Gradian to Degree Converter

Convert gradian to degree instantly. 1 gradian = 0.9 degree.

1 Gradian =
Degree
From
To

Gradian to Degree Table

GradianDegree
1 grad0.9 °
5 grad4.5 °
10 grad9.0 °
30 grad27.0 °
45 grad40.5 °
90 grad81.0 °
180 grad162.0 °
360 grad324.0 °

Quick Answer

Formula: Degree = Gradian × 0.9

Multiply any gradian value by 0.9 to get degree.

Reverse: Gradian = Degree × 1.111

Worked Examples

Right angle
100 grad × 0.9 = 90 °
100 grad = 90° — right angle.
Half circle
200 grad × 0.9 = 180 °
200 grad = 180°.
Full circle
400 grad × 0.9 = 360 °
400 grad = 360° — full circle.
Half right angle
50 grad × 0.9 = 45 °
50 grad = 45°.

Gradian to Degree Conversion Table

Common gradian values — factor: 1 grad = 0.9 °

Gradian (grad)Degree (°)Context
1 grad0.9 °1 grad
5 grad4.5 °5 grad
10 grad9 °10 grad
25 grad22.5 °22.5°
50 grad45 °45°
100 grad90 °90° right angle
150 grad135 °135°
200 grad180 °180° half circle
250 grad225 °225°
300 grad270 °270°
400 grad360 °360° full circle
800 grad720 °Two circles
1200 grad1080 °Three circles
2000 grad1800 °Five circles
4000 grad3600 °Ten circles

Mental Math Tricks

× 9/10

Gradians × 0.9 = degrees. Exact.

Right angle

100 grad = 90°. Quarter of 400 grad = 90°.

Reverse

Degrees × 10/9 = gradians.

Who Uses This Conversion?

Surveyor (European)

Uses gradians for land surveying in France, Sweden, and other European countries.

Civil Engineer

Applies gradians in road gradient calculations where 100 grad = right angle is convenient.

Geodesist

Works with national coordinate systems in countries that standardized on gradians.

Cartographer

Uses gradians in French topographic mapping traditions.

Mining Engineer

Applies gradians for dip and strike measurements in some European mining standards.

Artillery Gunner

Uses gradians in some European military targeting and range calculation systems.

Frequently Asked Questions

About Gradian and Degree

Gradian (grad)

The gradian (also called gon or grade) divides a full circle into 400 equal parts, so a right angle equals exactly 100 gradians. It was introduced during the French Revolution as part of the decimal metric system reform in the 1790s.

Gradians are used primarily in surveying, civil engineering, and some European geodetic systems. The advantage: since a right angle = 100 grad, slope percentages and bearing calculations involve simple arithmetic.

Interesting fact: France briefly mandated decimal angles (gradians) in the 1790s alongside the metric system, but the gradian never achieved the same global adoption as the meter and kilogram.

Degree (°)

The degree (°) divides a full circle into 360 equal parts. This system traces back to ancient Babylonian astronomy, which used a base-60 (sexagesimal) number system. The choice of 360 is practical: it is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, and 120.

Degrees remain the dominant angle unit in everyday life, navigation, surveying, and most engineering disciplines. Compass bearings, latitude and longitude, and architectural drawings all use degrees.

Interesting fact: The Babylonians may have chosen 360 because they approximated the solar year as 360 days, making each day of travel correspond to one degree of the Sun's apparent annual motion around the sky.

About Gradian to Degree Conversion

Converting gradian to degree is essential in mathematics, physics, engineering, and surveying. Degrees are used in everyday contexts and navigation; radians are the standard in calculus and physics; gradians are common in European surveying. Having accurate conversions ensures correct results across disciplines.

Key reference: a right angle (90°) = 90 °. A full circle (360°) = 360 °. Reverse: 1 ° = 1.111 grad. Exact factor: 1 grad = 0.9 °.

All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.