Convert Radians to Turns - Angle Converter
Convert angle measures from radians to gradians (also called grads or gon). A grad divides a full circle into 400 equal parts and is commonly used in surveying and some engineering fields.
This converter uses the exact mathematical equivalence between radians and gradians: a full turn is 2π radians = 400 grads, so conversions use the factor 200/π for radians→grads and π/200 for grads→radians.
Governance
Record df6a70735b82 • Reviewed by Fidamen Standards Committee
Interactive converter unavailable for this calculator.
We could not resolve compatible units for this experience. Please verify the slug follows the pattern `from-unit-to-unit-converter`.
Methodology
The conversion is derived from the definition of a full circle. One full circle equals 2π radians and 400 gradians, therefore 1 radian = 400 / (2π) = 200 / π gradians. This relationship is exact and independent of measurement system conventions.
For engineering and laboratory work, apply appropriate numeric precision for your instrument or dataset. Use double-precision arithmetic for programmatic conversions to preserve accuracy; round final displayed results to the number of significant digits required by your application or measurement tolerance.
Worked examples
0.5 rad → 0.5 × (200 / π) ≈ 31.8309886 grads
2 radians → 2 × (200 / π) ≈ 127.3239545 grads
50 grads → 50 × (π / 200) ≈ 0.785398163 rad (π/4)
F.A.Q.
What is the exact conversion factor between radians and gradians?
1 radian = 200 / π gradians (exact). Numerically 1 rad ≈ 63.6619772368 grads. Conversely, 1 grad = π / 200 radians.
Why would I use gradians instead of degrees or radians?
Gradians divide a circle into 400 units, which can simplify decimal-based surveying calculations and certain civil engineering tasks. Choice of unit is convention-driven; most scientific computing and calculus use radians for their direct relation to arc length and trigonometric derivatives.
How should I handle rounding and precision for lab or field measurements?
Perform conversions using double-precision arithmetic and round only for display or reporting. Match rounding to your instrument's resolution and the required tolerance (for example, arc-second precision for high-accuracy surveying). Document uncertainty propagation from the original measurement through the conversion.
Do I need to worry about angle wrap-around (values outside 0–400 grads or 0–2π radians)?
The mathematical conversion works for any real-valued angle. For normalized bearings or cyclic quantities, reduce the converted result modulo 400 grads (or modulo 2π radians) to produce an equivalent principal value in the desired range.
Are these conversions consistent with national and international standards?
Yes. The conversions use the standard definitions of angle units (full circle = 2π radians). For authoritative guidance on units and SI usage consult standards and references such as NIST publications and ISO standards.
Sources & citations
- NIST — Table of Units: Angle — https://physics.nist.gov/cuu/Units/angle.html
- NIST Special Publication 811: Guide for the Use of the International System of Units (SI) — https://www.nist.gov/pml/special-publication-811
- MIT OpenCourseWare — resources on angle measure and radians — https://ocw.mit.edu
- ISO — Quantities and units (relevant standards) — https://www.iso.org/standard/36025.html
- ISO 80000-3:2019 — Space and time — https://www.iso.org/standard/64974.html
Further resources
Related tools
External guidance
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: df6a70735b82What changed (latest)
v1.0.0 • 2025-11-01 • 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 • 2025-11-01 • 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 1, 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 • 2025-11-01 • 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: 29424c9cf1f7