Body Mass Index (BMI)
Body Mass Index (BMI) is a height-adjusted measure of body mass used as a quick screening indicator in
adult populations. It compares a person’s mass to the square of their height, so taller individuals are not
automatically classified as “heavier” simply because they are taller.
BMI formula
The BMI definition is:
\[
\mathrm{BMI}=\frac{m}{h^{2}}
\]
where \(m\) is body mass in kilograms (kg) and \(h\) is height in meters (m). BMI is often reported as a
unitless number, but its physical unit is \(\mathrm{kg\cdot m^{-2}}\).
Unit conversions used by the calculator
This calculator supports both metric and imperial inputs. Because the BMI formula uses meters and
kilograms, imperial values are converted first.
Metric (kg, cm/m)
If height is entered in centimeters, convert to meters:
\[
h(\mathrm{m})=\frac{h(\mathrm{cm})}{100}
\]
If height is entered directly in meters, no conversion is needed.
Imperial (lb, ft/in)
First convert height to inches, then to meters:
\[
\begin{aligned}
h(\mathrm{in}) &= 12\cdot h(\mathrm{ft}) + h(\mathrm{in}) \\
h(\mathrm{m}) &= h(\mathrm{in})\cdot 0.0254
\end{aligned}
\]
Convert weight from pounds to kilograms:
\[
m(\mathrm{kg}) = m(\mathrm{lb})\cdot 0.45359237
\]
How the calculator computes BMI
After converting inputs (if needed), BMI is computed directly from the definition:
\[
\mathrm{BMI}=\frac{m(\mathrm{kg})}{\left(h(\mathrm{m})\right)^{2}}
\]
Because height appears squared in the denominator, small errors in height can noticeably affect BMI.
Measuring height carefully (especially in cm) improves accuracy.
Adult BMI categories (interpretation)
The calculator assigns a category using common adult cutoffs:
- Underweight: BMI < 18.5
- Normal weight: 18.5 ≤ BMI < 25.0
- Overweight: 25.0 ≤ BMI < 30.0
- Obesity (Class I): 30.0 ≤ BMI < 35.0
- Obesity (Class II): 35.0 ≤ BMI < 40.0
- Obesity (Class III): BMI ≥ 40.0
These ranges are widely used for population-level screening. Clinical interpretation can differ based on age,
body composition, and medical context.
Healthy weight range for a given height
If the “healthy range” option is enabled, the calculator finds the mass interval corresponding to BMI
from 18.5 to 24.9 for the same height.
Start from the BMI definition and solve for mass:
\[
\begin{aligned}
\mathrm{BMI} &= \frac{m}{h^{2}} \\
m &= \mathrm{BMI}\cdot h^{2}
\end{aligned}
\]
Then substitute the healthy BMI limits:
\[
\begin{aligned}
m_{\min} &= 18.5\cdot h^{2} \\
m_{\max} &= 24.9\cdot h^{2}
\end{aligned}
\]
If the calculator is in imperial mode, the final healthy range is also shown in pounds using:
\(m(\mathrm{lb}) = \frac{m(\mathrm{kg})}{0.45359237}\).
Practical note
BMI is a fast screening measure, not a direct measurement of body fat. People with high muscle mass may have a
higher BMI without having excess fat, and health risk can vary even within the same BMI category. For a fuller
picture, BMI is often interpreted alongside other measures (for example, waist circumference, body composition,
fitness level, and clinical history).
