# Paper Size Converter

> Returns the dimensions of a standard paper size (ISO A0–A10, B0–B10, C4–C6, DL, US Letter, Legal, Tabloid, Executive, Statement, ANSI C–E) in millimetres and inches with area and aspect ratio, or finds the nearest standard size for given dimensions.

- Calculator id: `paper-size` · Category: Unit Conversion (`conversion`) · Tool name: `convert_paper_size`
- Canonical page: https://tttkmbb.com/conversion/paper-size · This document: https://tttkmbb.com/conversion/paper-size.md · JSON definition: https://tttkmbb.com/conversion/paper-size.json

## Purpose

Returns the dimensions of a standard paper size (ISO A0–A10, B0–B10, C4–C6, DL, US Letter, Legal, Tabloid, Executive, Statement, ANSI C–E) in millimetres and inches with area and aspect ratio, or finds the nearest standard size for given dimensions.

**Use when:** You need the exact size of a paper format, the inch equivalent of an A or B size (or vice versa), the area for paper-weight calculations, or want to identify a sheet you measured.

**Do not use when:** You need envelope fit for a folded sheet, printer margins, or photo/print sizes such as 4 × 6 in (use aspect-ratio for image proportions).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `size` | enum: a0 \| a1 \| a2 \| a3 \| a4 \| a5 \| a6 \| a7 \| a8 \| a9 \| a10 \| b0 \| b1 \| b2 \| b3 \| b4 \| b5 \| b6 \| b7 \| b8 \| b9 \| b10 \| c4 \| c5 \| c6 \| dl \| letter \| legal \| tabloid \| executive \| statement \| ansi_c \| ansi_d \| ansi_e \| custom |  | required | Standard size to look up, or custom to identify a sheet from width and height. |
| `width` | number |  | optional | Measured width in dimension_unit; used only with size=custom. (> 0, max 5000) |
| `height` | number |  | optional | Measured height in dimension_unit; used only with size=custom. (> 0, max 5000) |
| `dimension_unit` | enum: mm \| in |  | optional, default "mm" | Unit of the custom width and height. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `size_name` | string |  | Name and family of the size (for custom input: the dimensions given). |
| `width_mm` | number | mm | Short side in millimetres (portrait orientation). |
| `height_mm` | number | mm | Long side in millimetres. |
| `width_in` | number | in | Short side in inches. |
| `height_in` | number | in | Long side in inches. |
| `area_m2` | number | m² | Sheet area in square metres (multiply by grammage in g/m² for the sheet weight). |
| `area_in2` | number | in² | Sheet area in square inches. |
| `aspect_ratio` | number |  | Height divided by width; ISO sizes are √2 ≈ 1.4142. |
| `aspect_ratio_text` | string |  | Ratio as 1 : x. |
| `nearest_standard_size` | string |  | Closest standard size for custom dimensions (orientation ignored). |
| `deviation_percent` | number | % | Largest relative difference of the two sides from the nearest standard size (custom input only). |
| `series_note` | string |  | How the size relates to its family (halving, area, next sizes). |

## Formula

`ISO 216: A0 = 841 × 1189 mm (area ≈ 1 m²), each next size = previous long side halved, aspect √2; B(n) sides = geometric mean of A(n) and A(n−1); C(n) = geometric mean of A(n) and B(n); 1 in = 25.4 mm; area = width × height; aspect = height / width; nearest size = min over sizes of max(|w − w₀|/w₀, |h − h₀|/h₀)`

ISO dimensions are the standard's rounded millimetre values (tolerance ±1.5 mm for sizes up to 150 mm, ±2 mm up to 600 mm, ±3 mm above). US sizes follow ANSI/ASME Y14.1 and the customary Letter/Legal definitions.

## Data Sources

- ISO 216:2007 – Writing paper and certain classes of printed matter – Trimmed sizes – A and B series — https://www.iso.org/standard/36631.html (standard, retrieved 2026-09-24)
- Wikipedia – ISO 216 — https://en.wikipedia.org/wiki/ISO_216 (reference, retrieved 2026-09-24)
- Wikipedia – Paper size (North American sizes, ANSI/ASME Y14.1) — https://en.wikipedia.org/wiki/Paper_size (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/paper-size?size=…`
- `POST https://tttkmbb.com/api/v1/calculate/paper-size` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/paper-size · OpenAPI operationId `convert_paper_size` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "paper-size", "inputs": {…}}`

## Example

- A4: inputs `{"size":"a4"}` → `{"width_mm":210,"height_mm":297,"width_in":8.27,"height_in":11.69,"area_m2":0.0624,"area_in2":96.7,"aspect_ratio":1.4143,"size_name":"A4 (ISO 216)"}`
- US Letter: inputs `{"size":"letter"}` → `{"width_mm":215.9,"height_mm":279.4,"width_in":8.5,"height_in":11,"area_m2":0.0603,"area_in2":93.5,"aspect_ratio":1.2941}`

```
GET https://tttkmbb.com/api/v1/calculate/paper-size?size=a4
```

## Limitations

You need envelope fit for a folded sheet, printer margins, or photo/print sizes such as 4 × 6 in (use aspect-ratio for image proportions). ISO dimensions are the standard's rounded millimetre values (tolerance ±1.5 mm for sizes up to 150 mm, ±2 mm up to 600 mm, ±3 mm above). US sizes follow ANSI/ASME Y14.1 and the customary Letter/Legal definitions. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why is A4 not exactly 1/16 m²?**

Dimensions are rounded to whole millimetres at every halving step; A4 is 210 × 297 = 0.06237 m² instead of 0.0625 m², and its ratio 1.4143 differs from √2 in the fourth decimal.

**Is A4 the same as Letter?**

No. A4 is 6 mm narrower and 18 mm taller than US Letter (210 × 297 vs 215.9 × 279.4 mm); documents laid out for one usually need scaling (about 94 %) to print on the other.

**Which envelope fits an A4 sheet?**

C4 unfolded, C5 folded once, DL or C6/5 folded in thirds; C6 takes an A6 card or A4 folded twice.

## Related

- [Aspect Ratio Calculator](https://tttkmbb.com/everyday/aspect-ratio.md) — Aspect ratios of images and screens.
- [Area Converter](https://tttkmbb.com/conversion/area.md) — Convert the sheet area between units.
- [Length Converter](https://tttkmbb.com/conversion/length.md) — Convert individual dimensions between mm and inches.