How to Calculate BMI

Learn the BMI formula and calculate Body Mass Index manually. Step-by-step examples for both metric and imperial units with detailed explanations.

The BMI Formula

📐 Metric Formula (kg and meters)

BMI = kg / m²
Weight in kilograms divided by height in meters squared

Example: Person weighs 70 kg and is 1.75 meters tall

  • Height squared: 1.75 × 1.75 = 3.0625 m²
  • BMI calculation: 70 ÷ 3.0625 = 22.9
  • Category: Normal weight (18.5-24.9)

📏 Imperial Formula (lbs and inches)

BMI = (lbs × 703) / in²
Weight in pounds times 703, divided by height in inches squared

Example: Person weighs 154 lbs and is 5'9" (69 inches) tall

  • Height squared: 69 × 69 = 4,761 in²
  • Weight × 703: 154 × 703 = 108,262
  • BMI calculation: 108,262 ÷ 4,761 = 22.7
  • Category: Normal weight (18.5-24.9)

Step-by-Step Calculation Guide

📝 Method 1: Metric Units (Easier)

Step 1: Measure Your Height

Measure your height in centimeters, then convert to meters by dividing by 100.

Example: 175 cm ÷ 100 = 1.75 meters

Step 2: Measure Your Weight

Weigh yourself in kilograms. Use a digital scale for accuracy.

Example: 70 kg

Step 3: Square Your Height

Multiply your height in meters by itself.

Example: 1.75 × 1.75 = 3.0625 m²

Step 4: Divide Weight by Height Squared

Divide your weight by the squared height.

Example: 70 ÷ 3.0625 = 22.86 (round to 22.9)

Step 5: Interpret Your Result

Compare to BMI categories: <18.5 underweight, 18.5-24.9 normal, 25-29.9 overweight, ≥30 obese.

Example: 22.9 = Normal weight ✓

📝 Method 2: Imperial Units

Step 1: Measure Your Height

Measure height in feet and inches, then convert to total inches.

Example: 5 feet 9 inches = (5 × 12) + 9 = 69 inches

Step 2: Measure Your Weight

Weigh yourself in pounds.

Example: 154 lbs

Step 3: Square Your Height

Multiply your height in inches by itself.

Example: 69 × 69 = 4,761 in²

Step 4: Multiply Weight by 703

Multiply your weight in pounds by the conversion factor 703.

Example: 154 × 703 = 108,262

Step 5: Divide by Height Squared

Divide the result from step 4 by height squared from step 3.

Example: 108,262 ÷ 4,761 = 22.74 (round to 22.7)

Step 6: Interpret Your Result

Compare to BMI categories.

Example: 22.7 = Normal weight ✓

Worked Examples

Example 1: Woman, 5'4", 130 lbs

Given: Height = 5'4" (64 inches), Weight = 130 lbs

Calculation:

  • Height in inches: (5 × 12) + 4 = 64 inches
  • Height squared: 64 × 64 = 4,096 in²
  • Weight × 703: 130 × 703 = 91,390
  • BMI: 91,390 ÷ 4,096 = 22.3

Result: BMI 22.3 = Normal weight ✓

Example 2: Man, 6'0", 200 lbs

Given: Height = 6'0" (72 inches), Weight = 200 lbs

Calculation:

  • Height in inches: 6 × 12 = 72 inches
  • Height squared: 72 × 72 = 5,184 in²
  • Weight × 703: 200 × 703 = 140,600
  • BMI: 140,600 ÷ 5,184 = 27.1

Result: BMI 27.1 = Overweight (25-29.9)

Example 3: Person, 170 cm, 65 kg

Given: Height = 170 cm (1.70 m), Weight = 65 kg

Calculation:

  • Height in meters: 170 ÷ 100 = 1.70 m
  • Height squared: 1.70 × 1.70 = 2.89 m²
  • BMI: 65 ÷ 2.89 = 22.5

Result: BMI 22.5 = Normal weight ✓

Example 4: Person, 180 cm, 95 kg

Given: Height = 180 cm (1.80 m), Weight = 95 kg

Calculation:

  • Height in meters: 180 ÷ 100 = 1.80 m
  • Height squared: 1.80 × 1.80 = 3.24 m²
  • BMI: 95 ÷ 3.24 = 29.3

Result: BMI 29.3 = Overweight (25-29.9)

Example 5: Woman, 5'2", 110 lbs

Given: Height = 5'2" (62 inches), Weight = 110 lbs

Calculation:

  • Height in inches: (5 × 12) + 2 = 62 inches
  • Height squared: 62 × 62 = 3,844 in²
  • Weight × 703: 110 × 703 = 77,330
  • BMI: 77,330 ÷ 3,844 = 20.1

Result: BMI 20.1 = Normal weight ✓

Example 6: Man, 5'10", 250 lbs

Given: Height = 5'10" (70 inches), Weight = 250 lbs

Calculation:

  • Height in inches: (5 × 12) + 10 = 70 inches
  • Height squared: 70 × 70 = 4,900 in²
  • Weight × 703: 250 × 703 = 175,750
  • BMI: 175,750 ÷ 4,900 = 35.9

Result: BMI 35.9 = Obese Class II (35-39.9)

Why 703? Understanding the Conversion Factor

🔢 The Math Behind 703

The number 703 is a conversion factor that makes the imperial formula produce the same result as the metric formula. Here's where it comes from:

Conversion Facts:

  • 1 kilogram = 2.20462 pounds
  • 1 meter = 39.3701 inches
  • 1 meter² = 1,550.0031 inches²

Derivation:

To convert kg/m² to lbs/in², we need to multiply by (lbs per kg) and divide by (in² per m²):

2.20462 ÷ (1/1550.0031) = 2.20462 × 1550.0031 = 703.07

Rounded to 703 for simplicity!

✅ Verification Example

Let's verify that both formulas give the same result:

Person: 70 kg, 1.75 m (154 lbs, 69 inches)

Metric Calculation:

BMI = 70 ÷ (1.75)² = 70 ÷ 3.0625 = 22.86

Imperial Calculation:

BMI = (154 × 703) ÷ (69)² = 108,262 ÷ 4,761 = 22.74

Result: Both give approximately 22.8 BMI ✓

(Small difference due to rounding in conversions)

History of BMI

📜 Origins: Adolphe Quetelet (1832)

BMI was invented by Belgian mathematician Adolphe Quetelet in 1832. Originally called the "Quetelet Index," it was designed to describe the "average man" for population studies, not individual health assessment.

Quetelet's Goal: Find a simple mathematical relationship between height and weight in populations. He observed that weight tends to increase with the square of height in adults.

Important Note: Quetelet was a statistician, not a physician. BMI was never intended as a medical diagnostic tool.

🏥 Medical Adoption (1970s)

In 1972, researcher Ancel Keys coined the term "Body Mass Index" and promoted its use in medical research. Keys studied 7,400 men in five countries and found BMI was a good predictor of body fat percentage at the population level.

Why It Became Popular:

  • Simple calculation requiring only height and weight
  • No expensive equipment needed
  • Useful for large-scale population studies
  • Correlates reasonably well with body fat percentage

📊 Modern Usage (1990s-Present)

In 1998, the National Institutes of Health (NIH) adopted BMI categories for defining overweight and obesity in the United States. The World Health Organization (WHO) followed with international standards.

Current BMI Categories:

  • Underweight: <18.5
  • Normal weight: 18.5-24.9
  • Overweight: 25-29.9
  • Obese: ≥30

Today, BMI is used worldwide as a screening tool for weight-related health risks, despite its limitations.

Common Calculation Mistakes

❌ Mistake 1: Not Squaring Height

Wrong: BMI = 70 ÷ 1.75 = 40 (incorrect!)

Right: BMI = 70 ÷ (1.75 × 1.75) = 70 ÷ 3.0625 = 22.9

Remember: You must multiply height by itself (square it) before dividing.

❌ Mistake 2: Mixing Units

Wrong: Using pounds with meters, or kilograms with inches

Right: Use either all metric (kg, m) or all imperial (lbs, in)

If you have mixed units, convert everything to one system first.

❌ Mistake 3: Forgetting 703

Wrong: BMI = 154 ÷ (69)² = 0.03 (way too low!)

Right: BMI = (154 × 703) ÷ (69)² = 22.7

The 703 conversion factor is essential for imperial units.

❌ Mistake 4: Using Feet Instead of Inches

Wrong: Using 5.9 for 5'9" (should be 69 inches)

Right: Convert to total inches: (5 × 12) + 9 = 69 inches

Always convert feet and inches to total inches first.

❌ Mistake 5: Using Centimeters Instead of Meters

Wrong: BMI = 70 ÷ (175)² = 0.0023 (way too low!)

Right: Convert cm to m first: 175 cm = 1.75 m, then BMI = 70 ÷ (1.75)² = 22.9

Metric formula requires meters, not centimeters.

✅ Quick Check

Your calculated BMI should typically be between 15 and 50. If you get a number outside this range, you probably made a calculation error.

Typical BMI ranges:

  • Most adults: 18-35
  • Athletes: 20-28
  • Severe obesity: 40+

Frequently Asked Questions

What is the BMI formula?
The BMI formula is: BMI = weight (kg) / height (m)² for metric units, or BMI = (weight (lbs) × 703) / height (in)² for imperial units. The 703 is a conversion factor to make the imperial formula equivalent to the metric formula.
How do I calculate BMI manually?
To calculate BMI manually: (1) Measure your height in meters and weight in kilograms, (2) Square your height (multiply it by itself), (3) Divide your weight by the squared height. Example: 70 kg ÷ (1.75 × 1.75) = 70 ÷ 3.0625 = 22.9 BMI.
Why is 703 used in the imperial BMI formula?
The number 703 is a conversion factor that makes the imperial formula (using pounds and inches) produce the same result as the metric formula (using kilograms and meters). It comes from converting kilograms to pounds and meters to inches: (2.20462 lbs/kg) × (1550.0031 in²/m²) ≈ 703.
Can I calculate BMI without a calculator?
Yes, but it's challenging with imperial units due to the large numbers. With metric units, it's easier: if you're 1.75m tall and weigh 70kg, you can estimate: 1.75 × 1.75 ≈ 3, so 70 ÷ 3 ≈ 23. For precise results, use a calculator or our online tool.
Do I need to convert feet and inches to just inches?
Yes, for the imperial formula, you must convert your height to total inches. Multiply feet by 12 and add the remaining inches. Example: 5'9" = (5 × 12) + 9 = 69 inches total.
Is BMI the same calculation for men and women?
Yes, the BMI formula is identical for both men and women. However, women typically have more body fat than men at the same BMI due to biological differences. The BMI categories (18.5-24.9 for healthy weight) are the same for both sexes.

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