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Mathematical Mechanics

The BMI Formula: How to Calculate Body Mass Index

A transparent breakdown of the arithmetic behind Body Mass Index calculations using both standard Metric and US Imperial measurement systems.

International StandardMetric Units

Metric BMI Formula

BMI = weight (kg) ÷ [height (m)]²

The base formula devised by Adolphe Quetelet. Height must be expressed in meters (e.g., 175 cm = 1.75 m).

United States StandardUS Customary

US Customary Formula

BMI = 703 × weight (lbs) ÷ [height (in)]²

Height must be converted entirely into total inches (e.g., 5 feet 10 inches = (5 × 12) + 10 = 70 inches).

Step-by-Step Worked Arithmetic Examples

Example 1: Calculating with US Units (Pounds & Inches)

Individual Profile: Height: 5 ft 10 in | Weight: 165 lbs

  1. Convert height to total inches:
    (5 feet × 12 inches/foot) + 10 inches = 70 inches
  2. Square the height in inches:
    70 × 70 = 4,900
  3. Multiply weight in pounds by 703:
    703 × 165 = 115,995
  4. Divide step 3 by step 2:
    115,995 ÷ 4,900 = 23.6724...
Final Result: The calculated BMI is 23.7, which places this individual within the standard Healthy Weight category (18.5 – 24.9).
Example 2: Calculating with Metric Units (KG & Meters)

Individual Profile: Height: 175 cm | Weight: 72 kg

  1. Convert centimeters to meters:
    175 cm ÷ 100 = 1.75 meters
  2. Square the height in meters:
    1.75 × 1.75 = 3.0625
  3. Divide weight in kg by height squared:
    72 ÷ 3.0625 = 23.5102...
Final Result: The calculated BMI is 23.5, placing the individual comfortably within the Healthy Weight range.
Why Does the US Equation Use 703?

The constant 703 is the mathematical bridge that converts imperial units into metric kilogram-per-meter-squared values without requiring users to convert their weight to kilograms and height to meters first:

1 pound = 0.45359237 kg

1 inch = 0.0254 meters

1 inch² = 0.00064516 meters²

0.45359237 ÷ 0.00064516 = 703.069579...

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Helpful Reference

Frequently Asked Questions: BMI Formulas

Find clear, evidence-based answers to common questions about Body Mass Index calculation, accuracy, and interpretation.

Because BMI is fundamentally defined in metric units (kilograms per meter squared), calculating BMI with imperial pounds and inches requires unit conversion. One pound equals approximately 0.453592 kg, and one inch equals 0.0254 meters. Squaring the height factor (0.0254²) and dividing the mass conversion yields: 0.45359237 ÷ (0.0254)² ≈ 703.069579. Rounding to 703 provides a practical formula.