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 (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular arc equal in length to the radius. One full revolution is exactly 2π radians ≈ 6.2832 rad; one degree = π/180 radians ≈ 0.01745 rad. Radians are the native unit for calculus — derivative identities (d/dx sin x = cos x; d/dx cos x = −sin x) only hold when x is in radians, not degrees, because the small-angle limit lim x→0 sin(x)/x = 1 only equals 1 in radians — and for every physics and engineering formula involving rotational dynamics, wave-phase calculations (Fourier series, signal processing), angular frequency ω = 2πf in oscillation analysis, complex-number arguments (Argand-plane angle = radians by convention), and gyroscope output. Reference values: 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 360° = 2π rad. The radian is technically a dimensionless ratio (arc length / radius), but is treated as a unit by SI convention.
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 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 (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular arc equal in length to the radius. One full revolution is exactly 2π radians ≈ 6.2832 rad; one degree = π/180 radians ≈ 0.01745 rad. Radians are the native unit for calculus — derivative identities (d/dx sin x = cos x; d/dx cos x = −sin x) only hold when x is in radians, not degrees, because the small-angle limit lim x→0 sin(x)/x = 1 only equals 1 in radians — and for every physics and engineering formula involving rotational dynamics, wave-phase calculations (Fourier series, signal processing), angular frequency ω = 2πf in oscillation analysis, complex-number arguments (Argand-plane angle = radians by convention), and gyroscope output. Reference values: 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 360° = 2π rad. The radian is technically a dimensionless ratio (arc length / radius), but is treated as a unit by SI convention.
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 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 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 (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular 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 plane angle equal to exactly 1/400 of a full rotation (so 100 grad = 90°, exactly one 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.