Convert Radians to Gradians
Instantly convert Radians (rad) to Gradians (grad) with our free online calculator.
Formula: rad to grad — multiply by 63.662
Reference Table
| Radians (rad) | Gradians (grad) |
|---|---|
| 1 | 63.662 |
| 5 | 318.31 |
| 10 | 636.62 |
| 25 | 1591.55 |
| 50 | 3183.1 |
| 100 | 6366.2 |
How to Convert Radians to Gradians
Formula
To convert Radians (rad) to Gradians (grad): multiply by 63.662
Step-by-Step
- Start with your value in Radians (rad).
- Multiply by 63.662 to perform the conversion.
- The result is your value expressed in Gradians (grad).
Conversion Factor
1 rad = 63.662 grad
Reverse Factor
1 grad = 0.015708 rad
Worked Example
Convert 25 Radians to Gradians: 25 rad = 1591.55 grad
About Radian (rad)
The SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full revolution is 2π radians ≈ 6.283 rad. Radians are the native unit for calculus — derivatives of trigonometric functions (d/dx sin x = cos x) only hold when x is in radians — and for every physics and engineering formula involving rotational motion, wave phase, or angular frequency.
About Gradian (grad)
A decimal-friendly unit of angle equal to 1/400 of a full rotation (so 100 grad = 90°, a right angle). Also called the "gon". Developed during the French Revolution to decimalize angular measurement, gradians survive today primarily in European surveying and land-cadastre mapping, especially in France and Germany. Most scientific calculators include a "grad" mode alongside degrees and radians for this reason.
Quick Facts
- 1 Radian equals 63.662 Gradians
- 1 Gradian equals 0.015708 Radians
- Radian is a unit of angle
- Gradian is a unit of angle
- This conversion is commonly used in surveying, navigation, trigonometry, and mechanical design
Common Radian to Gradian Conversions
| Radians (rad) | Gradians (grad) |
|---|---|
| 0.01 | 0.63662 |
| 0.1 | 6.3662 |
| 0.25 | 15.9155 |
| 0.5 | 31.831 |
| 1 | 63.662 |
| 2 | 127.324 |
| 3 | 190.986 |
| 5 | 318.31 |
| 10 | 636.62 |
| 15 | 954.93 |
| 20 | 1273.24 |
| 25 | 1591.55 |
| 50 | 3183.1 |
| 75 | 4774.65 |
| 100 | 6366.2 |
| 250 | 15915.5 |
| 500 | 31831 |
| 1000 | 63662 |
| 5000 | 318310 |
| 10000 | 636620 |
Understanding Radians
The Radian (symbol: rad) is a unit of angle. The SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full revolution is 2π radians ≈ 6.283 rad. Radians are the native unit for calculus — derivatives of trigonometric functions (d/dx sin x = cos x) only hold when x is in radians — and for every physics and engineering formula involving rotational motion, wave phase, or angular frequency.
Radians 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 angle equal to 1/400 of a full rotation (so 100 grad = 90°, a right angle). Also called the "gon". Developed during the French Revolution to decimalize angular measurement, gradians survive today primarily in European surveying and land-cadastre mapping, especially in France and Germany. Most scientific calculators include a "grad" mode alongside degrees and radians for this reason.
Gradians are commonly used in surveying, navigation, trigonometry, and mechanical design.
Why Convert Radians to Gradians?
Converting between Radians 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 Radians to Gradians?
The SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. To convert Radians to Gradians, multiply by 63.662. For example, 25 rad equals 1591.55 grad.
How many Gradians are in 1 Radian?
There are 63.662 Gradians in 1 Radian.
How many Radians are in 1 Gradian?
There are 0.015708 Radians in 1 Gradian.
What is the formula for Radian to Gradian conversion?
The formula is: multiply by 63.662. This means 1 rad = 63.662 grad.
Is a Radian bigger than a Gradian?
No. One Radian is smaller than one Gradian because 1 rad equals 63.662 grad, which is greater than 1.
When do you need to convert between Radians and Gradians?
A decimal-friendly unit of angle equal to 1/400 of a full rotation (so 100 grad = 90°, a right angle). Radian 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.