Updated February 2026 • 13 min read

BMI Formula: How to Calculate Body Mass Index Step by Step

The BMI formula is one of the simplest and most widely used health calculations in the world. Whether you prefer metric or imperial units, this guide walks you through every step of the BMI calculation, explains where the formula came from, and shows you how to use it correctly with worked examples.

The BMI Formula Explained

Body Mass Index is calculated by dividing a person’s weight by the square of their height. The formula was designed to provide a simple numerical ratio that relates body weight to height, allowing healthcare professionals to quickly categorize individuals into weight status groups. According to the World Health Organization (WHO), BMI is a useful population-level measure of overweight and obesity.

There are two versions of the formula depending on which measurement system you use. Both produce the same result — BMI is a dimensionless number (it has no units) that typically falls between 15 and 40 for most adults. To understand more about how BMI is used to assess weight status, see our comprehensive BMI calculator guide.

Metric BMI Formula

What Each Part Means

• Weight (kg): Your body weight measured in kilograms
• Height (m): Your height measured in meters (not centimeters)
• Height²: Your height multiplied by itself (squared)

Step-by-Step Metric Calculation

Let us calculate the BMI for a person who weighs 75 kg and is 1.78 m tall:

Converting Centimeters to Meters

A common mistake is using centimeters instead of meters. The metric formula requires height in meters. To convert:

If you accidentally use centimeters without converting, your result will be absurdly small (about 0.0024 instead of 23.7), which is a clear sign of an error.

More Metric Examples

Imperial BMI Formula

What Each Part Means

• Weight (lbs): Your body weight measured in pounds
• Height (in): Your total height converted to inches
• Height²: Your height in inches multiplied by itself
• × 703: A conversion factor that adjusts the imperial result to match the metric BMI scale

Step-by-Step Imperial Calculation

Let us calculate the BMI for a person who weighs 165 lbs and is 5 feet 10 inches tall:

Converting Feet and Inches to Total Inches

The imperial formula requires total height in inches. To convert:

Common Height Conversions

More Imperial Examples

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Where Does the 703 Come From?

The number 703 in the imperial BMI formula is a unit conversion factor. It exists because the metric and imperial systems use different base units. Here is the mathematical derivation:

The metric formula is the “original” formula: BMI = kg / m². To use pounds and inches instead, we need to convert:

The precise conversion factor is 703.0696, which is rounded to 703 for practical use. This rounding introduces a negligible error of less than 0.01 BMI points, which has no clinical significance.

History of the BMI Formula

The formula that we now call BMI has a rich historical background spanning nearly two centuries:

Adolphe Quetelet (1830s)

Belgian mathematician and astronomer Adolphe Quetelet developed the formula in the early 1830s as part of his pioneering work in social statistics. Quetelet was interested in defining the characteristics of the “average man” (l’homme moyen) and observed that body weight in adult populations tends to scale with the square of height rather than the cube. He called this relationship the Quetelet Index.

Quetelet specifically chose height squared (rather than height cubed) because his empirical data showed that this power provided the best fit. If humans were perfectly proportional three-dimensional objects, weight would scale with the cube of height. But humans are not perfectly proportional — taller people tend to be relatively slimmer, making the square of height a better predictor.

Ancel Keys (1972)

The term “Body Mass Index” was coined by American physiologist Ancel Keys in a 1972 paper published in the Journal of Chronic Diseases. Keys compared several body weight indices (including weight/height, weight/height², weight/height³, and others) across populations in the United States, Finland, Italy, South Africa, and Japan. He concluded that weight/height² had the best correlation with body fat percentage while having the lowest correlation with height — meaning it measured fatness rather than tallness.

NIH Adoption (1985)

In 1985, the National Institutes of Health formally adopted BMI as the standard measure for defining obesity in the United States. Prior to this, ideal weight tables from the Metropolitan Life Insurance Company were the primary reference for weight assessment. For more context on how BMI evolved, read our history of BMI guide.

WHO Classification (1995–2000)

The World Health Organization established the current BMI classification system in 1995, defining underweight (below 18.5), normal weight (18.5–24.9), overweight (25–29.9), and obese (30+). These cutoffs were refined in a 2000 WHO technical report and have remained the global standard since. Read our BMI Categories guide for the full classification.

Why Height Is Squared (Not Cubed)

One of the most common questions about the BMI formula is: why use height squared? The short answer is that it works best empirically. Research from the Centers for Disease Control and Prevention (CDC) confirms this mathematical relationship. Here is a more detailed explanation:

In physics, if you scale up a three-dimensional object proportionally, its volume (and therefore its mass) increases with the cube of the linear dimension. A person twice as tall, if perfectly proportional, would weigh eight times as much (2³ = 8). Using this logic, weight/height³ would seem more appropriate.

However, humans are not perfectly proportional when scaled. Taller people do not simply grow in all three dimensions equally. They tend to be relatively thinner — their width and depth do not increase at the same rate as their height. Quetelet’s empirical data, and all subsequent studies, have confirmed that weight scales approximately with height², not height³, in adult populations. Learn more about what constitutes a healthy BMI range for your height.

This finding has been validated across many populations worldwide. The exponent that best eliminates the correlation between BMI and height is approximately 2.0 (actually closer to 2.0–2.5 depending on the population), making the square the best simple integer to use in the formula.

Some researchers have proposed alternative indices that use different exponents. The Ponderal Index uses height³, and the “New BMI” proposed by mathematician Nick Trefethen in 2013 uses height^2.5. However, none of these alternatives have gained widespread adoption because the practical differences are small and the established BMI cutoffs (18.5, 25, 30) would need to be recalibrated.

BMI Formula Variations and Alternatives

While the standard BMI formula is the most widely used, several variations and alternatives exist. Research from the National Institutes of Health (NIH) has explored various alternatives to address some of BMI's known limitations:

The Ponderal Index (PI)

The Ponderal Index uses height cubed instead of height squared. It is sometimes preferred for very tall and very short individuals because it better accounts for the non-linear relationship between height and weight at extreme heights. A healthy PI is approximately 11–15 kg/m³. However, it has not been widely adopted in clinical practice.

The New BMI (Trefethen’s Formula)

Proposed by Oxford mathematician Nick Trefethen in 2013, this formula uses an exponent of 2.5 instead of 2, which he argued better accounts for the relationship between height and weight, particularly for very tall and very short people. Under the standard formula, short people may be told they are thinner than they really are, while tall people may be told they are fatter. The New BMI aims to correct this bias. Try our New BMI calculator to see how your results compare.

SBMI (Smart BMI)

Smart BMI incorporates age and sex into the calculation, producing a result on a 0–70 scale where 30 represents the statistical median for the population. It was designed to address the fact that the same BMI value has different health implications at different ages and between sexes. While theoretically more accurate, it has not replaced standard BMI in clinical practice.

Surface-Based Body Shape Index (SBSI)

A newer metric that combines body surface area, vertical trunk circumference, waist circumference, and height. It requires more measurements than BMI but provides a better prediction of mortality risk. It has shown promise in research settings but is not yet practical for routine clinical use.

Comparison: Metric vs. Imperial Formula

Common BMI Calculation Mistakes

When calculating BMI by hand, these are the most frequent errors. For validated and error-free calculations, Mayo Clinic and Cleveland Clinic both recommend using digital calculators:

Mistake 1: Not Squaring the Height

The most common error. You must multiply height by itself before dividing. If you simply divide weight by height (without squaring), you get the Broca Index, not BMI, and the result will be far too high.

Mistake 2: Using Centimeters Instead of Meters

The metric formula requires meters. Using 178 instead of 1.78 produces a result of about 0.002, which is clearly wrong.

Mistake 3: Not Converting Feet to Total Inches

A person who is 5′7″ is 67 inches, not 57 inches. You must multiply the feet by 12 and add the remaining inches.

Mistake 4: Forgetting the 703 Multiplier

The imperial formula requires multiplying by 703. Without it, the result will be about 0.034 instead of 23.7.

Mistake 5: Squaring Weight Instead of Height

It is height that gets squared, not weight. Squaring weight produces absurdly large numbers.

Mistake 6: Rounding Too Early

Wait until the final step to round your result. Rounding intermediate calculations can compound errors. Round the final BMI to one decimal place (e.g., 23.7, not 24).

BMI Categories Reference

Once you have calculated your BMI, use this table to determine your category. These classifications are based on WHO international standards. Women and men can use our specialized calculators: BMI Calculator for Women or BMI Calculator for Men.

For a comprehensive explanation of each category, see our BMI Categories guide.

Unit Conversion Reference

Use these conversions when calculating BMI manually:

Practical Tips for Accurate BMI Calculation

Frequently Asked Questions

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Medical Disclaimer: This article is for informational purposes only and does not constitute medical advice. BMI is a screening tool, not a diagnostic measure. Always consult a qualified healthcare provider for personalized health assessment and recommendations.