How many gradians are in a right angle?

Exactly 100 gradians, compared with 90 degrees. This is the entire point of the gradian: it was designed alongside the metric system so a quarter-turn lands on a clean decimal number.

What's the conversion factor between gradians and degrees?

One gradian equals exactly 0.9 degrees, and one degree equals exactly 1.1111... gradians (10/9). A full circle is 360 degrees or exactly 400 gradians.

Do modern surveyors still use gradians?

Some European and continental surveying and civil engineering total-station instruments still offer a gradian (gon) display mode, particularly in France and parts of Central Europe where the unit originated, but degrees remain the dominant angle unit in most surveying practice worldwide today.

Is a gradian the same as a gon?

Yes. 'Gon' is the more common name in continental European surveying and geodesy literature, while 'gradian' is more common in English-language references — both refer to the identical unit, 1/400 of a full turn.

Guide

Gradians vs degrees: why surveying uses base-100 angles

A gradian (grad, or gon) divides a full turn into 400 parts instead of 360, so a right angle is exactly 100 gradians — a decimal-friendly convention some surveying and civil engineering instruments still use.

By Buğra SözeriPublished September 25, 2026

The gradian (also called the gon) was created for the same reason the meter and the liter were: to replace an awkward traditional division with a clean decimal one. Where a right angle in degrees is 90 — not a round number in base 10 — a right angle in gradians is exactly 100, and a full turn is exactly 400 gradians instead of 360 degrees.

The exact conversion

Because 400 gradians and 360 degrees both represent one full turn, one gradian equals exactly 0.9 degrees:

degrees = gradians × 0.9
gradians = degrees × (10 / 9) ≈ degrees × 1.1111

Reference angles in both units

Degrees	Gradians
0°	0 grad
45°	50 grad
90°	100 grad
180°	200 grad
270°	300 grad
360°	400 grad

Why it never overtook degrees

The gradian was introduced with the metric system in France for surveying and civil engineering, where its decimal relationship to a right angle simplifies certain hand calculations. But degrees had centuries of astronomical, navigational, and cartographic infrastructure already built around them by the time the metric system arrived, and that installed base — star charts, compasses, navigational tables — proved far harder to replace than length or mass units did. The result is a split adoption: gradians persist as a selectable mode on some surveying instruments, particularly in continental Europe, while degrees remain the default virtually everywhere else, including in most GPS, mapping, and consumer software.

If you're working with survey data or an instrument reading that's unexpectedly using a base-400 scale instead of a base-360 one, gradians are almost certainly the explanation — check the instrument's angle-unit setting before assuming the data is wrong.

Frequently asked questions

How many gradians are in a right angle?: Exactly 100 gradians, compared with 90 degrees. This is the entire point of the gradian: it was designed alongside the metric system so a quarter-turn lands on a clean decimal number.
What's the conversion factor between gradians and degrees?: One gradian equals exactly 0.9 degrees, and one degree equals exactly 1.1111... gradians (10/9). A full circle is 360 degrees or exactly 400 gradians.
Do modern surveyors still use gradians?: Some European and continental surveying and civil engineering total-station instruments still offer a gradian (gon) display mode, particularly in France and parts of Central Europe where the unit originated, but degrees remain the dominant angle unit in most surveying practice worldwide today.
Is a gradian the same as a gon?: Yes. 'Gon' is the more common name in continental European surveying and geodesy literature, while 'gradian' is more common in English-language references — both refer to the identical unit, 1/400 of a full turn.

Sources & references

Authoritative references cited by this piece. Verified by Buğra Sözeri on the dates shown and re-checked at every deploy.

BIPM — SI Brochure, 9th edition (gradian/gon as a non-SI unit accepted for use with SI) — Reference for the gradian's definition relative to the full turn(as of 2026-09-25)