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.
Interactive Converter
Convert between gradian and radian with precision rounding.
Quick reference table
| Gradian | Radian |
|---|---|
| 1 grad | 0.0157 rad |
| 5 grad | 0.0785 rad |
| 10 grad | 0.1571 rad |
| 25 grad | 0.3927 rad |
| 50 grad | 0.7854 rad |
| 100 grad | 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.
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
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.
Further resources
External guidance
Expert Q&A
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
- NIST Special Publication (Guide to the SI) — https://www.nist.gov/pml/special-publication-811
- MIT OpenCourseWare — Calculus (radian explanation and usage) — https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/
- International Organization for Standardization (ISO) — https://www.iso.org