BMI Formula Reference: Equation, Variables and Rearrangements

The metric BMI equation and variable definitions

The metric body mass index formula expresses BMI as mass in kilograms divided by height in meters squared. The standard published form is BMI = weight (kg) ÷ height (m)². The result carries the unit kg/m², which is the conventional way to report a BMI value.

The equation has only two variables: body mass in kilograms and standing height in meters. Because height is squared, small differences in measured height change the result more than a one-kilogram difference in weight, which is why consistent measurement matters.

• BMI is the primary output variable, expressed in kg/m².
• Weight is the numerator, entered in kilograms for the metric form.
• Height is the denominator, entered in meters and then squared.
• The equation is identical for males and females; interpretation differs by age and population.

Sources: Centers for Disease Control and Prevention (CDC), Calculator.net, CalculatorSoup, WeightWatchers (WW) USA

The imperial BMI equation and the 703 factor

In US customary units, the same relationship is written BMI = 703 × weight (lb) ÷ height (in)². The 703 figure is the multiplicative conversion factor applied so that pounds and inches produce a result that agrees with the metric kg/m² scale.

One widely used manual order is to divide weight in pounds by height in inches, divide the result by height in inches again, and then multiply by 703. The American Cancer Society describes the same operation in words: multiply weight in pounds by 703, then divide by height in inches, then divide by height in inches again. Both sequences arrive at the same number.

• Imperial form: BMI = 703 × lb ÷ in².
• The 703 factor is applied only in the pounds-and-inches version.
• Feet must be converted to inches before squaring height.
• The output is interpreted on the same kg/m² scale used for the metric form.

Sources: American Cancer Society, Calculator.net, CalculatorSoup, WeightWatchers (WW) USA

Rearranging the formula to solve for weight

Because BMI, weight and height are related by a single equation, algebra can rearrange the formula to solve for a weight that corresponds to a chosen BMI at a given height. Starting from BMI = weight ÷ height², multiply both sides by height² to isolate weight.

Metric rearrangement: weight (kg) = BMI × height (m)². Imperial rearrangement: weight (lb) = BMI × height (in)² ÷ 703. These rearrangements are algebraic consequences of the two published equation forms; they do not change the meaning of BMI, and they describe a hypothetical body mass at a fixed BMI, not a clinical target.

• Solve for weight in metric: multiply BMI by height in meters squared.
• Solve for weight in imperial: multiply BMI by height in inches squared, then divide by 703.
• The rearranged form is useful for checking arithmetic and for understanding how the variables relate.
• A rearranged result is an arithmetic output given the inputs, not a health recommendation.

Sources: National Heart, Lung, and Blood Institute (NHLBI), NIH, Calculator.net, CalculatorSoup

Rearranging the formula to solve for height

The equation can also be rearranged to solve for height given a BMI and a weight. From BMI = weight ÷ height², multiply both sides by height² and divide by BMI to obtain height² = weight ÷ BMI, then take the positive square root.

Metric rearrangement: height (m) = √(weight (kg) ÷ BMI). Imperial rearrangement: height (in) = √(703 × weight (lb) ÷ BMI). Because height appears squared in the original equation, the inverse requires a square root, and only the positive root is meaningful for a physical height. As with the weight rearrangement, the result is an algebraic value for the stated inputs.

• Solve for height in metric: take the square root of weight in kilograms divided by BMI.
• Solve for height in imperial: take the square root of 703 times weight in pounds divided by BMI.
• A negative square root is discarded because height cannot be negative.
• Rearranging the equation does not change the interpretation limits of BMI itself.

Sources: National Heart, Lung, and Blood Institute (NHLBI), NIH, Calculator.net, WeightWatchers (WW) USA

Unit system rules and why mixing units breaks results

Both equation forms require a consistent unit system. The metric form expects kilograms and meters. The imperial form expects pounds and inches. Mixing systems, such as entering pounds with meters, or kilograms with inches, produces a number that is not a BMI and cannot be compared with any category range.

The most common unit error is entering height in centimeters or feet directly into an equation that requires meters or inches. If height is recorded in centimeters, divide by 100 to obtain meters before squaring. If height is recorded in feet and inches, multiply feet by 12 and add the remaining inches to get total inches before squaring. The 703 factor is part of the imperial equation and should not be used with metric inputs.

• Metric equation: kilograms and meters only.
• Imperial equation: pounds and total inches only.
• Convert centimeters to meters by dividing by 100.
• Convert feet to inches by multiplying by 12, then add the remaining inches.
• Never apply the 703 factor to a metric calculation.

Sources: Centers for Disease Control and Prevention (CDC), Calculator.net, WeightWatchers (WW) USA, RegisteredNurseRN

How rounding affects reported BMI values

Because BMI is a calculated quotient, the number of decimal places used when reporting it changes the displayed value. Rounding only at the end of the calculation keeps the arithmetic accurate; rounding intermediate results can shift the final number slightly. A common reporting convention is to carry full precision through the steps and round to one decimal place at the end.

Rounding practice is not standardized across every setting. Educational sources sometimes specify a particular number of decimal places, and instructors may require a different convention. When a BMI value will be compared against a category range, keeping intermediate precision and rounding once at the end is the safest arithmetic habit. Category boundaries themselves are published with defined cut-points, so small rounding differences near a boundary should be treated as a reporting artifact rather than a change in classification.

• Carry full precision through the steps.
• Round once at the end, typically to one decimal place.
• Follow the reporting convention required by the context in which the number is used.
• A boundary value is defined by the published cut-point, not by the rounded display.

Sources: American Cancer Society, RegisteredNurseRN

What you need before calculating: height and weight

Two inputs are required before any calculation: a current weight and a current height. The units of those inputs determine which equation form is appropriate. For the metric form, record weight in kilograms and height in meters. For the imperial form, record weight in pounds and height in total inches.

Height is usually recorded once, while weight can change between measurements. For consistency, it helps to keep track of which unit system was used for each input so the correct equation is applied. The two forms are arithmetic equivalents when the inputs are converted correctly. The formula does not require any other input, such as age or sex, to produce a number.

• Weight: kilograms for the metric form; pounds for the imperial form.
• Height: meters for the metric form; total inches for the imperial form.
• Feet-and-inches height must be converted to total inches before squaring.
• Centimeters must be converted to meters before squaring.

Sources: Centers for Disease Control and Prevention (CDC), Calculator.net, WeightWatchers (WW) USA

Metric steps: kilograms and meters

The metric sequence follows directly from the equation BMI = kg ÷ m². Each step is a single arithmetic operation, which makes it easy to check for unit mistakes before moving on.

The result is already on the kg/m² scale used by published adult category ranges, so no additional conversion is needed.

1. Record weight in kilograms.
2. Record height in meters. If height is in centimeters, divide by 100.
3. Square the height in meters (multiply it by itself).
4. Divide weight in kilograms by the squared height.
5. The result is BMI in kg/m². Round once at the end for reporting.

Sources: National Heart, Lung, and Blood Institute (NHLBI), NIH, Calculator.net, WeightWatchers (WW) USA

Imperial steps: pounds and inches with the 703 factor

The imperial sequence uses the same relationship as the metric form, with the 703 conversion factor applied so the output matches the standard BMI scale. Converting height to total inches before squaring is the step where most manual errors occur.

An alternative order, described by the American Cancer Society, multiplies weight by 703 first, then divides by height in inches, then divides by height in inches again. The final number is the same.

1. Record weight in pounds.
2. Record height in feet and inches, then convert to total inches: feet × 12 + inches.
3. Square the total height in inches.
4. Divide weight in pounds by the squared height in inches.
5. Multiply the result by 703.
6. The result is BMI on the same kg/m² scale. Round once at the end for reporting.

Sources: American Cancer Society, Calculator.net, CalculatorSoup

Unit conversion checkpoints and common arithmetic errors

Most incorrect BMI results come from unit handling rather than from the division itself. Checking the units at each conversion point catches these errors before they affect the final number.

A second common error is applying the 703 factor to a metric calculation or omitting it from an imperial calculation. The factor belongs only to the pounds-and-inches form.

• Verify that height is in meters or inches before squaring, not in centimeters or feet.
• Convert 5 feet 10 inches to 70 total inches (5 × 12 + 10).
• Convert 6 feet to 72 total inches (6 × 12).
• Never mix kilograms with inches or pounds with meters.
• Apply 703 only in the imperial form.
• Do not round intermediate results if a precise final value is needed.

Sources: Centers for Disease Control and Prevention (CDC), Calculator.net, WeightWatchers (WW) USA, RegisteredNurseRN

Worked examples at three different heights

The following examples show the arithmetic for both unit systems. Each example uses a different height so the effect of squaring height is visible in the denominator. All results are rounded only at the end.

Example 1 (metric): weight 75 kg, height 1.75 m. Square 1.75 to get 3.0625. Divide 75 by 3.0625 to get approximately 24.49, reported as 24.5 kg/m².

Example 2 (imperial): weight 150 lb, height 5 feet 5 inches. Convert to 65 total inches. Square 65 to get 4,225. Divide 150 by 4,225 to get approximately 0.03550. Multiply by 703 to get approximately 24.96, reported as 25.0 kg/m².

Example 3 (imperial, taller height): weight 184 lb, height 5 feet 10 inches. Convert to 70 total inches. Square 70 to get 4,900. Divide 184 by 4,900 to get approximately 0.03755. Multiply by 703 to get approximately 26.4, reported as 26.4 kg/m².

Sources: American Cancer Society, Calculator.net, WeightWatchers (WW) USA

Verifying your result against a category range

Once a BMI value is calculated, it can be compared with published adult category ranges. The Centers for Disease Control and Prevention lists adult categories as: underweight below 18.5; healthy weight 18.5 to 24.9; overweight 25.0 to 29.9; and obesity 30.0 or greater. The American Cancer Society gives adults aged 20 or older a normal weight range of 18.5 to 24.9. Both sources use the same numeric lower bound for the healthy range and the same cut-points for overweight and obesity. The upper end of the healthy range is sometimes written as 24.9 and sometimes as 25; that is a boundary-labeling convention, not a different definition.

Category ranges are for adults aged 20 and older. Children and teens aged 2 through 19 use percentile-based charts rather than fixed adult numbers. The same formula applies to males and females; only the interpretation differs by age and population.

BMI is a screening measure. The CDC states that BMI is one potential health indicator and should be considered with other factors, and that it is not intended to diagnose disease or illness. The formula produces a number; it does not by itself determine health status.

Sources: American Cancer Society, Centers for Disease Control and Prevention (CDC), Calculator.net