How Do You Convert Degrees to Radians?
Convert degrees, radians, gradians, arcminutes, arcseconds, and turns with our free angle converter. Used in mathematics, engineering, navigation, and astronomy.
How it works
Degrees are the most familiar unit: a full circle is 360°. Radians are the SI unit for angles — one full circle is 2π radians (≈ 6.2832). To convert degrees to radians, multiply by π/180. Gradians divide the circle into 400 parts and are common in surveying.
Quick reference
Frequently Asked Questions
How do you convert degrees to radians?
Multiply degrees by π/180. For example, 90° × π/180 = 1.5708 radians.
How do you convert radians to degrees?
Multiply radians by 180/π. For example, 1 radian × 180/π ≈ 57.296°.
What is a gradian?
A gradian (grad) divides a full circle into 400 equal parts. 90° equals 100 grad. Gradians are used in surveying and some European engineering fields.
What is an arcminute?
An arcminute is 1/60 of a degree. There are 60 arcminutes in one degree and 3,600 arcseconds in one degree. Arcminutes and arcseconds are used in astronomy and navigation.
How many degrees is one full turn?
One full turn (revolution) equals 360 degrees, 2π radians, or 400 gradians.
How many degrees is a right angle?
A right angle is exactly 90 degrees. It is the angle formed at the corner of a square or rectangle. In radians, 90° = π/2 ≈ 1.5708 rad. Right angles are fundamental in construction, carpentry, and engineering — a "square" corner between two walls or a floor and wall is always 90°.
What is a 45-degree angle used for in everyday life?
A 45° angle is half a right angle and appears frequently in construction (roof pitches, mitre cuts for picture frames and door frames), sports (the optimal launch angle for maximum projectile range is 45°), and road design. In radians, 45° = π/4 ≈ 0.7854 rad.
How steep is a 10-degree slope?
A 10° slope rises about 17.6 cm for every 1 meter of horizontal distance (tan 10° ≈ 0.176). Roads rarely exceed 10°; mountain roads reach 12–15°. A typical staircase is about 35–40°. Wheelchair ramps are usually limited to 4.8° (1:12 ratio). Ski runs range from 18° (beginner) to 45°+ (expert).
What is the difference between degrees and radians?
Degrees divide a circle into 360 equal parts; radians measure angles by the arc length on a unit circle. A full circle = 360° = 2π radians ≈ 6.2832 rad. To convert: multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees. Radians are used in mathematics and physics; degrees in everyday life and navigation.
What angle is a typical roof pitch?
Roof pitch is often expressed as rise:run (e.g., 4:12 means 4 inches rise per 12 inches run). Common pitches in degrees: low slope 10–20°, standard residential 25–35°, steep 40–50°. A 4:12 pitch ≈ 18.4°, a 6:12 pitch ≈ 26.6°, a 12:12 pitch = 45°. Steeper roofs shed snow and rain better but cost more to build.