# Degrees to Gradians (° to grad)

> Convert degrees to gradians: 1 ° = 1.11111 grad. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

- Page id: `degrees-to-gradians` · Quantity: Angle (`angle`, base unit rad) · Tool: `convert_units`
- Canonical page: https://tttkmbb.com/conversion/degrees-to-gradians · This document: https://tttkmbb.com/conversion/degrees-to-gradians.md · JSON: https://tttkmbb.com/conversion/degrees-to-gradians.json (add `?value=` for a result)

## Formula

- `1 ° = 1.11111 grad`
- `gradians = degrees × 1.111111111`
- Reverse: `degrees = gradians × 0.9`

The factor follows from the SI definitions of both units (NIST SP 811); values below are rounded to 6 significant figures, the API returns up to 12.

## Worked examples

- 5 ° = 5.55556 grad
- 12.5 ° = 13.8889 grad
- 100 ° = 111.111 grad

## Conversion table

| Degrees (°) | Gradians (grad) |
| --- | --- |
| 1 | 1.11111 |
| 2 | 2.22222 |
| 3 | 3.33333 |
| 4 | 4.44444 |
| 5 | 5.55556 |
| 6 | 6.66667 |
| 7 | 7.77778 |
| 8 | 8.88889 |
| 9 | 10 |
| 10 | 11.1111 |
| 15 | 16.6667 |
| 20 | 22.2222 |
| 25 | 27.7778 |
| 30 | 33.3333 |
| 40 | 44.4444 |
| 50 | 55.5556 |
| 75 | 83.3333 |
| 100 | 111.111 |
| 200 | 222.222 |
| 250 | 277.778 |
| 500 | 555.556 |
| 1000 | 1111.11 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=deg&to_unit=grad` → unified JSON envelope with `result.values.result`, `formula`, `factor`, `sources`, `freshness`
- MCP: server `https://tttkmbb.com/mcp`, tool `convert_units` with `{"value":5,"from_unit":"deg","to_unit":"grad"}`
- All angle units: https://tttkmbb.com/api/v1/units?quantity=angle · full converter: [Angle Converter](https://tttkmbb.com/conversion/angle.md)
- Authentication: none. Freshness: `static` (fixed conversion factors).

## FAQ

**How many gradians are in one degree?**

1 ° = 1.11111 grad. The factor comes from the SI definitions of both units (NIST SP 811 / BIPM), so it is exact or correct to at least 10 significant figures.

**What is the formula to convert degrees to gradians?**

Multiply the value in degrees by 1.111111111: gradians = degrees × 1.111111111. For example, 5 ° = 5.55556 grad.

**How do I convert gradians back to degrees?**

Multiply by the inverse factor 0.9 (degrees = gradians × 0.9), or use the gradians-to-degrees page.

## Related conversions

- [Gradians to degrees](https://tttkmbb.com/conversion/gradians-to-degrees.md) (reverse)
- [Degrees to Radians](https://tttkmbb.com/conversion/degrees-to-radians.md)
- [Radians to Degrees](https://tttkmbb.com/conversion/radians-to-degrees.md)
- [Turns (revolutions) to Degrees](https://tttkmbb.com/conversion/turns-to-degrees.md)
- [Degrees to Turns (revolutions)](https://tttkmbb.com/conversion/degrees-to-turns.md)
- [Arcminutes to Degrees](https://tttkmbb.com/conversion/arcminutes-to-degrees.md)
- [Degrees to Arcminutes](https://tttkmbb.com/conversion/degrees-to-arcminutes.md)
- [Milliradians to Degrees](https://tttkmbb.com/conversion/milliradians-to-degrees.md)
- [Degrees to Milliradians](https://tttkmbb.com/conversion/degrees-to-milliradians.md)

## 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 2026-09-24)
- BIPM – The International System of Units (SI Brochure, 9th edition) — https://www.bipm.org/en/publications/si-brochure (standard, retrieved 2026-09-24)
- Wikipedia – Conversion of units — https://en.wikipedia.org/wiki/Conversion_of_units (reference, retrieved 2026-09-24)