Convert Turns to Radians - Angle Converter
This converter turns angles measured in gradians (also known as gons) into radians. Gradians divide a full circle into 400 equal parts; radians measure angles as arc length over radius and are the preferred unit in mathematical analysis and most scientific computing.
Use this tool for engineering, surveying, GIS data preparation, or any context where you need a precise, SI-consistent conversion. The calculation uses the exact relationship that 400 gradians = 2π radians to preserve accuracy for downstream numeric work.
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
Definition-based conversion: a full circle equals 400 gradians and 2π radians. Therefore 1 gradian = π/200 radians. This is an exact relationship derived from the geometric definitions of the units and used in metrology and standards documentation.
Computational guidance: the converter applies the exact symbolic factor (π/200). For highest numeric accuracy, implementations should use a high-precision math library or the platform's native constant for π (for example, IEEE double precision π) and avoid intermediate rounding until the final display step.
Practical notes: when converting measured angles, consider the instrument resolution and calibration uncertainty before specifying display precision. For regulatory or calibration-sensitive workflows consult published metrology guidance and calibration services.
Worked examples
400 gradians → 2π radians ≈ 6.283185307179586
200 gradians → π radians ≈ 3.141592653589793
100 gradians → π/2 radians ≈ 1.570796326794897
1 gradian → π/200 radians ≈ 0.015707963267949
Key takeaways
Use radians = gradians × (π / 200) for exact conversions. For applied work, match display precision to instrument uncertainty and preserve full-precision internally.
Radian output is ideal for mathematical functions, simulations, trigonometric computations, and statistical processing where SI-consistent angular units are required.
Expert Q&A
What is the exact mathematical relationship between gradians and radians?
Exact relationship: 1 gradian = π/200 radians, because 400 gradians equal a full circle and a full circle equals 2π radians. Use radians = gradians × (π / 200).
Is 'gradian' the same as 'gon'?
Yes. 'Gradian' and 'gon' are interchangeable terms for the same unit; both denote 1/400 of a full circle.
How many decimal places should I display?
Match display precision to the least precise element in your workflow. For survey-grade instruments, show fewer decimals and include uncertainty. For numeric computing or simulation, preserve double-precision internally and format output to the precision required by downstream functions.
Will this conversion introduce measurement error?
The conversion factor π/200 is exact. Any numeric error comes from the representation of π and floating-point arithmetic. For measurement error (instrument uncertainty), follow calibration and uncertainty reporting guidance from metrology authorities.
Where can I find authoritative guidance on units and calibration?
Refer to national metrology and standards organizations for unit definitions and calibration services. Practical resources include NIST documentation on units and calibration services and university resources on angular measure and trigonometry for correct application.
Sources & citations
- NIST — Guide to SI and unit definitions — https://physics.nist.gov/cuu/Units/units.html
- NIST — Calibration Services and Measurement Assurance — https://www.nist.gov/calibration-services
- MIT OpenCourseWare — foundational material on radians and trigonometry — https://ocw.mit.edu
- International Organization for Standardization (ISO) — https://www.iso.org