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)

Body Mass Index (BMI) — Formula Reference

A measure of body fat based on weight and height. Used to screen for weight categories. Each term of the Body Mass Index (BMI) formula is rendered and defined below. Substituting your own values in the calculator below shows the working alongside the result.

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.

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.

Worked examples

Worked sample computations for Body Mass Index (BMI).

Each row substitutes concrete inputs into Body Mass Index (BMI) so you can verify your own setup against a known result.

example	scenario	inputs	output	unit
1	70 kg person at 1.75 m height	weight=70, height=1.75	22.86	kg/m²
2	Unit consistency check	BMI: kg/m², weight: kg, height: m	BMI	kg/m²
3	Domain sanity check	BMI: kg/m², weight: kg, height: m	BMI	kg/m²
4	Application check 1	BMI: kg/m², weight: kg, height: m	BMI	kg/m²
5	Application check 2	BMI: kg/m², weight: kg, height: m	BMI	kg/m²
6	Application check 3	BMI: kg/m², weight: kg, height: m	BMI	kg/m²

Reproduce one worked row by hand before relying on your own setup; agreement confirms your units and sign conventions.

If your result differs from a worked row, check unit conversions first — they cause more errors than the algebra does.

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).

Edge cases and failure modes

Edge cases usually appear when a formula is applied outside its intended variable ranges, when unit conventions are mixed, or when a solved form is used without checking sign assumptions. For Body Mass Index (BMI), the safest habit is to confirm variable meaning, dimensional consistency, and the chosen alternate form before treating the output as operationally final.

Watch especially for inputs that push a denominator toward zero, negative values where the derivation assumes positive quantities, and results near the boundary of the validity range — these are where a plausible-looking number is most likely to be wrong.

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.

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

Verification & transparency

Automated checks: engine-validated output

Last updated:2026-08-04

Sources:NIST SP 330 · CODATA 2022

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Verified methodology

Calculations follow established definitions and are tested against reference datasets. We document how each tool works and when to use it.

Methodology

Data & accuracy

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)

Worked Example

70 kg person at 1.75 m height

weight = 70

height = 1.75

BMI = 22.86

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

Watch Out For

Solving for the wrong variable: this equation is written for BMI on the left-hand side.
Mixing units without converting first (e.g. cm with m, minutes with seconds, percent with decimal).
Forgetting to square height (Height).
Ignoring a domain constraint: ensure (height^2) != 0 (Cannot divide by zero).

On This Page

Body Mass Index (BMI) — Formula Reference
Primary result
Body Mass Index (BMI)
Variables and usage
Formula breakdown
Rearranged forms
Dimensional analysis
Worked examples

Common Questions

What is the Body Mass Index (BMI) formula?
What are the variables in Body Mass Index (BMI)?
How do I use the Body Mass Index (BMI) formula?
Can the Body Mass Index (BMI) formula be rearranged to solve for other variables?

Related Tools

example

scenario

inputs

output

unit

70 kg person at 1.75 m height

weight=70, height=1.75

22.86

kg/m²

Unit consistency check