Convert Gradians to Degrees - Angle Converter
Use this converter to transform angle measures given in gradians (also called grads or gon) into degrees. Gradians divide a full circle into 400 equal parts; degrees divide it into 360 parts, so the conversion is fixed and exact.
This tool is designed for engineers, surveyors, navigators, and students who need a reliable, standards-aligned conversion with practical guidance on precision and instrument calibration.
Governance
Record b6461a2dca3f • Reviewed by Fidamen Standards Committee
Interactive Converter
Convert between gradian and degree with precision rounding.
Quick reference table
| Gradian | Degree |
|---|---|
| 1 grad | 0.9 ° |
| 5 grad | 4.5 ° |
| 10 grad | 9 ° |
| 25 grad | 22.5 ° |
| 50 grad | 45 ° |
| 100 grad | 90 ° |
Methodology
The conversion derives from the geometric definition of angular subdivisions: a full rotation equals 400 gradians or 360 degrees. Therefore the degree value is 360/400 times the gradian value. Equivalently, 1 gradian = 0.9 degrees.
For contexts requiring SI-consistent reasoning, gradians relate to radians by the factor π/200, since 2π radians = 400 gradians. These relationships are exact and internationally referenced by metrology and standards bodies.
When applying results in practice, consider instrument resolution, measurement uncertainty, and rounding rules. For legal, safety-critical, or regulatory work consult national metrology guidance (for example, NIST) and applicable ISO standards for angle measurement and surveying.
Worked examples
Example 1: Convert 100 gradians → degrees: 100 × 0.9 = 90°
Example 2: Convert 250.5 gradians → degrees: 250.5 × 0.9 = 225.45°
Example 3 (via radians): 50 gradians → radians: 50 × π/200 = 0.785398... rad → in degrees 0.785398 × (180/π) = 45°
F.A.Q.
What is the exact relationship between gradians and degrees?
Exactly 1 gradian = 0.9 degrees because a full circle is defined as 400 gradians and 360 degrees, so degrees = gradians × (360/400). This is an exact arithmetic relation.
When are gradians used instead of degrees?
Gradians are commonly used in surveying, civil engineering, and some mapping contexts where dividing the right angle into 100 units simplifies calculations. Usage varies by country and industry; many modern applications use degrees or radians.
How should I handle rounding and instrument precision?
Round only at the final step and match rounding to the instrument's resolution and the required reporting precision. For critical measurements, propagate measurement uncertainty and refer to your instrument calibration certificate and national metrology guidance (for example, NIST) for handling uncertainty.
Can I convert small fractional gradians accurately?
Yes. The conversion is exact mathematically. For very small values, ensure your calculator or software preserves sufficient decimal places; consider using double-precision arithmetic for engineering-level tasks.
How do I verify my instrument or surveyor's angular readings?
Follow the manufacturer’s calibration procedure and check calibration against a known reference or reference network. For formal verification and traceability, consult national metrology institutes and relevant ISO standards for angle and surveying instruments.
Sources & citations
- BIPM — The International System of Units (SI Brochure) — https://www.bipm.org/en/publications/si-brochure
- NIST — SI Unit Information and Guidance — https://www.nist.gov/pml/weights-and-measures/si-units
- MIT OpenCourseWare — Mathematics and Trigonometry Resources — https://ocw.mit.edu
- ISO 80000-3:2019 — Space and time — https://www.iso.org/standard/64974.html
- NIST SP 811 — Guide for the Use of the International System of Units — https://www.nist.gov/pml/special-publication-811
Further resources
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: b6461a2dca3fWhat changed (latest)
v1.0.0 • 2025-11-24 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
What changed (latest)
v1.0.0 • 2025-11-24 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Engine
v1.0.0
Data
Baseline (no external datasets)
Content
v1.0.0
UI
v1.0.0
Governance
Last updated: Nov 24, 2025
Reviewed by: Fidamen Standards Committee (Review board)
Credentials: Internal QA
Risk level: low
Reviewer profile (entity)
Fidamen Standards Committee
Review board
Internal QA
Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person
Semantic versioning
- MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
- MINOR: New features or fields that do not change existing outputs for the same inputs.
- PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.
Review protocol
- Verify formulas and unit definitions against primary standards or datasets.
- Run golden-case regression suite and edge-case suite.
- Record reviewer sign-off with credentials and scope.
- Document assumptions, limitations, and jurisdiction applicability.
Assumptions & limitations
- Uses exact unit definitions from the Fidamen conversion library.
- Internal calculations use double precision; display rounding follows the unit's configured decimal places.
- Not a substitute for calibrated instruments in regulated contexts.
- Jurisdiction-specific rules may require official guidance.
Change log
v1.0.0 • 2025-11-24 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: c0d42966c43d