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Convert angles from radians to degrees instantly. Essential for calculus, physics, and mathematical applications.
degrees = radians × (180 / π)
Example: π radians = π × (180 / π) = 180°
Note: 1 radian ≈ 57.2958 degrees
| Radians (rad) | Exact Value | Degrees (°) |
|---|---|---|
| 0.000000 | 0 | 0° |
| 0.523599 | π/6 | 30° |
| 0.785398 | π/4 | 45° |
| 1.047198 | π/3 | 60° |
| 1.570796 | π/2 | 90° |
| 2.094395 | 2π/3 | 120° |
| 2.356194 | 3π/4 | 135° |
| 2.617994 | 5π/6 | 150° |
| 3.141593 | π | 180° |
| 4.712389 | 3π/2 | 270° |
| 6.283185 | 2π | 360° |
Radians are the standard unit of angular measurement in mathematics and physics. One radian is defined as the angle subtended at the center of a circle by an arc whose length equals the radius. A full circle contains 2π radians (approximately 6.28318 radians). The radian is a dimensionless unit, making it particularly useful in mathematical formulas.
While radians are preferred in mathematics, degrees are more intuitive for everyday use. Degrees divide a circle into 360 equal parts, making it easier to visualize angles in navigation, construction, astronomy, and general communication. Converting from radians to degrees helps bridge the gap between mathematical calculations and practical applications.
The conversion factor 180/π (approximately 57.2958) comes from the relationship that π radians equals 180 degrees. This means one radian is about 57.3 degrees. Understanding this relationship is crucial for working with trigonometric functions, calculus, and any application involving angular measurements.
Multiply the radian value by 180/π (approximately 57.2958). For example, π/2 radians = (π/2) × (180/π) = 90°. The π terms cancel out, leaving you with 90 degrees.
One radian equals approximately 57.2958 degrees. This comes from the formula: 1 rad = 180/π degrees. This conversion factor is essential for translating between the two measurement systems.
A circle's circumference is 2πr (where r is the radius). Since a radian is defined by an arc length equal to the radius, a complete circle contains circumference/radius = 2πr/r = 2π radians. This elegant relationship makes radians the natural unit for circular measurements.
Use degrees for navigation, surveying, construction, weather reporting, and whenever communicating angles to non-technical audiences. Use radians for calculus, physics equations, programming (most math libraries), and any situation where mathematical simplicity matters.