What is the formula to convert gradians to arcseconds?

Multiply the gradian value by 3240. This comes from: 1 gradian = 0.9 degrees, and 1 degree = 3600 arcseconds, so 1 grad = 0.9 × 3600 = 3240 arcseconds.

What is an arcsecond?

An arcsecond (symbol ″) is 1/3600 of a degree. It is used in astronomy, geodesy, and optics to measure very small angles. For example, 1 arcsecond is roughly the angular size of a dime seen from about 3.8 km away.

A gradian (also called grad or gon) divides a full circle into 400 equal parts. A right angle is exactly 100 gradians. The unit is common in surveying and civil engineering, particularly in continental Europe.

How many arcseconds are in a full circle in gradians?

400 gradians × 3240 = 1,296,000 arcseconds, which matches 360° × 3600 = 1,296,000 arcseconds for a full circle.

Why convert gradians to arcseconds?

Surveying instruments often output angles in gradians, while astronomy and precision optics work in arcseconds. This converter bridges those two systems without needing an intermediate degree step.

Gradians to Arcseconds Converter

Convert any angle from gradians (grad/gon) to arcseconds using the formula arcseconds = gradians × 3240, with a step-by-step breakdown and reference table.

Enter Angle in Gradians

Gradians (grad / gon)

Formula: arcseconds = grad × 3240

Common Angle Reference Table

Click any row to load that angle into the converter.

Gradians (grad)	Arcseconds (″)	Common Name

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Summary

This tool converts angle measurements from gradians to arcseconds using the formula: arcseconds = gradians × 3240. A gradian divides a full circle into 400 equal parts, and each gradian equals 3240 arcseconds (since 1 gradian = 0.9° and 1° = 3600 arcseconds). Arcseconds are used in astronomy, geodesy, and precision optics where very small angles must be expressed. Enter any gradian value to see the arcsecond equivalent with full calculation steps.

How it works

Enter an angle in gradians in the input field.
The converter applies the formula: arcseconds = gradians × 3240.
The step-by-step derivation is shown below the result.
Use the reference table to look up common angles instantly.
Click any row in the reference table to load that angle into the converter.

Use cases

Converting surveying measurements from gradians to arcseconds for precision reporting.
Expressing small telescope or optics alignment angles in arcseconds from gradian readings.
Checking astronomical coordinate conversions that involve gradian-based input.
Teaching the relationship between the gradian, degree, arcminute, and arcsecond hierarchy.
Verifying angle unit conversions in geodetic and cartographic work.
Converting calculator output in grad mode to arcseconds for scientific notation.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu