubing, a rate in the low 20s is expected. This is a common, manageable drip rate for a gravity infusion.

Review if missed: IV Drip Rate Calculations

Method: Cockcroft-Gault equation

$\text{CrCl} = \frac{(140 - 72) \times 85}{72 \times 1.8} = \frac{68 \times 85}{129.6} = \frac{5{,}780}{129.6} \approx 44.6 \text{ mL/min}$

Answer: Estimated CrCl is approximately 44.6 mL/min.

Clinical interpretation: A CrCl of 44.6 mL/min indicates moderate renal impairment (CKD Stage 3). Medications cleared by the kidneys — such as vancomycin, enoxaparin, and many antibiotics — will likely need dose reduction or extended intervals. Check the drug reference for renal dosing guidelines. Note: KDIGO sub-stages (3a vs 3b) are defined by eGFR, not CrCl — see the staging table on the Renal Dose Adjustments page for the distinction.

Review if missed: Renal Dose Adjustments

Method: D/H x Q (parenteral dosage)

$\text{mL} = \frac{4 \text{ mg}}{10 \text{ mg}} \times 1 \text{ mL} = 0.4 \text{ mL}$

Answer: Draw up 0.4 mL from the vial.

Reasonableness: 4 mg is less than half the concentration of a 10 mg/mL vial, so a volume of less than 0.5 mL is expected. Use a 1 mL syringe for accuracy at this small volume.

Review if missed: Parenteral Dosage

Method: Holliday-Segar 4-2-1 rule

Step 1: First 10 kg at 4 mL/kg/hr.

$10 \times 4 = 40 \text{ mL/hr}$

Step 2: Next 10 kg (11-20 kg) at 2 mL/kg/hr.

$10 \times 2 = 20 \text{ mL/hr}$

Step 3: Remaining 5 kg (21-25 kg) at 1 mL/kg/hr.

$5 \times 1 = 5 \text{ mL/hr}$

Step 4: Add all three components.

$40 + 20 + 5 = 65 \text{ mL/hr}$

Answer: The maintenance fluid rate is 65 mL/hr.

Reasonableness: For a 25 kg child, a rate between 60 and 70 mL/hr is typical. This is well below adult rates and well above infant rates, which matches a school-age child’s weight.

Review if missed: Pediatric Fluid Maintenance

Method: Critical care mcg/min to mL/hr (non-weight-based)

Step 1: Convert concentration to mcg/mL.

$\frac{4 \text{ mg}}{250 \text{ mL}} = 0.016 \text{ mg/mL} = 16 \text{ mcg/mL}$

Step 2: Apply the formula.

$\text{mL/hr} = \frac{12 \times 60}{16} = \frac{720}{16} = 45 \text{ mL/hr}$

Answer: Set the pump to 45 mL/hr.

Reasonableness: Norepinephrine dose ranges are typically 2 to 20 mcg/min. At 12 mcg/min with a standard 4 mg/250 mL mix, pump rates of 30 to 60 mL/hr are expected. A rate of 45 mL/hr is within range.

Review if missed: Critical Care Drip Calculations

Method: Mosteller formula + BSA-based dosing

Step 1: Calculate BSA.

$\text{BSA} = \sqrt{\frac{170 \times 68}{3{,}600}} = \sqrt{\frac{11{,}560}{3{,}600}} \approx \sqrt{3.211} \approx 1.79 \text{ m}^2$

Step 2: Calculate the drug dose.

$\text{Dose} = 75 \text{ mg/m}^2 \times 1.79 \text{ m}^2 \approx 134.3 \text{ mg}$

Answer: BSA is 1.79 m² and the chemotherapy dose is approximately 134 mg.

Reasonableness: Average adult BSA is 1.7 to 1.9 m², so 1.79 is within the expected range for a 170 cm, 68 kg individual. A dose of 134 mg from a 75 mg/m² order with a near-average BSA seems reasonable.

Review if missed: Dosage by BSA

Method: D/H x Q (tablet calculation)

$\text{Tablets} = \frac{60}{40} \times 1 = 1.5 \text{ tablets}$

Answer: Administer 1.5 tablets (one whole tablet plus one half of a scored tablet).

Reasonableness: 60 mg is 1.5 times the 40 mg available strength. Since the tablets are scored, half-tablet dosing is appropriate. If the tablets were not scored, you would need to contact the pharmacy for an alternative formulation.

Review if missed: Three Calculation Methods

Method: Cockcroft-Gault equation (with female correction)

$\text{CrCl} = \frac{(140 - 65) \times 60}{72 \times 1.2} \times 0.85 = \frac{75 \times 60}{86.4} \times 0.85 = \frac{4{,}500}{86.4} \times 0.85$

$\approx 52.08 \times 0.85 \approx 44.3 \text{ mL/min}$

Answer: CrCl is approximately 44.3 mL/min. This is below 50 mL/min, so standard-interval Vancomycin dosing (q12h) is not appropriate. The provider should be notified — Vancomycin can still be given at this CrCl, but requires extended-interval dosing (e.g., q24h or q48h) guided by trough levels.

Reasonableness: An elderly female patient with a creatinine of 1.2 (which appears only mildly elevated) actually has significantly reduced kidney function when age and sex are factored in. This is a classic example of why serum creatinine alone is misleading — the Cockcroft-Gault equation reveals the true picture.

Review if missed: Renal Dose Adjustments

Method: Weight-based dosing + IV rate calculation

Step 1: Convert weight to kg.

$\frac{176}{2.2} = 80 \text{ kg}$

Step 2: Calculate the hourly dose.

$18 \text{ units/kg/hr} \times 80 \text{ kg} = 1{,}440 \text{ units/hr}$

Step 3: Find the bag concentration.

$\frac{25{,}000 \text{ units}}{500 \text{ mL}} = 50 \text{ units/mL}$

Step 4: Calculate the pump rate.

$\text{mL/hr} = \frac{1{,}440 \text{ units/hr}}{50 \text{ units/mL}} = 28.8 \text{ mL/hr}$

Answer: Set the pump to 28.8 mL/hr (or 29 mL/hr per facility rounding policy).

Reasonableness: Heparin infusion rates of 20 to 35 mL/hr are common for standard-weight adults on a 25,000 units/500 mL concentration. A rate of 28.8 falls squarely in this range.

Review if missed: Weight-Based Dosing and IV Drip Rate Calculations

Method: Critical care mcg/kg/min to mL/hr (titration)

Step 1: Convert concentration to mcg/mL.

$\frac{250 \text{ mg}}{250 \text{ mL}} = 1 \text{ mg/mL} = 1{,}000 \text{ mcg/mL}$

Step 2: Calculate the old rate at 5 mcg/kg/min.

$\text{mL/hr} = \frac{5 \times 70 \times 60}{1{,}000} = \frac{21{,}000}{1{,}000} = 21 \text{ mL/hr}$

Step 3: Calculate the new rate at 7.5 mcg/kg/min.

$\text{mL/hr} = \frac{7.5 \times 70 \times 60}{1{,}000} = \frac{31{,}500}{1{,}000} = 31.5 \text{ mL/hr}$

Answer: The old rate was 21 mL/hr. The new rate is 31.5 mL/hr. The pump rate increases by 10.5 mL/hr, which represents a 50% increase in dose.

Reasonableness: Dobutamine is typically dosed at 2.5 to 20 mcg/kg/min. Both rates fall within this therapeutic range. A 50% dose increase (from 5 to 7.5 mcg/kg/min) produces a 50% increase in pump rate (from 21 to 31.5 mL/hr), which confirms the math is internally consistent.

Review if missed: Critical Care Drip Calculations and Titration Calculations