Convert Gradians to Degrees
Instantly convert Gradians (grad) to Degrees (°) with our free online calculator.
Formula: grad to ° — multiply by 0.9
Reference Table
| Gradians (grad) | Degrees (°) |
|---|---|
| 1 | 0.9 |
| 5 | 4.5 |
| 10 | 9 |
| 25 | 22.5 |
| 50 | 45 |
| 100 | 90 |
How to Convert Gradians to Degrees
Formula
To convert Gradians (grad) to Degrees (°): multiply by 0.9
Step-by-Step
- Start with your value in Gradians (grad).
- Multiply by 0.9 to perform the conversion.
- The result is your value expressed in Degrees (°).
Conversion Factor
1 grad = 0.9 °
Reverse Factor
1 ° = 1.11111 grad
Worked Example
Convert 25 Gradians to Degrees: 25 grad = 22.5 °
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.
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.
Quick Facts
- 1 Gradian equals 0.9 Degrees
- 1 Degree equals 1.11111 Gradians
- Gradian is a unit of angle
- Degree is a unit of angle
- This conversion is commonly used in surveying, navigation, trigonometry, and mechanical design
Common Gradian to Degree Conversions
| Gradians (grad) | Degrees (°) |
|---|---|
| 0.01 | 0.009 |
| 0.1 | 0.09 |
| 0.25 | 0.225 |
| 0.5 | 0.45 |
| 1 | 0.9 |
| 2 | 1.8 |
| 3 | 2.7 |
| 5 | 4.5 |
| 10 | 9 |
| 15 | 13.5 |
| 20 | 18 |
| 25 | 22.5 |
| 50 | 45 |
| 75 | 67.5 |
| 100 | 90 |
| 250 | 225 |
| 500 | 450 |
| 1000 | 900 |
| 5000 | 4500 |
| 10000 | 9000 |
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.
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.
Why Convert Gradians to Degrees?
Converting between Gradians and Degrees 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 Gradians to Degrees?
A decimal-friendly unit of plane angle equal to exactly 1/400 of a full rotation (so 100 grad = 90°, exactly one right angle). To convert Gradians to Degrees, multiply by 0.9. For example, 25 grad equals 22.5 °.
How many Degrees are in 1 Gradian?
There are 0.9 Degrees in 1 Gradian.
How many Gradians are in 1 Degree?
There are 1.11111 Gradians in 1 Degree.
What is the formula for Gradian to Degree conversion?
The formula is: multiply by 0.9. This means 1 grad = 0.9 °.
Is a Gradian bigger than a Degree?
Yes. One Gradian is larger than one Degree because 1 grad equals 0.9 °, which is less than 1.
When do you need to convert between Gradians and Degrees?
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... Gradian and Degree 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.