Degrees to Radians Converter
Convert degrees to radians for trigonometry and mathematics.
Result
1 ° = 0.0174533 rad
Results are provided for general informational purposes only. Always verify important calculations independently. Learn more
About These Units
DEG
A degree is 1/360th of a full circle rotation.
Common Uses: Navigation, geometry, protractors, compass bearings, angles
RAD
A radian is the angle where the arc length equals the radius.
Common Uses: Mathematics, physics, trigonometry, calculus, engineering
Conversion Formula
radians = degrees × π/180
Worked Example:
To convert DEG to RAD:
180° × π/180 = π radians
Other Formulas:
Common DEG to RAD Conversions
| DEG | RAD | DEG | RAD |
|---|---|---|---|
| 1 deg | 0.0175 rad | 50 deg | 0.8727 rad |
| 2 deg | 0.0349 rad | 75 deg | 1.309 rad |
| 5 deg | 0.0873 rad | 100 deg | 1.7453 rad |
| 10 deg | 0.1745 rad | 250 deg | 4.3633 rad |
| 25 deg | 0.4363 rad | 500 deg | 8.7267 rad |
Frequently Asked Questions
When should I use radians vs degrees?
Degrees are intuitive for everyday use, navigation, and engineering drawings (90° = right angle, 180° = straight line). Radians are essential for calculus, physics, and programming because they make trigonometric derivatives and integrals simpler. Scientific calculators and programming languages typically default to radians for trigonometric functions.
Why are there 360 degrees in a circle?
The 360-degree system originated with ancient Babylonian mathematics and astronomy. The number 360 has many divisors (24 factors), making it convenient for dividing circles into halves, thirds, quarters, fifths, sixths, eighths, and more. This divisibility made angle calculations easier before modern calculators, and the system persists today for its intuitive nature and widespread familiarity.
What exactly is a radian?
A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. Since a circle's circumference is 2πr, a full circle contains 2π radians. This makes π radians equal to 180 degrees. Radians are "natural" units because they eliminate conversion constants in mathematical formulas, particularly in calculus and physics equations.
How do I convert degrees to radians mentally?
Remember that 180° = π radians, so divide degrees by 180 and multiply by π. For common angles: 90° = π/2, 60° = π/3, 45° = π/4, 30° = π/6. For practical calculations, multiply degrees by 0.01745 to get radians (since π/180 ≈ 0.01745). For example, 45° × 0.01745 ≈ 0.785 radians.
What are gradians and when are they used?
Gradians (also called gon or grades) divide a circle into 400 equal parts, with 100 gradians in a right angle. This makes calculations in surveying slightly easier because right angles become whole numbers (100 grad). Gradians are used in some European surveying applications, but degrees and radians dominate most fields. 360° = 400 gradians = 2π radians.