Shoe Size Converter

Field	Value	Copy
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Shoe sizes are numeric labels tied to last length, the internal length inside a shoe. Sizes map the last, not the foot, so you add toe‑room to foot length before converting. Length‑based systems such as Mondopoint (JP) state the foot in centimetres, while US, UK and EU formulas apply fixed offsets to produce the familiar numbers.

You enter a foot length in centimetres or inches, or you can start from a size in a chosen system. The output shows counterparts across US Men and Women and UK and EU along with regional standards such as BR, JP/MX, CN and KR plus the implied last length so you can sanity‑check the fit. Results follow your step and rounding preferences to mirror catalog conventions.

For example, a 26 cm foot with 1.5 cm toe‑room implies a 27.5 cm last and converts to about EU 41.5 and US Men 8.5 with UK 7.5 and BR 39 given typical steps. That gives a clear starting point before you compare brand charts or try pairs on. Treat results as guidance because availability of half sizes and regional BR mappings can differ by one size.

Choosing allowance is your main lever. A snug 0.5 cm favors a closer feel, a standard 1.5 cm balances comfort, and a roomy 2.0 cm leaves space for thicker socks. You can also change step sizes and rounding to match catalog conventions or factory charts when you need reports that mirror a specific brand’s publishing style.

Technical Details:

The converter models last‑based sizing. It first adds your toe‑room allowance to foot length to obtain last length. From that value it derives raw sizes for US Men, US Women, UK and EU using linear equations with fixed offsets or multipliers, and treats BR as an EU‑derived variant with a configurable shift. JP and MX report the foot itself in centimetres; CN and KR report millimetres. Results are rounded to user‑selected steps with a chosen rounding mode. An effective allowance is also computed from the emphasized system to reflect actual toe space. The pipeline is deterministic and stateless.

\begin{matrix} L l_{cm} & = & L f_{cm} + A {cm}_{} \\ L {in}_{} & = & \frac{L}{L l_{cm}} / 2.54 \end{matrix}

\begin{matrix} S_{USM,raw} & = & 3 L {in}_{} - 24 \\ S_{USW,raw} & = & 3 L {in}_{} - 23 \\ S_{UK,raw} & = & 3 L {in}_{} - 25 \\ S_{EU,raw} & = & 1.5 L l_{cm} \\ S_{BR,raw} & = & S_{EU,raw} - 2 + O {br}_{} \\ S_{JP} & = & L f_{cm} \\ S_{MX} & = & L f_{cm} \\ S_{CN,mm} & = & 10 L f_{cm} \\ S_{KR,mm} & = & S_{CN,mm} \end{matrix}

\begin{matrix} S_{sys} & = & round_m (S_{sys,raw}, Δ {sys}_{}) \end{matrix}

Symbols and units
Symbol	Meaning	Unit/Datatype	Source
L_f,cm	Foot length	cm	Input
A_cm	Toe‑room allowance	cm	Input
L_l,cm	Last length	cm	Derived
L_in	Last length	in	Derived
S_USM,raw	Unrounded US Men size	number	Derived
S_USW,raw	Unrounded US Women size	number	Derived
S_UK,raw	Unrounded UK size	number	Derived
S_EU,raw	Unrounded EU size	number	Derived
S_BR,raw	Unrounded BR size	number	Derived
S_JP	JP/Mondopoint size	cm	Derived
S_MX	MX size	cm	Derived
S_CN,mm	CN size	mm	Derived
S_KR,mm	KR size	mm	Derived
Δ_sys	Step size per system	number	Input
O_br	BR offset relative to EU	number	Input
A_eff	Effective allowance	cm	Derived

Toe‑room interpretation bands
Threshold Band	Lower Bound	Upper Bound	Interpretation	Action Cue
Minimal	0 mm	5 mm	Likely snug or short	Consider one size up
Typical	5 mm	15 mm	Common everyday space	Test both adjacent sizes
Roomy	15 mm	25 mm	Extra space for socks	Secure heel or size down

Parameters overview
Parameter	Meaning	Unit/Datatype	Typical Range	Sensitivity	Notes
Allowance	Toe‑room added to foot	cm	0.5–2.0	High	Presets: snug, standard, roomy
Rounding mode	How sizes snap to steps	nearest/floor/ceil	N/A	Medium	Nearest uses half‑up for positives
US/UK step	Size increment	number	0.25–1.0	Medium	Default 0.5
EU step	Size increment	number	0.5–1.0	Medium	Half sizes uncommon
JP/MX step	Increment on centimetres	number	0.5–1.0	Low	Default 0.5
CN step	Increment on millimetres	mm	1–10	Low	Default 5
KR step	Increment on millimetres	mm	1–10	Low	Default 5
BR step	Size increment	number	0.5–2.0	Medium	Default 1
BR offset	Shift relative to EU	number	−4–+4	Medium	Typical −2 button available
Width code	Display‑only width tag	A–Z, 0–9	N/A	None	Sanitized to uppercase alphanumerics

Constants and coefficients
Constant	Value	Unit	Source	Notes
cm per inch	2.54	cm/in	Code	Used for inch conversions
EU points per cm	1.5	EU size/cm	Code	Linear mapping from last
US Men offset	24	size	Code	Applied to 3×last inches
US Women offset	23	size	Code	Applied to 3×last inches
UK offset	25	size	Code	Applied to 3×last inches
Toe gauge maximum	25	mm	Code	Gauge upper bound

Units, precision & rounding policy. Lengths display with a dot as the decimal separator and typically use two decimal places. Size displays trim trailing zeros based on step precision. “Nearest” rounds half up for positive values; “floor” and “ceil” use small safeguards to avoid boundary flicker. All math uses base‑10 decimals.

Validation and bounds from code
Field	Type	Min	Max	Step/Pattern	Error Text	Placeholder
Value	number	0	—	step 0.01	—	—
Input type	select	—	—	foot_cm, foot_in, us_m, us_w, uk, eu, jp_cm, mx_cm, cn_mm, kr_mm, br	—	—
Audience	radio	—	—	men / women	—	—
Allowance	number	0	—	step 0.1	—	—
Width code	text	—	—	^[A‑Z0‑9]+$ (sanitized)	—	D · E · 2E · 4E · B · C
Rounding	select	—	—	nearest / floor / ceil	—	—
US/UK step	number	0.25	—	step 0.5	—	—
EU step	number	0.5	—	step 0.5	—	—
JP/MX step	number	0.5	—	step 0.5	—	—
CN step (mm)	number	1	—	step 1	—	—
KR step (mm)	number	1	—	step 1	—	—
BR step	number	0.5	—	step 0.5	—	—
BR offset	number	—	—	step 0.5	—	—

I/O formats
Input	Accepted Families	Output	Encoding/Precision	Rounding
Foot length	cm, in	Sizes and last	dot decimal, 2 dp typical	Step‑aware
Size (US/UK/EU/BR)	number	Foot and last	dot decimal where shown	Step‑aware
Size (JP/MX)	cm	As entered	0.5 cm typical	Step‑aware
Size (CN/KR)	mm	As entered	5 mm typical	Step‑aware
CSV export	Table rows	Field, Value	UTF‑8 text	As displayed
JSON export	Inputs, derived, sizes	Structured object	Lengths 2 dp; raw sizes 3 dp; CN/KR 1 dp	Includes both raw and rounded

Networking & storage behavior. All calculations run in your browser, and copy/download actions use browser APIs. No data is transmitted to or stored on a server.

Performance & complexity. Conversions are constant‑time per system and memory usage is negligible. Rendering of charts or tables scales with the small number of systems shown and remains responsive on typical devices.

Diagnostics & determinism. The engine is deterministic for identical inputs. It issues human‑readable warnings when foot length sits outside a typical adult range, when allowance is unusual, when EU half sizes are selected, or when BR mapping is approximate.

Security considerations. Inputs are sanitized where applicable; the width tag keeps only uppercase letters and digits. Exports reflect your entries verbatim. Review content before pasting into external systems that interpret commands or formulas.

Worked example.

\begin{matrix} Given: & L f_{cm} = 26, A {cm}_{} = 1.5 \\ Last: & L l_{cm} = 27.5 \\ EU: & S_{EU,raw} = 41.25 \to S_{EU} \approx 41.5 \\ US Men: & S_{USM,raw} \approx 8.48 \to S_{USM} = 8.5 \\ UK: & S_{UK,raw} \approx 7.48 \to S_{UK} = 7.5 \\ BR: & S_{BR,raw} = 39.25 \to S_{BR} = 39 \\ JP/MX: & S_{JP} = S_{MX} = 26 cm \\ CN/KR: & S_{CN,mm} = S_{KR,mm} = 260 mm \end{matrix}

Interpret near boundaries in context rather than as absolutes.

Heads‑up Brand charts can diverge by about one size; BR is explicitly approximate.
Heads‑up EU half sizes may be unavailable; check retailer availability.
Heads‑up Foot lengths outside 18–31 cm trigger a caution to recheck units.
Allowance outside 0.5–2.0 cm triggers a caution; verify your fit intent.
Rounding affects the effective allowance; different modes shift fit direction.
Width tags are informational and do not alter calculations.

Edge cases: non‑numeric input becomes zero; negative values clamp to zero.
NaN or Infinity is coerced to zero before calculations.
Signed‑zero has no effect; results depend on absolute magnitudes.
Rounding ties at exactly half step round up in “nearest”.
Very fine steps can reveal floating‑point quirks; safeguards minimize jitter.
Alphanumeric width code drops spaces and punctuation, then uppercases.
Switching primary emphasis changes the displayed effective allowance only.
Millimetre systems (CN/KR) round to their mm step before display.

Step‑by‑Step Guide:

Set your starting point, adjust fit intent, then read the equivalents.

Select Input type for a foot length or a known size.
Enter the Value in the shown unit.
Pick Audience to emphasize US Men or US Women.
Set Allowance; use presets for snug, standard, or roomy.
Optionally adjust Rounding, step sizes, and BR offset.
Review the table and toe‑room band; copy or export if needed.

Example: enter 26 cm with 1.5 cm allowance; you’ll see EU 41.5 and US Men 8.5 as practical targets.

You leave with a short, explainable list ready for checkout or comparison.

FAQ:

Is my data stored?

No. Calculations run in your browser, and exports are created locally. Nothing is sent to a server.

How accurate are the results?

They follow explicit equations and your rounding choices. Brand charts vary, and BR is approximate, so consider results a well‑informed starting point.

Which units and systems are supported?

Foot length in centimetres or inches; sizes for US Men, US Women, UK, EU, BR, JP/MX (cm), and CN/KR (mm).

Do half sizes appear?

Yes when the step supports them. EU half sizes are uncommon in inventory and may not be available from certain brands.

What does BR offset do?

It shifts BR relative to EU. A typical setting is −2; use it to match a brand’s printed chart when required.

How do I convert US to EU shoe size?

Choose US as the input, set your allowance and steps, then read the EU row. Check the toe‑room band to confirm fit intent.

Can I use it without a connection?

Yes after the page loads. Everything runs in the browser with no sign‑in required.

Are width codes used in math?

No. Width is captured for display only and sanitized to uppercase letters and digits.

Troubleshooting:

No results show: enter a positive value and confirm the correct input type.
EU halves look odd: set the EU step to whole sizes to mirror inventory.
BR feels off by one: adjust the BR offset; try the typical −2 shortcut.
Too many decimals: increase step sizes so displays trim trailing zeros.
Toe‑room band feels wrong: check which system is emphasized and the rounding mode.

Blocking issue: an empty or zero value yields “No data.” Enter a valid number and recheck units.

Advanced Tips:

For thicker socks, start at 2.0 cm allowance, then test one step down.
Use “floor” to bias tighter fits; use “ceil” to bias roomier fits.
Match CN/KR steps to retailer increments to keep exports consistent.
Keep BR offset stable across sessions when aligning to a specific brand.
When values sit on a boundary, compare both adjacent sizes and note toe‑room.

Glossary:

Foot length: Distance from heel to longest toe, measured barefoot.
Last length: Internal shoe length that a size represents.
Toe‑room allowance: Extra space added to foot length for comfort.
Step size: Granularity that sizes snap to in each system.
Rounding mode: Rule used to snap values to steps.
Mondopoint: Length‑based sizing used for JP and some standards.
BR offset: Adjustment applied to BR relative to EU.
Effective allowance: Toe‑room implied by the emphasized system after rounding.