Waist to Hip Ratio Formula: Complete Calculation Guide

The WHR Formula

The waist to hip ratio formula is remarkably simple. It requires only two measurements and basic division:

In mathematical notation, this can be expressed as:

WHR = W / H

Where W is the waist circumference and H is the hip circumference. Both measurements must be in the same units (both inches or both centimeters) for the calculation to work correctly.

The result is a dimensionless ratio, meaning it has no units attached. A WHR of 0.85 means that the waist circumference is 85% of the hip circumference, regardless of whether the original measurements were in inches, centimeters, or any other unit of length.

Step-by-Step Calculation

Let's walk through the complete process of calculating waist to hip ratio:

Step 1: Measure Your Waist

Using a flexible measuring tape, measure the circumference of your waist at the narrowest point. See our detailed measurement guide for step-by-step instructions. This is typically at or slightly above your belly button. Keep the tape parallel to the floor and snug but not tight. Record this number.

Step 2: Measure Your Hips

Measure the circumference of your hips at the widest point, which is usually around the fullest part of your buttocks. Again, keep the tape parallel to the floor and record this measurement.

Step 3: Apply the Formula

Divide your waist measurement by your hip measurement. The result is your waist to hip ratio.

Step 4: Interpret the Result

Compare your calculated WHR to the health risk thresholds for your gender. For women, 0.85 or below is considered healthy; for men, 0.90 or below is healthy.

Calculation Examples

Here are several worked examples to illustrate how the formula is applied:

Example 1: Woman with Low Risk WHR

Example 2: Man with Moderate Risk WHR

Example 3: Metric Units

Example 4: High Risk WHR

10-Row Worked Examples Grid

The table below presents ten calculated WHR values across a range of body sizes, showing both imperial and metric measurements alongside the corresponding risk classifications for females (F) and males (M):

Dashes indicate values outside the typical range for that sex. Rows 4-6 illustrate how the same WHR value can signal different risk levels depending on sex, underscoring the importance of gender-specific thresholds endorsed by the WHO.

Understanding the Math

The waist to hip ratio is a simple proportion that expresses the relationship between two body measurements. Let's explore what the numbers actually mean:

Ratio Interpretation

A ratio is a comparison of two quantities by division. When we calculate WHR, we're essentially asking: "For every unit of hip circumference, how many units of waist circumference are there?"

• WHR = 0.70: Waist is 70% of hip circumference
• WHR = 0.80: Waist is 80% of hip circumference
• WHR = 0.90: Waist is 90% of hip circumference
• WHR = 1.00: Waist equals hip circumference
• WHR = 1.10: Waist is 110% of hip circumference (10% larger)

Why Division Works

Using division normalizes the measurements to account for different body sizes. A person with measurements of 28/36 inches has the same WHR (0.78) as someone with 35/45 inches, even though their absolute measurements are quite different. This allows WHR to be compared across people of different sizes and between populations.

Unit Independence

Because WHR is a ratio of two measurements in the same units, the units cancel out mathematically. This is why you get the same result whether measuring in inches or centimeters:

Health Risk Thresholds

The formula itself is just mathematics; the health significance comes from comparing results to established thresholds:

Women's Thresholds

Men's Thresholds

These thresholds were established by the World Health Organization based on extensive research linking body fat distribution to cardiovascular disease, diabetes, and other health conditions. For a visual reference, see our complete WHR chart. Learn more about the specific health risks associated with each category.

Common Calculation Mistakes

While the formula is simple, errors can occur. Here are common mistakes to avoid:

Mixing Units

If you measure your waist in inches and hips in centimeters, your calculation will be meaningless. Always use the same unit for both measurements.

Dividing in the Wrong Order

WHR is specifically waist divided by hips, not the reverse. Dividing hips by waist would give you a different number with different interpretation.

Rounding Too Early

While final WHR is typically reported to two decimal places, avoid rounding your raw measurements before calculating. Use the exact measurements for the division, then round the result.

Measurement Errors

The formula is only as accurate as your measurements. Taking measurements at the wrong locations or with improper technique will produce inaccurate WHR regardless of correct calculation.

Related Formulas

WHR is part of a family of body ratio and composition formulas used in health assessment. Understanding these related calculations provides context:

Waist-to-Height Ratio (WHtR)

Similar to WHR but compares waist circumference to height:

WHtR = Waist ÷ Height

A WHtR of 0.5 or below is generally considered healthy. Learn more in our WHtR calculator guide. The simple rule is that your waist should be less than half your height.

Body Mass Index (BMI)

BMI relates weight to height but uses a different formula structure:

BMI = Weight (kg) ÷ Height² (m²)

Or in imperial units:

BMI = (Weight (lbs) × 703) ÷ Height² (in²)

BMI measures overall weight relative to height but doesn't indicate fat distribution, which is why WHR provides complementary information. The NHLBI and CDC provide further detail on BMI classifications. See our BMI vs WHR comparison for a full analysis.

Body Adiposity Index (BAI)

BAI attempts to estimate body fat percentage using hip circumference and height:

BAI = (Hip (cm) ÷ Height (m)^1.5) - 18

This formula is more complex and less commonly used than WHR or BMI.

Formula Comparison

The following table compares WHR to other widely used body composition formulas across several practical dimensions:

Using Technology for Calculations

While manual calculation is straightforward, various tools can help:

Online Calculators

Our WHR calculator automatically computes your ratio and interprets the results. Simply enter your waist and hip measurements, and the tool does the math for you.

Smartphone Apps

Many health and fitness apps include WHR calculators. Some can track your measurements over time and show trends.

Spreadsheets

If you're tracking multiple measurements over time, a simple spreadsheet formula can calculate WHR automatically:

=A2/B2

(Where A2 contains waist measurement and B2 contains hip measurement)

Basic Calculator

Any calculator with division capability can compute WHR. Simply enter your waist measurement, press the division key, enter your hip measurement, and press equals.

Precision and Rounding

Understanding how to handle decimal places ensures accurate and meaningful results:

Measurement Precision

Most tape measures allow measurement to the nearest quarter or half inch (or half centimeter). Recording measurements to this precision is appropriate for health assessment purposes.

Calculation Precision

When you divide, you'll often get a long decimal. For example, 31 ÷ 39 = 0.794871... The extra decimal places don't add meaningful information for health assessment.

Reporting Precision

WHR is typically reported to two decimal places (e.g., 0.79 or 0.85). This level of precision is appropriate given the accuracy of tape measure readings and natural day-to-day variation in body measurements.

Rounding Rules

Use standard rounding: if the third decimal place is 5 or higher, round up; if 4 or lower, round down.

• 0.794 rounds to 0.79
• 0.795 rounds to 0.80
• 0.846 rounds to 0.85

Scientific Basis of the Formula

The WHR formula's simplicity belies the extensive research supporting its use:

Historical Development

The concept of using waist and hip measurements to assess health risk emerged in the 1980s and 1990s when researchers began understanding that body fat distribution was as important as total body fat. Dr. Per Bjorntorp and colleagues were among the early researchers to establish the significance of central obesity.

Physiological Rationale

The formula captures the difference between android (apple-shaped) and gynoid (pear-shaped) fat distribution. The waist measurement primarily reflects visceral fat around internal organs, while the hip measurement reflects subcutaneous fat in the gluteal and femoral regions. Harvard's Nutrition Source provides an excellent overview of why measuring fat distribution matters more than total weight alone.

Research Validation

Numerous large-scale studies have validated WHR as a predictor of cardiovascular disease, diabetes, and mortality. The INTERHEART study, involving over 27,000 participants, found WHR to be among the strongest predictors of heart attack risk, outperforming BMI.

WHO Endorsement

The World Health Organization formally endorsed WHR as a health assessment tool, establishing the cutoff values that remain in use today. These thresholds were derived from population studies linking WHR to disease outcomes.

Limitations of the Formula

While useful, the WHR formula has limitations that users should understand:

Doesn't Measure Fat Directly

WHR is an indirect measure of fat distribution based on body circumferences. It doesn't directly quantify visceral or subcutaneous fat. Medical imaging (CT scans, MRI) provides more precise fat measurement but isn't practical for routine screening.

Affected by Muscle Mass

A person with well-developed gluteal muscles might have a larger hip measurement not due to fat but muscle. Similarly, strong oblique muscles could affect waist measurements. In very athletic individuals, WHR may be less accurate as a fat distribution indicator.

Population Variations

The standard WHR thresholds were developed primarily from studies of European populations. Research suggests that optimal cutoffs may differ for Asian, African, and other ethnic groups, though the general principle that lower WHR indicates better health applies universally.

Age Considerations

Body composition changes with age, and the relationship between WHR and health risk may vary across age groups. The formula doesn't account for these age-related differences.

Converting Between Units

If you need to convert measurements before calculating, here are the conversion formulas:

Inches to Centimeters

Centimeters = Inches × 2.54

Example: 30 inches × 2.54 = 76.2 cm

Centimeters to Inches

Inches = Centimeters ÷ 2.54

Example: 100 cm ÷ 2.54 = 39.37 inches

Remember, you only need to convert if your measurements are in different units. If both are already in the same unit, proceed directly to the WHR calculation.

Unit Conversion Quick Reference

Keep this table handy whenever you need to convert between measurement systems before calculating WHR:

Practice Problems

Test your understanding with these practice calculations:

Problem 1

A woman has a waist of 27 inches and hips of 36 inches. What is her WHR and risk category?

Problem 2

A man has a waist of 95 cm and hips of 100 cm. What is his WHR and risk category?

Problem 3

If a person's WHR is 0.88 and their hip measurement is 42 inches, what is their waist measurement?

Summary

The waist to hip ratio formula (WHR = Waist ÷ Hips) is a simple yet powerful tool for assessing health risk related to body fat distribution. The calculation requires only two measurements and basic division, making it accessible to anyone.

Key points to remember:

• Always use the same units for both measurements
• Divide waist by hips (not the reverse)
• Round final results to two decimal places
• Compare results to gender-specific health thresholds
• Lower WHR values indicate healthier fat distribution

Use our WHR calculator for automatic calculation and interpretation, or apply the formula manually. To understand ideal target values, check our guide on what WHR to aim for.

Related Formulas: ABSI and BAI

Beyond WHR, BMI, and WHtR, two additional body composition formulas have gained attention in clinical research: A Body Shape Index (ABSI) and Body Adiposity Index (BAI). Both attempt to address shortcomings in simpler metrics, though each comes with its own trade-offs.

A Body Shape Index (ABSI)

ABSI was developed in 2012 by Krakauer and Krakauer to capture body shape information that is independent of BMI. The formula is:

ABSI = WC / (BMI^2/3 × Height^1/2)

Where WC is waist circumference in meters, BMI is the standard body mass index, and height is measured in meters. The exponents (2/3 and 1/2) were derived from allometric regression analysis of NHANES data, specifically chosen so that ABSI would be statistically uncorrelated with both BMI and height. This independence is what makes ABSI valuable: a high ABSI indicates that a person carries more abdominal fat than would be expected for their overall size, regardless of whether they are classified as normal weight, overweight, or obese by BMI standards.

Research has shown that ABSI is a significant predictor of all-cause mortality even after adjusting for BMI, age, and other risk factors. However, the formula's complexity makes it impractical for quick clinical screening, and its thresholds are population-specific, requiring age- and sex-adjusted z-scores for meaningful interpretation. Most clinicians find WHR or waist circumference alone more practical for everyday use.

Body Adiposity Index (BAI)

BAI was proposed in 2011 by Bergman and colleagues as a way to estimate body fat percentage without needing a scale. The formula is:

BAI = (Hip circumference (cm) / Height (m)^1.5) − 18

The appeal of BAI lies in its simplicity and the fact that it requires only a tape measure and a height measurement -- no scale is needed. This makes it particularly useful in field studies or resource-limited settings where accurate scales may be unavailable. The result approximates body fat percentage directly, without the need for separate interpretation tables.

However, validation studies have shown that BAI tends to overestimate body fat in lean individuals and underestimate it in those with higher adiposity. It also performs inconsistently across ethnic groups and between sexes. Unlike WHR, BAI does not specifically capture visceral fat distribution, so it provides less targeted cardiovascular risk information. For these reasons, BAI has not been widely adopted in clinical practice and remains more of a research tool than a replacement for established metrics like WHR and BMI.

How ABSI and BAI Compare to WHR

Both ABSI and BAI address real limitations of WHR -- ABSI by isolating shape from size, and BAI by eliminating the need for a scale. However, WHR's enduring advantage is its simplicity, well-validated thresholds, and strong evidence base from studies like INTERHEART. For most people seeking a quick, practical assessment of fat distribution and cardiovascular risk, WHR remains the best starting point. ABSI and BAI are best understood as complementary tools that may be useful in specific research or clinical contexts.

Historical Development of WHR

The waist-to-hip ratio did not emerge overnight as a clinical tool. Its development spans more than half a century, reflecting the evolving understanding of how body fat distribution affects health outcomes.

1947: Jean Vague and Body Fat Typology

The intellectual roots of WHR trace back to French physician Jean Vague, who published a landmark paper in 1947 distinguishing between two patterns of fat deposition. He described "android" obesity (fat concentrated around the trunk and abdomen) and "gynoid" obesity (fat concentrated around the hips and thighs). Vague observed that patients with android fat patterns were far more likely to develop diabetes, atherosclerosis, and gout. Although his work was largely overlooked by the English-speaking medical community for decades, Vague's observations laid the conceptual foundation for all subsequent research on fat distribution and health risk.

1980s: Bjorntorp and the Swedish Studies

In the 1980s, Swedish researcher Per Bjorntorp and his colleagues at the University of Gothenburg conducted a series of prospective studies that revived and refined Vague's ideas. They measured waist and hip circumferences in large population cohorts and tracked health outcomes over years. Their findings were striking: the ratio of waist to hip circumference was a powerful independent predictor of cardiovascular disease, stroke, and type 2 diabetes -- often stronger than body weight or BMI alone. Bjorntorp's work established WHR as a formal clinical measurement and introduced the concept that where fat is stored matters as much as, or more than, how much fat a person carries.

1990s: WHO Adoption

By the late 1990s, the accumulated evidence was strong enough for the World Health Organization to formally incorporate WHR into its guidelines for assessing obesity-related health risk. The WHO established the gender-specific threshold values that remain in use today -- 0.85 for women and 0.90 for men -- based on meta-analyses of population studies linking WHR to disease incidence and mortality. This institutional endorsement transformed WHR from a research metric into a standard clinical screening tool used worldwide.

2004: The INTERHEART Study

The INTERHEART study, published in The Lancet in 2004, provided perhaps the most compelling validation of WHR's clinical importance. This massive case-control study enrolled over 27,000 participants from 52 countries across every inhabited continent. The researchers found that WHR was one of the strongest modifiable risk factors for myocardial infarction -- stronger than BMI, and significant across all age groups, sexes, and ethnic populations studied. INTERHEART cemented WHR's position as a frontline tool for cardiovascular risk assessment and demonstrated that its predictive power was universal, not limited to the European populations where it was originally studied.

Current Status

Today, WHR is recognized by major health organizations worldwide and is routinely used alongside BMI and waist circumference in clinical practice. While newer indices like ABSI and BAI have emerged, none have displaced WHR from its role as the most practical and well-validated measure of body fat distribution. As Harvard's Nutrition Source notes, measuring where fat is distributed remains one of the most important steps in understanding individual health risk -- and the simple act of dividing waist by hip circumference remains the most accessible way to do it.

WHR vs BMI vs WHtR: Side-by-Side Comparison

Choosing the right body composition metric depends on what you want to measure and the tools you have available. Here is a direct comparison of the three most commonly used formulas:

Mathematical Properties of WHR

The waist-to-hip ratio has several mathematical properties that are worth understanding in depth. These properties affect how the formula behaves across different body sizes, measurement systems, and clinical thresholds.

WHR Is Dimensionless

Because WHR divides one length measurement by another, the units cancel out entirely. The formula produces the same numerical result whether you measure in inches, centimeters, millimeters, or even meters. This property is called dimensional homogeneity -- both the numerator and denominator carry the same unit (length), so the result is a pure number with no unit attached. This makes WHR universally comparable across countries and medical systems without any conversion needed.

For example, a woman with a waist of 71.1 cm and hips of 96.5 cm gets the same WHR (0.737) as if she measured 28 inches and 38 inches. This unit-independence is one reason WHR was adopted as a global health metric by the WHO.

Sensitivity Analysis: Impact of Small Changes

A critical but often overlooked property of WHR is that the same absolute change in waist circumference produces a larger shift in WHR for people with smaller hips. This is a direct consequence of the division formula: when the denominator (hip measurement) is smaller, each unit added to the numerator (waist) has a proportionally greater effect on the quotient.

Consider what happens when waist circumference increases by just 1 inch across different hip sizes:

The pattern is clear: a single inch of waist gain shifts WHR by 0.029 for someone with 34-inch hips, but only 0.024 for someone with 42-inch hips. This means individuals with narrower builds are mathematically more sensitive to small increases in abdominal fat, and even minor waist changes can push them across a clinical threshold.

Non-Linear Risk Relationship

While the WHR formula itself is linear (a simple ratio), the relationship between WHR and health risk is decidedly non-linear. Below approximately 0.80 for women and 0.90 for men, cardiovascular risk increases gradually with rising WHR. However, once these thresholds are crossed, risk begins to accelerate. Research from the INTERHEART study demonstrated that each 0.01 increase in WHR above the high-risk threshold was associated with a disproportionately larger increase in myocardial infarction risk compared to the same 0.01 increase below the threshold.

This non-linearity means that the clinical urgency of reducing WHR is not constant. A person with a WHR of 1.02 lowering it by 0.05 points achieves a much greater absolute risk reduction than a person with a WHR of 0.78 achieving the same 0.05-point decrease. Understanding this acceleration effect is important for setting realistic and meaningful health improvement targets. The NHLBI guidelines on weight management reflect this principle by emphasizing the outsized health benefits of even modest fat reduction in high-risk individuals.

All Body Measurement Formulas Compared

WHR is one of several anthropometric formulas used in clinical and research settings. Each metric captures a different aspect of body composition, and no single formula tells the whole story. The table below provides a side-by-side comparison of six widely referenced body measurement metrics, including their formulas, required inputs, strengths, and limitations.

For most individuals performing a self-assessment at home, WHR and WHtR offer the best combination of simplicity and clinical relevance. Both require only a tape measure. BMI adds value when you want a general weight classification, but it should never be used alone to assess fat-distribution risk. Body Fat %, Body Roundness Index, and Conicity Index are most useful in research or clinical settings where specialized equipment and expertise are available.

Our BMI vs WHR comparison guide explores the differences between these two metrics in greater detail. For waist-to-height guidance, see the WHtR calculator guide. Additional context on anthropometric data collection methods is available from the CDC's NHANES program, and Harvard's Nutrition Source provides an accessible overview of how different body measurements relate to disease risk.

Additional Practice Problems

The following problems cover scenarios not addressed in the earlier examples, including metric-only measurements, borderline values near clinical thresholds, and tracking WHR changes over time. Try solving each one before revealing the answer.

Problem 4: Metric Measurement Near Female Threshold

A woman measures her waist at 72 cm and her hips at 90 cm. Calculate her WHR and determine her risk category. How close is she to the moderate-risk boundary?

Problem 5: Male with Borderline High-Risk WHR

A man has a waist of 37.5 inches and hips of 40 inches. What is his WHR? If he reduces his waist by 1.5 inches through exercise and dietary changes, what will his new WHR be, and does his risk category change?

Problem 6: Tracking WHR Over Three Months (Metric)

A woman records the following measurements over three months. Calculate her WHR at each time point and describe the trend.

• Month 1: Waist 84 cm, Hips 98 cm
• Month 2: Waist 81 cm, Hips 98 cm
• Month 3: Waist 78 cm, Hips 99 cm

Problem 7: Reverse Calculation -- Finding the Target Waist

A man has hips measuring 41 inches and a current WHR of 0.98 (high risk). What waist measurement does he need to achieve to reach a WHR of 0.90 (low risk), assuming his hip size remains constant?