# Gradians to Degrees (grad to °)

> Convert gradians to degrees: 1 grad = 0.9 °. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

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

## Formula

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

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 grad = 4.5 °
- 12.5 grad = 11.25 °
- 100 grad = 90 °

## Conversion table

| Gradians (grad) | Degrees (°) |
| --- | --- |
| 1 | 0.9 |
| 2 | 1.8 |
| 3 | 2.7 |
| 4 | 3.6 |
| 5 | 4.5 |
| 6 | 5.4 |
| 7 | 6.3 |
| 8 | 7.2 |
| 9 | 8.1 |
| 10 | 9 |
| 15 | 13.5 |
| 20 | 18 |
| 25 | 22.5 |
| 30 | 27 |
| 40 | 36 |
| 50 | 45 |
| 75 | 67.5 |
| 100 | 90 |
| 200 | 180 |
| 250 | 225 |
| 500 | 450 |
| 1000 | 900 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=grad&to_unit=deg` → 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":"grad","to_unit":"deg"}`
- 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 degrees are in one gradian?**

1 grad = 0.9 °. 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 gradians to degrees?**

Multiply the value in gradians by 0.9: degrees = gradians × 0.9. For example, 5 grad = 4.5 °.

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

Multiply by the inverse factor 1.111111111 (gradians = degrees × 1.111111111), or use the degrees-to-gradians page.

## Related conversions

- [Degrees to gradians](https://tttkmbb.com/conversion/degrees-to-gradians.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)