A gradian (also called grad or gon) is a unit of angle where a full circle equals 400 gradians. A right angle is exactly 100 grad, which simplifies calculations in surveying and civil engineering.

What is a turn in angle measurement?

A turn (also called a revolution or cycle) represents one complete rotation — 360 degrees, 2π radians, or 400 gradians. It is a natural unit when counting full rotations.

What is the formula to convert gradians to turns?

Divide the gradian value by 400. For example, 200 grad / 400 = 0.5 turns (a half rotation). This works because one full turn equals exactly 400 gradians.

How many gradians make one full turn?

400 gradians equal exactly 1 turn (one full circle). A quarter turn (right angle) is 100 grad, and a half turn (straight angle) is 200 grad.

Where are gradians used in practice?

Gradians are commonly used in surveying, civil engineering, and military applications, particularly in continental Europe. Many scientific calculators include a "grad" mode alongside degrees and radians.

Gradians to Turns Converter

Convert any angle from gradians (grad/gon) to turns (full rotations) using the formula turns = gradians / 400, with step-by-step breakdown and reference table.

Enter Angle in Gradians

Gradians (grad / gon)

Formula: turns = grad / 400

Common Angle Reference Table

Click any row to load that angle into the converter.

Gradians (grad)	Turns	Common Name

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Summary

This tool converts angle measurements from gradians to turns using the formula: turns = gradians / 400. A gradian (also called grad or gon) divides a full circle into 400 equal parts, so 400 gradians equal exactly 1 turn. A turn represents one complete 360-degree rotation. Turns are used in mathematics, physics, and computer graphics where expressing multiples of full rotations is more intuitive than using degrees or radians.

How it works

Enter an angle in gradians in the input field.
The converter applies the formula: turns = gradians / 400.
The step-by-step calculation 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 gradian angles to turn-based rotation counts.
Translating gradian values from scientific calculators into turns for physics calculations.
Learning the relationship between grad, gon, and full-circle turns.
Verifying angle measurements when switching between unit systems.
Converting angles output from GIS or mapping software in grad mode.
Teaching angle unit conversions alongside degrees, radians, and turns.

Frequently Asked Questions

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