Degrees to Radians Converter
Convert an angle between degrees and radians — and see the exact answer as a multiple of π, not just a decimal.
Calculator
- Degrees → radians
- Radians → degrees
- Exact π multiple
- Reverse-conversion check
Result & calculation receipt
- Method
- Multiply degrees by π/180
- Formula
radians = degrees × π / 180- Substitution
- 180° × π/180 = π = 3.1415926536 rad
- Steps
- 180 × π / 180 = π
- = 3.1415926536 radians
- Verification
- 3.14159265 × 180/π = 180°. ✓
- Exact result
- π
- Decimal result
- 3.1415926536
- Engine
- math-solvers v1.4.0
How this calculator works
A full turn is 360° or 2π radians, so the two units differ by a factor of π/180. To go from degrees to radians the calculator multiplies by π/180; to go the other way it multiplies by 180/π. It reports the exact multiple of π where possible and confirms the answer by converting it back.
Worked example
180° × π/180 = π radians ≈ 3.1416. Converting back, π × 180/π = 180°. A common angle like π/6 radians converts to 30°, and 90° converts to π/2 ≈ 1.5708 radians. The exact-π form makes the standard angles instantly recognizable.
Key insight
Radians are the "natural" unit for angles because arc length equals radius times angle, which makes the calculus of trigonometric functions clean. Degrees are a human convention (360 divides nicely); radians are what the math prefers.
Frequently asked questions
How do I convert degrees to radians?
Multiply the degree measure by π/180. So 180° = 180 × π/180 = π radians, and 90° = π/2 radians.
How do I convert radians to degrees?
Multiply the radian measure by 180/π. So π/6 radians × 180/π = 30°.
Why are there 2π radians in a full circle?
A radian is the angle that subtends an arc equal to the radius, and a full circle’s circumference is 2π radii, so it spans 2π radians — the same turn as 360°.
Why show the answer as a multiple of π?
Standard angles are cleanest in that form: π/6, π/4, π/3, π/2. The exact multiple avoids the rounding you get from a decimal like 0.5236.
Which unit should I use for trig functions?
It depends on the mode: scientific calculators offer both DEG and RAD. This converter lets you switch an angle into whichever the rest of your work uses.
Methodology & verification
Angles convert with radians = degrees × π/180 and degrees = radians × 180/π. The exact result is expressed as a multiple of π (degrees → radians) or in degrees, alongside the decimal. Non-numeric inputs return a structured error. The receipt performs the reverse conversion and confirms it recovers the original angle.
Engine: math-solvers v1.4.0 · Last reviewed: · Every result is computed client-side and never sent to a server. See the verification methodology and the scientific calculator validation.