Convert Radians to Gradians - Angle Converter
This converter converts an angle measured in radians to gradians (also written grads or gons). The relationship is exact and based on the definition of a full circle: 2π radians equals 400 gradians, so conversion is deterministic and reversible.
Gradians are commonly used in surveying, civil engineering, and some mapping conventions because they subdivide a right angle into 100 centesimal units. Radians are the standard angular measure in mathematics, physics, and many engineering formulas because they relate directly to arc length and trigonometric series.
Use this tool for quick conversions, checking calculation results, or cross-referencing instruments. For high-precision needs (metrology, instrument calibration, standards compliance), pair numerical results with calibrated equipment and reference labs following NIST/BIPM guidance.
Interactive Converter
Convert between radian and gradian with precision rounding.
Quick reference table
| Radian | Gradian |
|---|---|
| 1 rad | 63.662 grad |
| 5 rad | 318.3099 grad |
| 10 rad | 636.6198 grad |
| 25 rad | 1,591.5494 grad |
| 50 rad | 3,183.0989 grad |
| 100 rad | 6,366.1977 grad |
Methodology
The conversion derives from the circle partition: 360 degrees = 400 gradians = 2π radians. Rearranging gives the exact factor between radians and gradians. This is a pure unit-scale conversion (no approximation introduced by the definition).
For display and downstream calculations we provide both the exact symbolic conversion and typical decimal approximations. When reporting results for regulatory or instrument-traceable work, indicate the numeric precision used and the calibration status of the measuring device.
Standards and unit definitions used as authoritative references include the SI and national metrology guidance (BIPM and NIST). For calibration or legal metrology questions consult national measurement institutes or accredited calibration laboratories.
Worked examples
Convert 1 radian → 1 × (200/π) ≈ 63.66197723675813 gradians.
Convert 0.5 radian → 0.5 × (200/π) ≈ 31.830988618379066 gradians.
Convert π radians → π × (200/π) = 200 gradians (exact).
Expert Q&A
What is the exact relationship between radians and gradians?
A full circle equals 2π radians and 400 gradians, so 1 radian = 200/π gradians and 1 gradian = π/200 radians. These are exact mathematical identities.
Why use gradians instead of degrees or radians?
Gradians divide a right angle into 100 units, which can simplify decimal-based calculations in surveying and some engineering workflows. Radians are preferred in calculus and physics because they connect angle measure directly to arc length and series expansions.
How many decimal places should I show for conversions?
That depends on your application and instrument precision. For everyday use 4–6 decimal places are usually sufficient. For metrology or regulatory reports, match the number of significant digits to the instrument's calibrated uncertainty and document calibration traceability (e.g., NIST-traceable).
Does this conversion account for instrument calibration or measurement error?
No. This tool performs an exact unit conversion only. Measurement error and instrument calibration are separate concerns — for critical measurements use calibrated instruments and consult accredited calibration services or national metrology institutes for traceability.
How do I convert back from gradians to radians?
Use the inverse formula: radians = gradians × (π / 200). This reverses the conversion exactly.
Are gradians commonly used internationally?
Gradians are used in some countries and in surveying contexts, but degrees and radians are more globally widespread. Follow project or regulatory conventions for the preferred unit.
Sources & citations
- NIST Reference on Constants, Units, and Uncertainty (Units) — https://physics.nist.gov/cuu/Units/units.html
- BIPM — The International System of Units (SI) and related materials — https://www.bipm.org/en/publications/si-brochure
- MIT OpenCourseWare — Single Variable Calculus (reference on radians and angle measure) — https://ocw.mit.edu/courses/18-01sc-single-variable-calculus/
- NIST — Information on measurement, calibration, and traceability — https://www.nist.gov/calibrations