Convert Gradian (grad) to Radian (rad) instantly. Enter any value and get the result immediately.
grad → rad Converter
| Gradian (grad) | Radian (rad) |
|---|---|
| 0.1 grad | 0.0015708 rad |
| 0.5 grad | 0.00785398 rad |
| 1 grad | 0.01570796 rad |
| 2 grad | 0.03141592 rad |
| 5 grad | 0.07853979 rad |
| 10 grad | 0.15707958 rad |
| 20 grad | 0.31415915 rad |
| 50 grad | 0.78539788 rad |
| 100 grad | 1.57079577 rad |
| 200 grad | 3.14159153 rad |
| 500 grad | 7.85397883 rad |
| 1000 grad | 15.70795765 rad |
| 5000 grad | 78.53978826 rad |
| 10000 grad | 157.07957651 rad |
Converting gradians to radians connects two very different but equally systematic approaches to angular measurement — the decimal metric gradian (used in European professional surveying) and the mathematically natural radian (the SI standard unit used in calculus, physics, and all scientific computing). Both are rigorously defined units, but they serve different communities: surveyors work in gradians for the convenience of 100-grad right angles, while mathematicians and engineers use radians because they simplify trigonometric derivatives and rotational physics equations. Since a full circle contains 400 gradians and 2π radians, the exact conversion factor is π/200. To convert, multiply the gradian value by π/200 (approximately 0.015708). Use the converter above for instant results, or follow the formula and examples below.
Step-by-step example — Convert 100 grad to radians:
Step-by-step example — Convert 200 grad to radians:
Step-by-step example — Convert 50 grad to radians:
Gradian (grad), also called a gon or grade, is a metric unit of angular measurement that divides a full circle into exactly 400 equal parts. Introduced during the French Revolution as part of the broader decimalization of measurement, the gradian was designed so that a right angle equals exactly 100 grad — a round, base-10 value that streamlines calculations involving perpendicular angles in a decimal arithmetic framework. The gradian is the standard angular unit on professional surveying instruments — theodolites, total stations, and digital levels — used across continental Europe, particularly in France, Germany, the Netherlands, Switzerland, and Scandinavia. On scientific calculators, the GRAD or GON mode activates gradian-based trigonometric computation. One gradian equals exactly π/200 radians or 0.9 degrees.
Radian (rad) is the SI standard unit of angular measurement and the natural unit of angle in mathematics and physics. One radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. Since a circle's circumference is 2π times its radius, a full rotation contains exactly 2π radians. This geometric definition makes radians uniquely powerful in calculus: the derivatives of sin(x) and cos(x) are cos(x) and −sin(x) only when x is measured in radians — no correction factors required. Radians are the default angular unit in all major programming languages and scientific libraries, including Python, MATLAB, C, JavaScript, and R. Every trigonometric function call in code expects radian input unless explicitly converted. One radian equals approximately 57.2958° or 63.6620 gradians.
| Gradians (grad) | Radians (exact) | Radians (decimal) | Degrees equivalent |
|---|---|---|---|
| 0 grad | 0 | 0 rad | 0° |
| 25 grad | π/8 | 0.3927 rad | 22.5° |
| 50 grad | π/4 | 0.7854 rad | 45° |
| 66.67 grad | π/3 | 1.0472 rad | 60° |
| 100 grad | π/2 | 1.5708 rad | 90° — right angle |
| 133.33 grad | 2π/3 | 2.0944 rad | 120° |
| 150 grad | 3π/4 | 2.3562 rad | 135° |
| 200 grad | π | 3.1416 rad | 180° — straight angle |
| 300 grad | 3π/2 | 4.7124 rad | 270° |
| 400 grad | 2π | 6.2832 rad | 360° — full circle |
The exact formula is: rad = grad × (π ÷ 200). This comes directly from the definition: a full circle = 400 grad = 2π rad, so 1 grad = 2π/400 = π/200 rad. The decimal approximation is rad = grad × 0.01570796.
One gradian equals exactly π/200 radians (approximately 0.015708 rad). Since π/200 ≈ 0.01571, each gradian is a very small fraction of a radian — reflecting that gradians (400 per circle) are a finer division than radians (≈6.283 per circle).
100 grad = π/2 radians (approximately 1.5708 rad). This is the right angle benchmark — 100 gradians, 90 degrees, and π/2 radians all represent the same quarter-circle rotation, expressed in three different angular unit systems.
400 grad = 2π radians (approximately 6.2832 rad). A full circle is 400 gradians and 2π radians — the two defining values of each system. This relationship is the source of the π/200 conversion factor.
200 grad = π radians (approximately 3.14159 rad). A straight angle (half circle) is exactly 200 gradians and exactly π radians — one of the cleanest cross-system benchmarks, useful for quick mental verification of conversions.
The factor π/180 converts degrees to radians (since a full circle = 360° = 2π rad, giving 1° = π/180 rad). The factor π/200 converts gradians to radians (since a full circle = 400 grad = 2π rad, giving 1 grad = 2π/400 = π/200 rad). The difference between 180 and 200 reflects the different circle divisions: 360 degrees vs 400 gradians per full rotation.
On a scientific calculator, set the mode to RAD, then multiply your gradian value by π/200. Alternatively, first convert gradians to degrees by multiplying by 0.9, then convert degrees to radians by multiplying by π/180. Both routes give the same result. Some advanced calculators have a direct unit conversion function (often under CONV or ANGLE menus) that handles grad → rad automatically.
No major programming language has built-in gradian support — all standard trigonometric functions in Python, JavaScript, C, Java, MATLAB, and R use radians exclusively. To work with gradian input in code, you must manually convert: rad = grad * Math.PI / 200 (JavaScript) or rad = grad * math.pi / 200 (Python) before passing the value to sin(), cos(), or tan(). Some surveying-specific libraries and GIS toolkits include gradian conversion utilities, but the underlying math always operates in radians.