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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.

Updated Nov 1, 2025

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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)

Further resources

Expert Q&A

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