BMI Formula: Body Mass Index Calculator

Calculate BMI using weight(kg)/height²(m). Find your BMI category.

Formula Equation

BMI = \frac{\text{weight}}{\text{height}^2}

Weight(kg)

Height(m)

BMI(Body Mass Index)

22.857143kg/m²

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Apply this formula or open connected references.

Formula hub This formula (canonical)

Primary result

Output variable: BMI

BMI (Body Mass Index)

Body Mass Index (BMI) solves for BMI, body mass index in kg/m². Confirm what each input symbol means and which unit it expects before substituting values — a mismatched unit passes through the algebra silently and corrupts the result.

BMI Formula: Body Mass Index Calculator | weight/height²

BMI = m / h² — mass in kilograms divided by height in meters squared — has been the standard body-size index since Ancel Keys named it in 1972, though the ratio itself is Adolphe Quetelet's, from the 1830s. Quetelet was a statistician studying populations, not a physician treating patients, and the formula's strengths and weaknesses both trace to that origin.

Body Mass Index (BMI)

A measure of body fat based on weight and height. Used to screen for weight categories.

BMI = \frac{\text{weight}}{\text{height}^2}

Variables and usage

A measure of body fat based on weight and height. Used to screen for weight categories. Each symbol in the equation has one fixed meaning and an expected unit; the relationship only holds when every input follows that contract.

BMI = Body Mass Index (kg/m²). BMI value weight = Weight (kg). Body weight in kilograms height = Height (m). Height in metres

Treat these definitions as fixed. If a textbook or spreadsheet uses a different symbol for the same quantity, map it to the definition here before substituting values, so the worked examples still apply to your setup.

Most wrong answers with Body Mass Index (BMI) come from misreading a symbol or mixing unit systems, not from the algebra. Before computing, write down what each input represents and which unit it is in; convert everything to one consistent system first, then substitute.

Notation overlaps across subjects: the same letters often stand for different quantities in different fields. Body Mass Index (BMI) belongs to medicine / anthropometry, and its symbols carry the meanings defined above — an equation from another field that looks similar is not interchangeable with it.

Formula breakdown

Body Mass Index is determined by the interaction of the remaining variables in the expression.

BMI = \frac{\text{weight}}{\text{height}^2}

Rearranged forms

The same relationship can be rearranged depending on which variable you need to solve for.

BMI=\frac{ weight}{\left({ height}^{2}\right)}

Dimensional analysis

Dimensional analysis keeps the formula trustworthy. BMI uses kg/m²; weight uses kg; height uses m. Before using the equation in a calculator or external model, confirm that all inputs follow the same unit convention.

Mixed sources are the usual failure point: SI textbooks, lab sheets, spreadsheets, and regional engineering conventions can each state the same quantity in different units.

Alternate forms table

Reviewed solved forms so readers can quickly see which variable each alternate expression isolates.

Each solved form isolates a different variable, so you can compute whichever quantity is unknown without re-deriving the algebra.

solve for	equation	latex
BMI	BMI = weight / (height ^ 2)	$BMI=\frac{ weight}{\left({ height}^{2}\right)}$
weight	Rearrange the canonical form to isolate weight	$-$
height	Rearrange the canonical form to isolate height	$-$
BMI	Rearrange the canonical form to isolate BMI	$-$
weight	Rearrange the canonical form to isolate weight	$-$
height	Rearrange the canonical form to isolate height	$-$

Pick the row whose solve-for variable matches your unknown, then substitute the values you already have.

To check a rearrangement done by hand, compare it against the listed form for the same variable.

Example response curve

Visual Analysis1 series2 points

The curve shows how the output moves as the first input changes, with the remaining inputs taken from the worked examples.

Trend

Upward

Min

Max

Insight

Use the chart for qualitative behavior and the example table for exact values.

Insight

When a formula has sparse stored examples, the plot remains illustrative rather than exhaustive.

X-axis: BMIY-axis: BMI

Illustrative plot built from stored worked examples when available, used to visualize how the formula behaves across representative inputs.

Standards and derivation context

This formula is part of the medicine domain. Knowing where a relationship comes from tells you when it applies: a definition holds by construction, a physical law holds within its stated conditions, and an empirical rule holds only for the cases it was fitted to.

No formal derivation steps are listed for this formula.

Where this formula is used

The calculators listed below apply Body Mass Index (BMI) directly — the fastest way to evaluate it without transcribing the algebra by hand.

BMI Calculator (calculator, uses); Bmi (calculator, uses); Tdee (formula, related-to)

Related formula context

Body Mass Index (BMI) rarely stands alone: the related formulas below share variables or assumptions with it, and one of them may fit your problem better.

Body Mass Index (BMI): Index relating body weight to height; used to classify weight status.
Mifflin-St Jeor BMR (Male): Mifflin-St Jeor equation for Basal Metabolic Rate in males — calories burned at rest per day.
Ideal Body Weight — Men (Devine): Devine formula for ideal body weight in men (height > 5 feet).
Ideal Body Weight — Women (Devine): Devine formula for ideal body weight in women (height > 5 feet).

Worked examples: the BMI formula

Metric and imperial, same person
82 kg at 1.78 m: 82 ÷ 3.1684 = 25.9. The same person in imperial: 180.8 lb at 70.1 in gives 180.8 ÷ 4,914 × 703 = 25.9 — agreement confirming the 703 factor's job. Dropping the factor gives 0.0368; squaring 178 cm instead of 1.78 m gives 0.0026. Both wrong answers announce themselves, which is the one mercy of this formula's unit-strictness.

the BMI formula — frequently asked questions

Why divide by height squared instead of height?
Dividing by height once still leaves taller people with systematically higher scores (weight grows faster than height); dividing by height cubed overcorrects (humans do not scale isometrically — adults grow taller faster than wider). Quetelet found h² made his population's index roughly independent of height, and that empirical fit, not a derivation, is the formula's foundation.

How sensitive is BMI to measurement errors?
The squared denominator doubles height's leverage: a 1 % height error moves BMI 2 %, while a 1 % weight error moves it 1 %. Self-reported data compounds this in a known direction — surveys find people over-report height and under-report weight, deflating self-reported BMI by roughly half a unit on average.

What are the WHO cutoffs this formula feeds?
Underweight below 18.5, normal 18.5–24.9, overweight 25–29.9, and obesity at 30 and above, subdivided into classes I (30–34.9), II (35–39.9), and III (40+). A 2004 WHO consultation additionally recommended action points of 23 and 27.5 for many Asian populations. The cutoffs attach to the formula's output; the formula itself is just the ratio.

Explanation

To apply Body Mass Index (BMI) reliably: identify which variable is unknown, choose the solved form that isolates it, convert every input to a consistent unit system, substitute, and compare the result against a worked example or a rough estimate.

A measure of body fat based on weight and height. Used to screen for weight categories. The equation holds only while its variables keep the meanings defined above; reinterpreting a symbol produces a different — and usually wrong — calculation.

Order-of-magnitude checks catch most substitution errors. Before accepting a result, ask whether its size and sign are plausible for the scenario. A value thousands of times larger or smaller than expected almost always signals a unit mismatch rather than an exotic answer.

When rearranging by hand, apply each operation to both sides and watch for divisions by terms that can reach zero. A rearranged form is easy to verify: substitute a worked example into it and confirm it reproduces the original numbers.

Round once, at the end. Carrying rounded intermediates through multi-step work compounds error, especially where the formula involves powers, roots, or differences between similar-sized terms.

Source and methodology

Formula sources and assumptions are recorded in the derivation and source blocks.

FAQ: Body Mass Index (BMI) Formula

What is the Body Mass Index (BMI) formula?
The Body Mass Index (BMI) formula is: Body Mass Index (BMI). A measure of body fat based on weight and height. Used to screen for weight categories.

What are the variables in Body Mass Index (BMI)?
The formula uses these variables: BMI (Body Mass Index, in kg/m²), weight (Weight, in kg), height (Height, in m).

How do I use the Body Mass Index (BMI) formula?
Identify each variable's value and substitute into: Body Mass Index (BMI). Substitute your values into the formula: Body Mass Index (BMI).

Can the Body Mass Index (BMI) formula be rearranged to solve for other variables?
Yes — Body Mass Index (BMI) can be rearranged algebraically to isolate any variable, provided no step divides by a term that can be zero. Verify a rearranged form by substituting a worked example back into the original equation.

Common mistakes with the BMI formula

Forgetting the 703 in imperial units. Pounds over inches squared gives numbers near 0.035; the 703 factor (10,000 × 0.4536 ÷ 0.0254² rounded) rescales to the metric result. Its absence or double application is instantly visible; a subtler slip is using 700 for mental math and letting the 0.4 % error stand in records.

Squaring height in centimeters. 175 cm entered unconverted makes the denominator 30,625 instead of 3.0625 — a result 10,000× too small. The formula is unit-strict: meters, or the full imperial form, nothing between.

Sources & Standards

National Institute of Standards and Technology. "The International System of Units (SI)." NIST Special Publication 330, 2019 Edition.SI unit definitions used in all conversion calculations
CODATA Task Group on Fundamental Constants. "2022 CODATA Recommended Values." NIST, 2024.Speed of light, gravitational constant, Avogadro number, and other fundamental constants

Verify this result

This answer is computed by FormulaEvaluator.evaluate (v1.0.0). The same inputs always produce the same figure and the same fingerprint below, so you can reproduce and cite it.

Assumptions

EquationBMI = weight / (height^2)
Domainmedicine
VariablesBMI (kg/m²), weight (kg), height (m)
Validity constraints(height^2): != 0

Inputs & outputs

in · formulabody-mass-index
in · equationBMI = weight / (height^2)
out · equationBMI = weight / (height^2)
out · solvesForBMI

Computation fingerprint (SHA-256)

a4710fb8814751a3508ed120e4d291c050690f73561238f2c3f75909d31c7d1f

Verification & transparency

Automated checks: engine-validated output

Last updated:2026-10-11

Sources:NIST SP 330 · CODATA 2022

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Methodology

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Unit conversions follow SI and common measurement standards. We use careful numeric handling to reduce rounding surprises.

Sources & standards

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Quick Reference

BMI Body Mass Index (kg/m²)
weight Weight (kg)
height Height (m)

Rearranged Forms

$BMI=\frac{ weight}{\left({ height}^{2}\right)}$

Common Values

height = 1.75

weight	BMI (kg/m²)
17.5	5.714286
35	11.428571
70	22.857143
140	45.714286
280	91.428571

On This Page

Primary result
BMI Formula: Body Mass Index Calculator | weight/height²
Body Mass Index (BMI)
Variables and usage
Formula breakdown
Rearranged forms
Dimensional analysis
Alternate forms table

Common Questions

Why divide by height squared instead of height?
How sensitive is BMI to measurement errors?
What are the WHO cutoffs this formula feeds?

Related Tools

solve for

equation

latex

BMI

BMI = weight / (height ^ 2)

BMI=\frac{ weight}{\left({ height}^{2}\right)}

weight

Rearrange the canonical form to isolate weight

-

height

Rearrange the canonical form to isolate height

-

BMI

Rearrange the canonical form to isolate BMI

-

weight

Rearrange the canonical form to isolate weight

-

height

Rearrange the canonical form to isolate height

-

the BMI formula — frequently asked questions

FAQ: Body Mass Index (BMI) Formula

What is the Body Mass Index (BMI) formula?
The Body Mass Index (BMI) formula is: Body Mass Index (BMI). A measure of body fat based on weight and height. Used to screen for weight categories.

What are the variables in Body Mass Index (BMI)?
The formula uses these variables: BMI (Body Mass Index, in kg/m²), weight (Weight, in kg), height (Height, in m).

How do I use the Body Mass Index (BMI) formula?
Identify each variable's value and substitute into: Body Mass Index (BMI). Substitute your values into the formula: Body Mass Index (BMI).

Primary result

BMI Formula: Body Mass Index Calculator | weight/height²

Body Mass Index (BMI)

Variables and usage

Formula breakdown

Rearranged forms

Dimensional analysis

Alternate forms table

Example response curve

Standards and derivation context

Where this formula is used

Related formula context

Worked examples: the BMI formula

the BMI formula — frequently asked questions

Explanation

Source and methodology

FAQ: Body Mass Index (BMI) Formula

Common mistakes with the BMI formula

Sources & Standards

Verify this result

Formula navigation

Related formula links

Related calculators

Formula hub

This formula (canonical)

Can't find what you're looking for?

Verification & transparency

Verified methodology

Data & accuracy

Privacy & ethics

Primary result

BMI Formula: Body Mass Index Calculator | weight/height²

Body Mass Index (BMI)

Variables and usage

Formula breakdown

Rearranged forms

Dimensional analysis

Alternate forms table

Example response curve

Standards and derivation context

Where this formula is used

Related formula context

Worked examples: the BMI formula

the BMI formula — frequently asked questions

Explanation

Source and methodology

FAQ: Body Mass Index (BMI) Formula

Common mistakes with the BMI formula

Sources & Standards

Verify this result

Formula navigation

Related formula links

Related calculators

Formula hub

This formula (canonical)

Can't find what you're looking for?

Verification & transparency

Verified methodology

Data & accuracy

Privacy & ethics