Convert Degrees to Gradians
Instantly convert Degrees (°) to Gradians (grad) with our free online calculator.
Formula: ° to grad — multiply by 1.11111
Reference Table
| Degrees (°) | Gradians (grad) |
|---|---|
| 1 | 1.11111 |
| 5 | 5.55556 |
| 10 | 11.1111 |
| 25 | 27.7778 |
| 50 | 55.5556 |
| 100 | 111.111 |
How to Convert Degrees to Gradians
Formula
To convert Degrees (°) to Gradians (grad): multiply by 1.11111
Step-by-Step
- Start with your value in Degrees (°).
- Multiply by 1.11111 to perform the conversion.
- The result is your value expressed in Gradians (grad).
Conversion Factor
1 ° = 1.11111 grad
Reverse Factor
1 grad = 0.9 °
Worked Example
Convert 25 Degrees to Gradians: 25 ° = 27.7778 grad
About Degree (°)
A unit of plane angle equal to exactly 1/360 of a full rotation (= π/180 radians), inherited from ancient Babylonian astronomy's sexagesimal (base-60) number system circa 2000 BCE — the 360-degree convention reflects the ~360-day Babylonian solar year. Degrees are the universal everyday angle unit in non-scientific contexts: compass bearings and ship/aircraft heading per ICAO and IMO conventions (0° = magnetic north, 90° = east), latitude / longitude geographic coordinates per WGS84 (the GPS datum), machine-tool protractors and CNC G-code, GIS data (Esri ArcGIS, QGIS), CAD-software 2D-sketch dimensions (Autodesk Inventor, SolidWorks, Fusion 360, CATIA), and architectural drawings. Reference values: a right angle is exactly 90°, a straight line 180°, a full turn 360°, an equilateral triangle has 60° interior angles, a regular pentagon 108°, a regular hexagon 120°. Trigonometry education worldwide introduces sine and cosine in degrees before transitioning students to radians for calculus. Convert degrees to radians by multiplying by π/180 ≈ 0.01745.
About Gradian (grad)
A decimal-friendly unit of plane angle equal to exactly 1/400 of a full rotation (so 100 grad = 90°, exactly one right angle). Also called the 'gon' or 'grade'. Developed during the French Revolution (specifically the 1791 French Academy of Sciences proposal that also gave us the metric system) to decimalize angular measurement alongside the metric system's decimalization of length, mass, and time. Gradians survive today primarily in European surveying and land-cadastre mapping (especially in France, where French cadastral surveys per IGN standards still use gradians; and in parts of Germany and Switzerland), some military artillery applications (the Soviet/Russian military uses the related 'mil' = 1/6,400 of a circle for fire-direction calculations), and certain mining-survey traditions. Most pocket scientific calculators include a 'grad' mode alongside 'deg' and 'rad' for this reason. Reference values: 50 grad = 45°, 100 grad = 90°, 200 grad = 180°, 400 grad = 360°. Convert grad to degrees by multiplying by 0.9; to radians by multiplying by π/200.
Quick Facts
- 1 Degree equals 1.11111 Gradians
- 1 Gradian equals 0.9 Degrees
- Degree is a unit of angle
- Gradian is a unit of angle
- This conversion is commonly used in surveying, navigation, trigonometry, and mechanical design
Common Degree to Gradian Conversions
| Degrees (°) | Gradians (grad) |
|---|---|
| 0.01 | 0.0111111 |
| 0.1 | 0.111111 |
| 0.25 | 0.277778 |
| 0.5 | 0.555556 |
| 1 | 1.11111 |
| 2 | 2.22222 |
| 3 | 3.33333 |
| 5 | 5.55556 |
| 10 | 11.1111 |
| 15 | 16.6667 |
| 20 | 22.2222 |
| 25 | 27.7778 |
| 50 | 55.5556 |
| 75 | 83.3333 |
| 100 | 111.111 |
| 250 | 277.778 |
| 500 | 555.556 |
| 1000 | 1111.11 |
| 5000 | 5555.56 |
| 10000 | 11111.1 |
Understanding Degrees
The Degree (symbol: °) is a unit of angle. A unit of plane angle equal to exactly 1/360 of a full rotation (= π/180 radians), inherited from ancient Babylonian astronomy's sexagesimal (base-60) number system circa 2000 BCE — the 360-degree convention reflects the ~360-day Babylonian solar year. Degrees are the universal everyday angle unit in non-scientific contexts: compass bearings and ship/aircraft heading per ICAO and IMO conventions (0° = magnetic north, 90° = east), latitude / longitude geographic coordinates per WGS84 (the GPS datum), machine-tool protractors and CNC G-code, GIS data (Esri ArcGIS, QGIS), CAD-software 2D-sketch dimensions (Autodesk Inventor, SolidWorks, Fusion 360, CATIA), and architectural drawings. Reference values: a right angle is exactly 90°, a straight line 180°, a full turn 360°, an equilateral triangle has 60° interior angles, a regular pentagon 108°, a regular hexagon 120°. Trigonometry education worldwide introduces sine and cosine in degrees before transitioning students to radians for calculus. Convert degrees to radians by multiplying by π/180 ≈ 0.01745.
Degrees are commonly used in surveying, navigation, trigonometry, and mechanical design.
Understanding Gradians
The Gradian (symbol: grad) is a unit of angle. A decimal-friendly unit of plane angle equal to exactly 1/400 of a full rotation (so 100 grad = 90°, exactly one right angle). Also called the 'gon' or 'grade'. Developed during the French Revolution (specifically the 1791 French Academy of Sciences proposal that also gave us the metric system) to decimalize angular measurement alongside the metric system's decimalization of length, mass, and time. Gradians survive today primarily in European surveying and land-cadastre mapping (especially in France, where French cadastral surveys per IGN standards still use gradians; and in parts of Germany and Switzerland), some military artillery applications (the Soviet/Russian military uses the related 'mil' = 1/6,400 of a circle for fire-direction calculations), and certain mining-survey traditions. Most pocket scientific calculators include a 'grad' mode alongside 'deg' and 'rad' for this reason. Reference values: 50 grad = 45°, 100 grad = 90°, 200 grad = 180°, 400 grad = 360°. Convert grad to degrees by multiplying by 0.9; to radians by multiplying by π/200.
Gradians are commonly used in surveying, navigation, trigonometry, and mechanical design.
Why Convert Degrees to Gradians?
Converting between Degrees and Gradians is a frequent requirement for engineers, scientists, and students working with angle values. Different industries and regions favour different unit systems, so having a dependable conversion tool saves time and prevents errors in technical calculations. Whether you are verifying a specification sheet, cross-checking simulation results, or preparing a report for an international audience, accurate angle conversion is essential.
Frequently Asked Questions
How do I convert Degrees to Gradians?
A unit of plane angle equal to exactly 1/360 of a full rotation (= π/180 radians), inherited from ancient Babylonian astronomy's sexagesimal (base-60) number system circa 2000 BCE — the 360-degree convention reflects the... To convert Degrees to Gradians, multiply by 1.11111. For example, 25 ° equals 27.7778 grad.
How many Gradians are in 1 Degree?
There are 1.11111 Gradians in 1 Degree.
How many Degrees are in 1 Gradian?
There are 0.9 Degrees in 1 Gradian.
What is the formula for Degree to Gradian conversion?
The formula is: multiply by 1.11111. This means 1 ° = 1.11111 grad.
Is a Degree bigger than a Gradian?
No. One Degree is smaller than one Gradian because 1 ° equals 1.11111 grad, which is greater than 1.
When do you need to convert between Degrees and Gradians?
A decimal-friendly unit of plane angle equal to exactly 1/400 of a full rotation (so 100 grad = 90°, exactly one right angle). Degree and Gradian are both angle units, so conversion comes up whenever one source of information uses one unit and another uses the other — a classic cross-reference challenge in engineering, trade, travel, and everyday life.