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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.
Formula
1 grad = 0.9 °
degrees = gradians × 0.9 — reverse: gradians = degrees × 1.111111111
The factor is derived from the SI definitions of both units (base unit: rad) as listed in NIST SP 811; results on this page are shown to 6 significant figures, the API returns up to 12.
Worked examples
- 5 grad = 4.5 °
- 12.5 grad = 11.25 °
- 100 grad = 90 °
Gradians to degrees 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 |
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
Machine access
- API:
GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=grad&to_unit=deg - MCP: server
https://tttkmbb.com/mcp, toolconvert_unitswith{"value":5,"from_unit":"grad","to_unit":"deg"} - Markdown: https://tttkmbb.com/conversion/gradians-to-degrees.md · JSON: https://tttkmbb.com/conversion/gradians-to-degrees.json (add
?value=for a result) · Units: /api/v1/units?quantity=angle - OpenAPI operationId:
convert_units. Freshness:static. Authentication: none.