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Convert Degrees to Gradians - Angle Converter

Convert angles between degrees and gradians (gons). Gradians subdivide a full circle into 400 units, while degrees subdivide it into 360 units. This converter uses the exact mathematical relationship between these units so results are consistent with international metrology guidance.

Use this tool for surveying, civil engineering, cartography, navigation, or any calculation where angle units must be switched reliably. The conversion is exact: 360 degrees equals 400 gradians; any difference in output is due to rounding.

Updated Nov 15, 2025

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Methodology

The conversion is derived from the definition of a full circle. Because a circle is 360 degrees or 400 gradians, the conversion factor is 400/360 (which simplifies to 10/9) for degrees → gradians and 360/400 (0.9) for gradians → degrees. These are exact rational factors; numeric results can be rounded to the precision you require.

For engineering and metrology work follow national and international guidance on measurement uncertainty and instrument calibration. Trusted authorities (NIST, BIPM, ISO) provide best-practice guidance for calibration, traceability, and reporting of angular measurements.

Worked examples

Example 1 — Quick: 1° = 1 × 10/9 = 1.111111... gon. Rounded to 6 decimals: 1.111111 gon.

Example 2 — Surveying: 200 gon = 200 × 0.9 = 180°. Use the same numeric precision that your instrument or specification requires.

Example 3 — Wrap-around: an angle of -10° converts to -11.111111... gon (or 400 - 11.111111... = 388.888888... gon if you express it modulo a full circle).

Further resources

Expert Q&A

What is the exact mathematical relationship between degrees and gradians?

Exactly: 360 degrees = 400 gradians. Therefore degrees → gradians uses the factor 10/9 (≈1.111111...) and gradians → degrees uses 9/10 (0.9). These are exact rational factors.

When should I use gradians instead of degrees?

Gradians are common in some surveying and civil-engineering contexts, and in countries or industries that prefer decimal subdivisions of the right angle. Use the unit specified by project standards, tender documents, or local surveying practice.

How many decimal places should I keep for surveying or engineering?

Precision depends on the instrument and the task. For high-precision surveying, report values to the resolution your theodolite or total station provides and follow calibration/uncertainty statements from your lab. In many practical workflows, 0.001 gon (or finer) may be used, but always follow project specs and national metrology guidance.

Will rounding introduce significant errors?

Rounding introduces small numerical differences but not systematic unit conversion error—the conversion factor is exact. Manage rounding according to the precision requirements of your calculation and document the number of significant digits and uncertainty per ISO/NIST recommendations.

How do I handle negative angles or angles greater than a full circle?

Convert the numeric value directly using the formula. If you need a principal value within one revolution, reduce modulo 360° or 400 gon after conversion (e.g., result modulo 400 gon).

How do instrument calibration and traceability affect angle conversions?

Conversion between units is exact mathematically, but measurement uncertainty arises from instruments. Ensure instruments are calibrated and traceable to national standards (for example, through a National Metrology Institute) and include calibration uncertainty when reporting converted values.

Sources & citations