Convert Gradians to Radians
Instantly convert Gradians (grad) to Radians (rad) with our free online calculator.
Formula: grad to rad — multiply by 0.015708
Reference Table
| Gradians (grad) | Radians (rad) |
|---|---|
| 1 | 0.015708 |
| 5 | 0.0785398 |
| 10 | 0.15708 |
| 25 | 0.392699 |
| 50 | 0.785398 |
| 100 | 1.5708 |
How to Convert Gradians to Radians
Formula
To convert Gradians (grad) to Radians (rad): multiply by 0.015708
Step-by-Step
- Start with your value in Gradians (grad).
- Multiply by 0.015708 to perform the conversion.
- The result is your value expressed in Radians (rad).
Conversion Factor
1 grad = 0.015708 rad
Reverse Factor
1 rad = 63.662 grad
Worked Example
Convert 25 Gradians to Radians: 25 grad = 0.392699 rad
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 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.
Quick Facts
- 1 Gradian equals 0.015708 Radians
- 1 Radian equals 63.662 Gradians
- Gradian is a unit of angle
- Radian is a unit of angle
- This conversion is commonly used in surveying, navigation, trigonometry, and mechanical design
Common Gradian to Radian Conversions
| Gradians (grad) | Radians (rad) |
|---|---|
| 0.01 | 0.00015708 |
| 0.1 | 0.0015708 |
| 0.25 | 0.00392699 |
| 0.5 | 0.00785398 |
| 1 | 0.015708 |
| 2 | 0.0314159 |
| 3 | 0.0471239 |
| 5 | 0.0785398 |
| 10 | 0.15708 |
| 15 | 0.235619 |
| 20 | 0.314159 |
| 25 | 0.392699 |
| 50 | 0.785398 |
| 75 | 1.1781 |
| 100 | 1.5708 |
| 250 | 3.92699 |
| 500 | 7.85398 |
| 1000 | 15.708 |
| 5000 | 78.5398 |
| 10000 | 157.08 |
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 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.
Why Convert Gradians to Radians?
Converting between Gradians and Radians 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 Radians?
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 Radians, multiply by 0.015708. For example, 25 grad equals 0.392699 rad.
How many Radians are in 1 Gradian?
There are 0.015708 Radians in 1 Gradian.
How many Gradians are in 1 Radian?
There are 63.662 Gradians in 1 Radian.
What is the formula for Gradian to Radian conversion?
The formula is: multiply by 0.015708. This means 1 grad = 0.015708 rad.
Is a Gradian bigger than a Radian?
Yes. One Gradian is larger than one Radian because 1 grad equals 0.015708 rad, which is less than 1.
When do you need to convert between Gradians and Radians?
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. Gradian and Radian 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.