BMI Calculation Formulas
Comprehensive formulas for calculating Body Mass Index and health assessments
Basic BMI Formula
Universal BMI Definition
Body Mass Index measures body fat based on height and weight for adults aged 18+
Metric System Formula
Standard Formula:
Weight in kilograms, height in meters
With Height in cm:
Equivalent: BMI = (Weight × 10,000) ÷ Height²
Imperial System Formula
With Conversion Factor:
Weight in pounds, height in inches
Step-by-Step:
1. Square your height in inches
2. Divide weight (lbs) by height² (in²)
3. Multiply result by 703
BMI Classification Ranges
WHO Standard Classifications
| Category | BMI Range | Health Risk |
|---|---|---|
| Underweight | BMI < 18.5 | Increased risk of malnutrition |
| Normal Weight | 18.5 ≤ BMI < 25.0 | Lowest health risk |
| Overweight | 25.0 ≤ BMI < 30.0 | Moderate health risk |
| Obese Class I | 30.0 ≤ BMI < 35.0 | High health risk |
| Obese Class II | 35.0 ≤ BMI < 40.0 | Very high health risk |
| Obese Class III | BMI ≥ 40.0 | Extremely high health risk |
Children & Adolescents
For ages 2-18, BMI is interpreted using percentiles:
• Underweight: < 5th percentile
• Healthy weight: 5th to < 85th percentile
• Overweight: 85th to < 95th percentile
• Obese: ≥ 95th percentile
BMI percentiles account for normal growth patterns
Special Populations
Different BMI ranges may apply for:
• Asian populations (lower thresholds)
• Athletes (muscle mass considerations)
• Elderly individuals (≥65 years)
• Pregnant women (specialized charts)
Consult healthcare providers for personalized assessment
Advanced BMI Calculations
BMI Prime
BMI Prime is a dimensionless ratio where:
• BMI Prime = 1.0 corresponds to BMI = 25
• Values > 1.0 indicate overweight
• Values < 1.0 indicate underweight
Ponderal Index
Alternative to BMI, better for very tall/short individuals
Normal range: 11-15 kg/m³
BMI Calculation Examples
Metric Example
Given:
• Weight: 70 kg
• Height: 175 cm (1.75 m)
Calculation:
Result: BMI = 22.9 (Normal Weight)
Imperial Example
Given:
• Weight: 154 lbs
• Height: 5'7" (67 inches)
Calculation:
Result: BMI = 24.1 (Normal Weight)
BMI Limitations & Alternative Formulas
BMI Limitations
• Doesn't distinguish muscle from fat
• Less accurate for athletes
• May not apply to all ethnicities
• Doesn't consider body composition
• Age-related changes not considered
• Different accuracy for men vs women
• Doesn't account for bone density
• Less reliable for children/elderly
Waist-to-Height Ratio
Better predictor of cardiovascular risk
Healthy range: < 0.5 for both units in same measurement
Body Adiposity Index
Direct estimate of body fat percentage
More accurate for certain populations
Health Risk Assessment Formulas
Relative Risk Calculation
Where β varies by condition:
• Type 2 Diabetes: β ≈ 0.09
• Hypertension: β ≈ 0.05
• Reference BMI typically 22.5
Mortality Risk Index
J-shaped relationship with BMI:
• Lowest risk: BMI 22.5-25.0
• Increased risk: BMI < 18.5 or > 30
• Risk doubles: BMI > 35
Age, smoking, and comorbidities modify risk