FPGEE Calculations & Biostatistics Guide 2026

FPGEE Exam Tip: A calculator is available on the FPGEE. However, knowing the formula and setup before reaching for the calculator saves critical time. Practice setting up calculations quickly — calculation questions often reward candidates who recognize the approach within seconds.

1. Concentration & Percent Strength Calculations

Percent Weight/Volume (% w/v)

Percent w/v = grams of solute per 100 mL of solution. This is the most common concentration expression for liquid preparations.

Formula

% w/v = (grams of solute ÷ mL of solution) × 100

Worked Example

How many grams of NaCl are needed to prepare 500 mL of 0.9% NaCl solution?

0.9 g per 100 mL → 500 mL × (0.9 g/100 mL) = 4.5 g NaCl

Ratio Strength

Ratio strength expresses concentration as 1 gram per X mL (e.g., 1:1000 = 1g per 1000 mL = 0.1% w/v).

Conversion: 1:1000 = 0.1% | 1:200 = 0.5% | 1:100 = 1% | 1:10 = 10%

Worked Example

Epinephrine 1:1000 solution — how many mg of epinephrine are in a 1 mL prefilled syringe?

1:1000 = 1g/1000mL = 1mg/mL → 1 mL syringe contains 1 mg epinephrine

2. Dilution Calculations

When a concentrated solution is diluted, the amount of solute stays constant. Use the dilution equation: C₁V₁ = C₂V₂

Formula

C₁ × V₁ = C₂ × V₂

Worked Example

How many mL of a 70% alcohol solution are needed to make 500 mL of 40% alcohol?

70 × V₁ = 40 × 500 → V₁ = 20,000 / 70 = 285.7 mL of 70% alcohol + QS to 500 mL with water

Alligation Method

Alligation is used when mixing two solutions of known concentrations to achieve a desired intermediate concentration.

Worked Example

Mix a 90% and a 20% alcohol solution to make 1,000 mL of 60% alcohol. How much of each do you need?

Higher (90%) − Target (60%) = 30 parts of lower
Target (60%) − Lower (20%) = 40 parts of higher
Total parts = 70 | 90% stock: (40/70) × 1000 = 571 mL | 20% stock: (30/70) × 1000 = 429 mL

3. Dosage Calculations

Weight-Based Dosing

Formula

Dose = mg/kg × patient weight (kg)

Worked Example

A 6-year-old child weighs 22 kg. The dose of amoxicillin is 40 mg/kg/day in 3 divided doses. What is each dose?

Daily dose = 40 × 22 = 880 mg/day | Per dose = 880 ÷ 3 = 293 mg per dose

Creatinine Clearance (Cockcroft-Gault)

Formula

CrCl = [(140 − age) × weight(kg)] / [72 × SCr] × 0.85 (if female)

Worked Example

65-year-old female, 60 kg, SCr 1.2 mg/dL. Calculate CrCl.

= [(140−65) × 60] / [72 × 1.2] × 0.85
= [75 × 60] / [86.4] × 0.85
= 4500/86.4 × 0.85 = 52.1 × 0.85 = 44.3 mL/min

Clinical note: CrCl 44 mL/min affects dosing of renally cleared drugs: nitrofurantoin contraindicated <30, dose-adjust vancomycin, metformin caution <30.

4. IV Flow Rate Calculations

Key Formulas

Flow rate (mL/hr) = Volume (mL) / Time (hr)

Drip rate (gtt/min) = [Volume × Drop factor] / Time (min)

Worked Examples

Example 1: Infuse 1,000 mL NS over 8 hours. What is the flow rate?
1000 mL / 8 hr = 125 mL/hr

Example 2: Dopamine 400 mg in 250 mL D5W. Order: 5 mcg/kg/min for 70 kg patient. What is the infusion rate in mL/hr?
Concentration = 400,000 mcg / 250 mL = 1,600 mcg/mL
Dose = 5 mcg/kg/min × 70 kg = 350 mcg/min
Rate = (350 mcg/min × 60 min) / 1,600 mcg/mL = 13.1 mL/hr

5. Biostatistics — FPGEE High-Yield Concepts

NNT and NNH

NNT (Number Needed to Treat)

NNT = 1 / ARR
ARR = Control rate − Treatment rate

Lower NNT = more effective drug. NNT of 10 means 10 patients treated to prevent 1 event.

NNH (Number Needed to Harm)

NNH = 1 / ARI
ARI = Treatment risk − Control risk

Higher NNH = safer drug. Compare NNT vs NNH to assess overall benefit-risk balance.

FPGEE Example

Drug A reduces MI risk from 15% to 10%. What is the NNT?

ARR = 15% − 10% = 5% = 0.05 | NNT = 1/0.05 = 20

Sensitivity, Specificity, PPV, NPV

Measure	Formula	Clinical Use	Memory Aid
Sensitivity	TP/(TP+FN)	Detect true positives; screening tests	SnNout — high Sensitivity rules OUT
Specificity	TN/(TN+FP)	Detect true negatives; confirmatory tests	SpPin — high Specificity rules IN
PPV	TP/(TP+FP)	Probability disease present given (+) test	Affected by prevalence (↑ prevalence = ↑ PPV)
NPV	TN/(TN+FN)	Probability disease absent given (−) test	↑ prevalence = ↓ NPV

Study Design Hierarchy

Level 1 (Highest)

Systematic review + Meta-analysis of RCTs

Level 2

Individual Randomized Controlled Trial (RCT)

Level 3

Cohort study (prospective/retrospective)

Level 4

Case-control study

Level 5 (Lowest)

Case series / Expert opinion

Quick Reference: High-Yield FPGEE Calculation Formulas

Calculation Type	Formula	Key Units
% w/v concentration	(g/mL) × 100	g per 100 mL
Dilution (C1V1=C2V2)	C₁V₁ = C₂V₂	Consistent units
Weight-based dose	mg/kg × weight	mg total dose
Creatinine clearance	[(140-age) × wt] / [72 × SCr] × 0.85♀	mL/min
IV flow rate	Volume (mL) / Time (hr)	mL/hr
Drip rate	[Vol × Drop factor] / Time (min)	gtt/min
NNT	1 / ARR	Patients
ARR	Control rate − Treatment rate	Decimal or %
RRR	ARR / Control rate	%

Test Your Calculation Skills

Practice NAPLEX-style calculations — the same types tested on the FPGEE clinical and pharmaceutical sciences sections.

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