How do I convert gradians to degrees?

Formula : Degrees = Gradians × 0.9 (or Gradians × 9/10) Examples : 100 gradians = 90° 200 gradians = 180° 400 gradians = 360° 50 gradians = 45° 25 gradians = 22.5° Gradians to Degrees converter →

How do I convert gradians to radians?

Formula : Radians = Gradians × (π/200) ≈ Gradians × 0.01571 Examples : 100 gradians = π/2 ≈ 1.571 radians 200 gradians = π ≈ 3.142 radians 400 gradians = 2π ≈ 6.283 radians 50 gradians = π/4 ≈ 0.785 radians Gradians to Radians converter →

What's the difference between gradians and gons?

No difference - they're the same unit: Gradian : Traditional name, widely recognized Gon : Modern ISO standard term (ISO 31-1) Grad : Common abbreviation used on calculators Grade : French name (le grade) All represent 1/400 of a circle. "Gon" is preferred in modern technical standards to avoid confusion with other meanings of "grade" (road grade, academic grade, etc.).

Why were gradians created?

Decimal system alignment : Part of French Revolution's metrication effort to create base-10 measurements. Historical context : Created in 1795 alongside metric system Right angle = 100 (easier than 90 degrees) Full circle = 400 (divisible by 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200) Percentage calculations simpler: 25 gradians = 25% of right angle Advantages over degrees : Pure decimal arithmetic (no sexagesimal base-60 calculations) Easier mental math: 50 gradians = half right angle Better integration with metric measurements Simpler for computing and digital systems Modern usage : While degrees dominate globally, gradians remain standard in European surveying, civil engineering, and cadastral work. France, Switzerland, and Germany extensively use gradians in official surveying.

Gradian (grad) - Unit Information & Conversion

Symbol:grad

Plural:gradians

Category:Angle

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What is a Gradian?

Gradian (also gon or grad) is 1/400 of a full circle, designed for decimal angle measurements. 100 gradians = 90 degrees. Widely used in European surveying, civil engineering, and construction for easier calculations.

History of the Gradian

Created during French Revolution (1795) as part of metric system. Designed to replace degrees with decimal-friendly unit. Still standard in many European countries for surveying and engineering work.

Quick Answer

What is a Gradian? A gradian (also called gon or grad) is 1/400th of a full circle. 100 gradians = 90° (right angle), 400 gradians = 360° (full circle). Designed for decimal convenience in surveying and engineering. Use our angle converter for instant conversions.

Key Facts: Gradian

Property	Value
Symbol	grad
Quantity	Angle
System	Metric/SI Derived
Derived from	Radian
Category	Angle
Standard Body	NIST / ISO

Definition

1 gradian = 1/400 of a full circle = 0.9 degrees = 0.01571 radians

Key conversions:

100 gradians = 90 degrees (right angle)
200 gradians = 180 degrees (straight angle)
400 gradians = 360 degrees (full circle)
1 gradian = 0.9° = π/200 radians

Symbols: grad, gon, or superscript "g" (e.g., 100ᵍ)

Common Uses

Surveying: Primary angle unit in France, Germany, Switzerland, and Scandinavia for land surveys. Civil Engineering: Building construction, road design, slope measurements in Europe. Military: Artillery calculations and targeting in European armed forces. Geodesy: Precise Earth measurements and coordinate systems in metric countries.

Real-World Examples

European Construction

Building foundations: Right angles measured as 100 gradians
Road curves: Highway banking angles specified in gradians
Bridge design: Structural angles calculated in gradians for simplicity
Tunnel boring: Alignment measured in gradians for precision

Surveying Instruments

Theodolites: Many European models display gradians as default
Total stations: Often switchable between degrees, gradians, and mils
Digital levels: Construction lasers with gradian readouts
GPS receivers: Some European units support gradian coordinates

Calculator Applications

Scientific calculators: "GRAD" mode (400 gradians = full circle)
Casio calculators: Marked with "G" or "GRAD" for gradian mode
TI calculators: Mode switch between Degree, Radian, Gradian
Engineering software: AutoCAD, QGIS support gradian input in European versions

Slope and Gradient Measurements

Ski slopes: Sometimes rated in gradians (25 gradians = moderate slope)
Railway grades: Track inclines measured in gradians
Wheelchair ramps: Accessibility slopes specified in gradians
Drainage systems: Pipe slopes calculated in gradians

The Gradian: The Metric Approach to Angles

The gradian, also known as the gon or grad, is a unit of plane angle defined as one-hundredth of a right angle. In this system, a right angle is exactly \text{ grads}$, and a full circle is \text{ grads}$. The gradian was introduced during the French Revolution as part of the broader decimalization (metrication) of all measurements. The goal was to align angular measurement with the base-10 system used for length (meters), mass (kilograms), and volume (liters).

While the gradian never achieved the universal adoption of the degree or the radian, it remains significant in several specialized fields, particularly in land surveying, artillery, and some branches of European civil engineering. Its primary advantage is that mental arithmetic for quarters of a circle is simplified (, 200, 300, 400$ instead of , 180, 270, 360$).

Gradians in Surveying and Mapping

In surveying, especially in France and Germany, the gradian has long been the standard. Many surveying instruments (theodolites) are equipped with 400-grad scales. This is because the metric system originally defined the kilometer such that the distance from the Equator to the North Pole was exactly ,000\text{ kilometers}$. Since this distance corresponds to a ^{\circ}$ (or \text{ grad}$) angle at the Earth's center, \text{ centigrad}$ of latitude corresponds to exactly \text{ kilometer}$ of distance on the surface. This elegant relationship between angle and distance was a primary driver for the unit's creation.

The Global Gradian Index: 100 Technical Benchmarks

**\text{ grad}*: /bin/zsh.9^{\circ}$; One-hundredth of a right angle.
**\text{ grads}*: ^{\circ}$; A small standard increment in metric surveying.
**\text{ grads}*: ^{\circ}$; Half of a right angle.
**\text{ grads}*: ^{\circ}$; A perfect orthogonal line.
**\text{ grads}*: ^{\circ}$; A straight line; opposition.
**\text{ grads}*: ^{\circ}$; Three-quarters of a turn.
**\text{ grads}*: ^{\circ}$; One full revolution.
**/bin/zsh.01\text{ grad}*: $ centigrad; Corresponds to \text{ km}$ on the Earth's surface (originally).
**/bin/zsh.0001\text{ grad}*: $ milligrad; Corresponds to \text{ meters}$ on the surface.
Artillery Mill: Often defined as /6400$ of a circle, though sometimes /6000$; Gradians provided the base for many military MIL systems.
European Railway Slopes: Often measured in gradients that reference gradian angles in technical plans.
Theodolite Precision: High-end metric theodolites resolve to /bin/zsh.0001\text{ grad}$.

Gradian Conversion Formulas

To Degree:

1 grad = 0.9 °

Example: 5 gradians = 4.5 degrees

To Radian:

1 grad = 0.015708 rad

Example: 5 gradians = 0.07854 radians

To Arcminute:

1 grad = 54 ′

Example: 5 gradians = 270 arcminutes

To Arcsecond:

1 grad = 3240 ″

Example: 5 gradians = 16200 arcseconds

To Turn:

1 grad = 0.0025 turn

Example: 5 gradians = 0.0125 turns

To Revolution:

1 grad = 0.0025 rev

Example: 5 gradians = 0.0125 revolutions

To Quadrant:

1 grad = 0.01 quad

Example: 5 gradians = 0.05 quadrants

To Gon:

1 grad = 1 gon

Example: 5 gradians = 5 gons

To Mil:

1 grad = 16 mil

Example: 5 gradians = 80 mils

Frequently Asked Questions

Formula: Degrees = Gradians × 0.9 (or Gradians × 9/10) Examples:

100 gradians = 90°
200 gradians = 180°
400 gradians = 360°
50 gradians = 45°
25 gradians = 22.5° Gradians to Degrees converter →

Convert Gradian

Need to convert Gradian to other angle units? Use our conversion tool.

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