Degrees to Radians Converter – Convert Angles Online
Convert any angle from degrees to radians or radians to degrees with our free online converter. Instant and accurate angle conversions using π-based formulas.
0°
=
0
30°
=
π/6
45°
=
π/4
60°
=
π/3
90°
=
π/2
180°
=
π
270°
=
3π/2
360°
=
2π
Degrees and radians are two ways to measure angles. Degrees split a circle into 360 equal parts. Radians use the radius of a circle – one radian is the angle you get when you wrap the radius around the circumference.
A full circle is 360° or 2π radians. That means 180° = π radians. This relationship gives us the conversion formulas: multiply by π/180 to go from degrees to radians, multiply by 180/π to go from radians to degrees.
Radians are the natural unit for math. Calculus formulas work cleanly with radians. Degrees are more intuitive for everyday use – we're used to thinking in 90° angles and 360° circles.
Degrees to Radians
Examples:
Radians to Degrees
Examples:
Calculus Works Better
The derivative of sin(x) is cos(x) only when x is in radians. With degrees, you'd need an extra factor of π/180. Same for integrals. Radians make the math cleaner.
Arc Length Formula
Arc length s = rθ is simple with radians. With degrees, it becomes s = rθ × π/180.
Degrees: s = rθ × π/180
Natural Unit
Radians come from the geometry of circles, not an arbitrary choice of 360. One radian is about 57.3° – that's not random, it's the angle where arc length equals radius.
How do I convert degrees to radians without a calculator?
Multiply by π/180. For common angles, memorize the pattern: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2. The denominator decreases as the angle increases (6, 4, 3, 2).
What is 1 radian in degrees?
1 radian = 180/π ≈ 57.296°. It's not a nice round number because radians aren't based on dividing a circle into convenient chunks – they're based on the radius.
Should I leave my answer in terms of π?
In math classes, yes – exact answers with π are preferred. In physics or engineering, decimal approximations are often more useful. This calculator shows both.
Why is a full circle 2π radians?
Circumference = 2πr. One radian is the angle where arc length = r. So a full circle (arc length = circumference) is 2πr/r = 2π radians.
Can I convert negative angles?
Absolutely. Negative angles just mean rotation in the opposite direction. -90° = -π/2 rad. The conversion formulas work the same way.
What's the difference between π and 180°?
They're the same angle in different units. π radians = 180°. It's like asking the difference between 1 kilometer and 1000 meters – same distance, different units.
Other Free Tools
Trig Function Calculator – Calculate Sin Cos Tan Online
Calculate any trigonometric function value including sin, cos, tan, csc, sec, and cot for any angle in degrees or radians with our free online trig calculator.
Inverse Trig Calculator – Find arcsin arccos arctan Online
Calculate inverse trigonometric functions including arcsin, arccos, and arctan with our free online inverse trig calculator. Get angle results in both degrees and radians.
Trig Identity Verifier – Verify Trigonometric Identities Online
Verify any trigonometric identity online with our free trig identity verifier. Simplifies both sides of an equation to check if the identity holds using fundamental trig rules.
Unit Circle Reference Tool – Interactive Unit Circle Chart
Explore the complete unit circle with our free interactive unit circle reference tool. View all key angles in degrees and radians with their exact trig values and coordinates.
Triangle Angle Calculator – Find Missing Angles in a Triangle
Find any missing angle in a triangle with our free online angle calculator. Enter known angles or sides and instantly solve for the remaining angles using trigonometry rules.
Polygon Interior Angle Sum Calculator – Find Angle Sum of Polygon
Calculate the sum of interior angles of any polygon with our free online calculator. Enter the number of sides and instantly find the total interior angle sum and each angle for regular polygons.
Free Online Scientific Calculator – Advanced Math Functions
Perform complex scientific calculations online with our free scientific calculator. Supports trigonometry, logarithms, exponents, roots, and more – ideal for students and professionals.
Angle of Elevation & Depression Calculator – Solve Word Problems
Calculate the angle of elevation or depression with our free online solver. Enter height and distance to find the angle, or the angle to find missing dimensions – perfect for trig word problems.