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

What is the formula to convert radians to gradians?

Multiply the radian value by 200/π. For example, π/2 radians × (200/π) = 100 gradians, confirming a right angle is 100 grad.

How many gradians are in a full circle?

A full circle (2π radians or 360°) equals exactly 400 gradians.

What is 1 radian in gradians?

1 radian equals 200/π gradians, which is approximately 63.6620 grad.

Where are gradians used in practice?

Gradians are mainly used in surveying, civil engineering, and some European countries for land measurement. They simplify arithmetic because right angles and quarter-circles come out as round numbers.

Is the result exact or approximate?

Because π is irrational, the decimal result is always an approximation. This tool shows up to 6 decimal places for practical accuracy.

Radians to Gradians Converter

Convert any angle from radians to gradians (grad/gon) using the formula gradians = radians × 200/π, with a step-by-step breakdown and common angle reference table.

Enter Angle in Radians

Radians (rad)

Common Angle Reference Table

Click any row to load that angle into the converter.

Radians	Degrees (°)	Gradians (grad)

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Summary

This tool converts angle measurements from radians to gradians using the formula: gradians = radians × (200/π). Gradians (also called gon or grad) divide a full circle into 400 equal parts, making right angles exactly 100 grad — a convenient property used in surveying and civil engineering. Enter any radian value to get the precise gradian equivalent with a full step-by-step calculation.

How it works

Enter an angle in radians in the input field.
The converter applies the formula: gradians = radians × (200 / π).
The result is displayed in gradians (grad/gon) rounded to 6 decimal places.
The step-by-step panel shows the substituted formula so you can verify the math.
Click any row in the reference table to load that angle into the converter.

Use cases

Converting radian angles to gradians for surveying and geodesy calculations.
Checking gradian values when working with civil engineering or land measurement tools.
Verifying manual radian-to-gradian conversions for coursework or exams.
Preparing angles for GIS software that accepts gradian input.
Teaching or learning the relationship between radians, degrees, and gradians.
Quick lookup of common angles like π/2 rad = 100 grad or π rad = 200 grad.

Frequently Asked Questions

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