Fidamen

Convert Gradians to Radians - Angle Converter

Use this converter to transform angles measured in gradians (sometimes abbreviated grad or gon) into radians with an exact mathematical factor. Gradians partition a full circle into 400 equal parts; radians partition a circle by arc length relative to radius and are the SI coherent angular measure.

The conversion here uses the exact relationship derived from circle geometry and the definition of radian, ensuring results are suitable for calculations, engineering checks, and scientific workflows that require SI-consistent units.

Updated Nov 27, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record 85efb2df7814 • Reviewed by Fidamen Standards Committee

Interactive Converter

Convert between gradian and radian with precision rounding.

Quick reference table

GradianRadian
1 gradRAD 0.0157 rad
5 gradRAD 0.0785 rad
10 gradRAD 0.1571 rad
25 gradRAD 0.3927 rad
50 gradRAD 0.7854 rad
100 gradRAD 1.5708 rad

Methodology

The conversion derives from the relationship between full-circle measures: 400 gradians correspond to 2π radians. Dividing both sides by 400 gives the exact factor to convert a single gradian to radians.

When using results in instrumentation, surveying, or numerical computations, keep sensor resolution and rounding in mind. For applied work consult national standards and measurement best practices (for example, NIST guidance on SI units) to determine required decimal precision and calibration procedures.

Key takeaways

Conversion is exact: multiply gradians by π/200 to get radians.

Use radians for SI-consistent calculations; apply calibration and uncertainty workflows separately for measurement tasks.

Worked examples

100 gradians → π/2 radians ≈ 1.57079632679 rad

200 gradians → π radians ≈ 3.14159265359 rad

1 gradian → π/200 radians ≈ 0.01570796327 rad

F.A.Q.

What is the exact relationship between gradians and radians?

Exactly 1 gradian = π/200 radians, because 400 gradians equal a full circle (2π radians). This is an exact geometric identity, not an approximation.

Why use radians instead of gradians?

Radians are the SI coherent unit for plane angles and are preferred in mathematical analysis, calculus, and many engineering calculations because they make trigonometric derivatives and integral formulas directly applicable without extra scale factors.

How many significant digits should I trust when converting for measurements?

Trust depends on the precision of your measuring instrument. For most surveying and surveying-grade instruments, report conversions to the instrument's resolution. For computations, keep at least 8–12 decimal places internally and round only for display or reporting in accordance with standards or project requirements.

Does this conversion account for instrument calibration or measurement error?

No. This converter performs a mathematical unit conversion only. For field measurements, apply instrument calibration corrections, error budgets, and uncertainty analysis separately following your lab or regulatory protocols.

Are gradians commonly used?

Gradians are used in some surveying and engineering contexts, and in certain national conventions. Degrees and radians are more widespread in scientific literature. When transferring data, confirm the unit convention and convert using the exact factor to avoid systematic errors.

Where can I find authoritative references on angle units and the radian definition?

Authoritative descriptions and SI guidance are available from national measurement institutes and university mathematics resources. Consult NIST and academic calculus course materials for definitions and implications of using radians in analysis.

Sources & citations

Further resources

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: 85efb2df7814

What changed (latest)

v1.0.0 • 2025-11-27 • 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 27, 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 • 2025-11-27 • 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: 0cf808bba0f8