Cernarus

Convert Gradians to Arcminutes - Angle Converter

This converter converts gradians (gon) to arcminutes (′) using the fixed geometric relationship between circle subdivisions. Gradians partition a full circle into 400 units; arcminutes partition a degree into 60 minutes.

Use this tool for surveying, mapping, geodesy, education, or any situation where you need a precise, reproducible unit conversion. Results are exact arithmetically (no empirical approximation) — apply rounding only to match instrument resolution or reporting requirements.

Updated Nov 22, 2025

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Methodology

A full circle equals 400 gradians and also equals 360 degrees. Therefore one gradian is 1/400 of a circle, which equals 360/400 = 9/10 degrees.

Because one degree equals 60 arcminutes, multiply the gradian value by 9/10 and then by 60 to convert to arcminutes. That reduces to a single conversion factor: 1 gradian = 54 arcminutes.

When converting measured values, consider instrument resolution and uncertainty. Report converted values to a precision consistent with the original measurement (for example, if a theodolite reads to 0.01 gon, convert and round to a precision that reflects that resolution).

Worked examples

Example 1: 1 grad → arcminutes: 1 × 54 = 54 arcminutes.

Example 2: 2.5 grad → arcminutes: 2.5 × 54 = 135 arcminutes.

Example 3 (inverse): 270 arcminutes → gradians: 270 / 54 = 5 gradians.

Further resources

Expert Q&A

What is a gradian (gon)?

A gradian, also called a gon, is an angular unit where a full circle equals 400 gradians. It is commonly used in surveying and civil engineering in some countries and contexts.

Why is the conversion factor exactly 54?

Because 1 gradian = 9/10 degree and 1 degree = 60 arcminutes, so 1 gradian = 0.9 × 60 = 54 arcminutes. This is a fixed geometric relationship, not an empirical approximation.

How should I handle rounding after conversion?

Round converted results to reflect the resolution and uncertainty of the original measurement. For example, if the instrument reports to 0.01 gon, convert then round so the reported arcminutes do not imply more precision than the original reading supports.

Is the gradian an SI unit?

The gradian is not a base SI unit. Conventional angular units such as the degree are widely accepted for use with the SI; references on unit usage and conventions are published by standards organizations and NIST.

Are there practical limits or calibration considerations?

Yes. Surveying instruments (theodolites, total stations, GNSS-based attitude sensors) have finite resolution and systematic errors. Always check instrument calibration certificates and apply appropriate uncertainty propagation when reporting converted values.

Can I convert large arrays of values programmatically?

Yes. Use the exact factor 54 to convert numerically: arcminutes = grads × 54. For batch conversions, propagate numeric precision consistent with your data type and rounding policy.

Sources & citations