Fat Mass Index (FMI) Calculator

Calculate height-normalized fat mass from body fat percentage or a known fat mass, with a transparent breakdown of FMI, FFMI and BMI.

Calculation inputs

Start with a documented fat measurement

1
Choose your data source
Select body fat percentage or known fat mass from a body-composition report.
2
Keep height and mass units clear
The calculation converts to kilograms and metres before dividing by height squared.
3
Keep the components separate
FMI tracks fat mass; FFMI tracks the fat-free remainder. Neither is a direct muscle measurement.

Measurement and method sources are linked below. Illustrations explain the workflow; they do not supply measurement data.

Explore the calculation model

Body mass components

Calculation results

Fat Mass Index4.9 kg/m²Fat mass normalized to height squared

Fat mass15 kg

Fat-free remainder60 kg

Body fat20%

FFMI19.59 kg/m²

BMI24.49 kg/m²

FMI + FFMI24.49 kg/m²

Step-by-step solution

Choose the formula
$FMI = \frac{fat mass (kg)}{{height (m)}^{2}}$
Substitute your measurements
$Fat mass = 75 × 20 ÷ 100$
Calculate in order
$Height² = 1.75² = 3.0625 m²; 15 ÷ 3.0625$
Write the result
$4.9 kg/m²$

Representative whole-body composition scanning equipment, not a patient scan — Representative illustration · not a scan, patient measurement or image to scale.

1
Find the fat component
75 kg × 20% = 15 kg
2
Normalize to the same height
1.75 m × 1.75 m = 3.0625 m²
3
Check the mass decomposition
FMI 4.9 + FFMI 19.59 ≈ BMI 24.49

The components add up to your entered weight. The fat-free remainder includes water, bone and organs as well as muscle.

FMI inherits any error in the entered fat measurement. No universal healthy range or diagnosis is assigned here.

Measurements & calculation details

4.9 kg/m²

Quantity	Value
Height squared	3.0625 m²
Fat mass	15 kg
Fat-free remainder	60 kg
FMI	4.897959 kg/m²
FFMI	19.591837 kg/m²
BMI = FMI + FFMI	24.489796 kg/m²

Try a worked example

Choose an example to load its measurements into the calculator. Each result uses the same calculation engine as your own inputs. Back to your calculation

Understand the calculation

Concept & meaning

FMI isolates the fat component of weight and divides it by height squared. BMI uses total weight; it cannot distinguish fat from the fat-free remainder. This page uses the same height for all three indices.

Formula & special cases

If body fat is p%, fat mass = weight × p/100. The remainder = weight − fat mass; FFMI = remainder / height². Algebraically FMI + FFMI = BMI, apart from display rounding. Body weight is also entered in known-fat-mass mode to check the measurement and produce this decomposition.

Scope & limitations

The 2009 NHANES paper proposed sex-specific FMI reference classifications from prevalence matching in young adults. Those research bands are not universal diagnostic thresholds, so this tool shows the numerical result without a healthy/unhealthy label.

FMI = \frac{fat mass (kg)}{{height (m)}^{2}}

Result from your current inputs

Fat Mass Index: 4.9 kg/m²

Frequently asked questions

Why do I need body fat percentage?

Weight and height alone do not identify fat mass. Use a documented body-fat measurement or select known fat mass.

Why do FMI and BMI have the same units?

Both divide a mass in kilograms by height in metres squared. Their numerators differ: fat mass versus total mass.

Is FFMI a muscle-mass index?

It uses the fat-free remainder, which includes water, bone and organs as well as muscle. It does not measure skeletal muscle alone.

Why are there no diagnostic color bands?

Published FMI classifications depend on sex, reference population and measurement assumptions. A numerical calculation cannot establish an individual diagnosis.

Show all questions (5 more)Show fewer questions

What does the Fat Mass Index (FMI) calculate?

Calculate height-normalized fat mass from body fat percentage or a known fat mass, with a transparent breakdown of FMI, FFMI and BMI.

Which values should I enter?

Use the labeled fields above. Values outside the supported range clear the result and show an explanation.

What formula does this calculator use?

FMI = fat mass (kg) / height (m)²

Why might my result differ from another source?

Results can differ because measurement methods, rounding and assumptions vary. This calculator is an estimate and is not a medical diagnosis.

Does the result update automatically?

Yes. Inputs and presets update the result, teaching diagram and expandable steps together. Invalid input clears the previous result.

One height, three different numerators

Calculation	Formula	Interpretation
FMI	Fat mass / height²	Fat component
FFMI	Fat-free remainder / height²	All non-fat components in the two-component model
BMI	Total weight / height²	Sum of FMI and FFMI

Sources & References

Kelly, Wilson & Heymsfield · 2009NHANES DXA study · fat mass divided by height squaredRead the reference

NIDDK · adult weight managementIndividualized goals and adult health contextRead the reference

References document the methods and their limitations; links and logos do not imply institutional endorsement or expert review.