# Temperature Converter

> Converts temperatures between Celsius, Fahrenheit, Kelvin and Rankine with the exact defining relations (°F = °C × 9/5 + 32, K = °C + 273.15, °R = °F + 459.67) and rejects values below absolute zero.

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

## Purpose

Converts temperatures between Celsius, Fahrenheit, Kelvin and Rankine with the exact defining relations (°F = °C × 9/5 + 32, K = °C + 273.15, °R = °F + 459.67) and rejects values below absolute zero.

**Use when:** You need a weather, cooking, body or laboratory temperature in another scale, e.g. Fahrenheit to Celsius or Celsius to Kelvin.

**Do not use when:** You need to convert a temperature difference (a change of 10 °C is 18 °F, not 50 °F: multiply by 9/5 without the offset) or heat energy (use energy).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `value` | number |  | required | Amount to convert, expressed in from_unit. |
| `from_unit` | enum: C \| F \| K \| R |  | required | Unit of the input value. Accepted symbols: C, F, K, R; spelled-out names and common abbreviations are accepted too. |
| `to_unit` | enum: C \| F \| K \| R |  | required | Unit to convert into (same symbols as from_unit). |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `result` | number |  | Converted value expressed in to_unit (rounded to 6 decimals; see result_text for very small or very large values). |
| `result_text` | string |  | The conversion as text with 6 significant figures, e.g. "5 mi = 8.04672 km". |
| `formula` | string |  | Relation used, e.g. "1 mi = 1.609344 km". |
| `factor` | number |  | Multiplier from from_unit to to_unit (result = value × factor); absent for non-linear conversions. |
| `conversion_table` | object |  | The input value expressed in every supported temperature unit (6 significant figures), keyed by unit symbol. |

## Formula

`°F = °C × 9/5 + 32; °C = (°F − 32) × 5/9; K = °C + 273.15; °R = °F + 459.67 = K × 9/5`

Kelvin is the base: the input is converted to kelvin and then to the target scale. Results below 0 K raise OUT_OF_RANGE.

## Data Sources

- NIST Special Publication 811 – Guide for the Use of the International System of Units (SI), Appendix B conversion factors — https://www.nist.gov/pml/special-publication-811 (standard, retrieved 2026-09-23)
- BIPM – The International System of Units (SI Brochure, 9th edition) — https://www.bipm.org/en/publications/si-brochure (standard, retrieved 2026-09-23)
- Wikipedia – Conversion of units — https://en.wikipedia.org/wiki/Conversion_of_units (reference, retrieved 2026-09-23)

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/temperature?value=…&from_unit=…&to_unit=…`
- `POST https://tttkmbb.com/api/v1/calculate/temperature` 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/temperature · OpenAPI operationId `convert_temperature` 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: `convert_temperature` (dedicated) or `run_calculator` with `{"calculator_id": "temperature", "inputs": {…}}`

## Example

- 100 °F to °C: inputs `{"value":100,"from_unit":"F","to_unit":"C"}` → `{"result":37.777778,"formula":"°C = (°F − 32) × 5/9","result_text":"100 °F = 37.7778 °C","conversion_table":{"K":310.928,"R":559.67}}`
- 25 °C to °F: inputs `{"value":25,"from_unit":"C","to_unit":"F"}` → `{"result":77,"formula":"°F = °C × 9/5 + 32","conversion_table":{"K":298.15,"R":536.67}}`

```
GET https://tttkmbb.com/api/v1/calculate/temperature?value=100&from_unit=F&to_unit=C
```

## Limitations

You need to convert a temperature difference (a change of 10 °C is 18 °F, not 50 °F: multiply by 9/5 without the offset) or heat energy (use energy). Kelvin is the base: the input is converted to kelvin and then to the target scale. Results below 0 K raise OUT_OF_RANGE. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why is there no factor output?**

Temperature scales have different zero points, so the conversion is affine (multiply and add), not a simple multiplication. The formula output shows the exact relation used.

**Where do the scales coincide?**

−40 °C = −40 °F. Absolute zero is 0 K = −273.15 °C = −459.67 °F = 0 °R; water freezes at 273.15 K and boils at 373.15 K at 1 atm.

**Can I convert a temperature difference?**

Not with this tool: a difference of Δ °C equals Δ × 9/5 °F and Δ K; entering it here would wrongly apply the 32 or 273.15 offset.

## Related

- [Specific Heat Calculator](https://tttkmbb.com/physics/specific-heat.md) — Heat needed for a temperature change.
- [Ideal Gas Law Calculator](https://tttkmbb.com/chemistry/ideal-gas-law.md) — Gas calculations need absolute temperature in kelvin.