Degrees to Radians conversion
Convert degrees to radians. Exact relation: π rad = 180°. Free online tool — no sign-up. Clear formulas and worked examples. Runs locally in your browser.
Enter values to convert.
Formulas
Core equations used by this converter.
How to use
Choose ° → rad or rad → °
Use the tabs to switch direction. Forward mode needs °; reverse uses the opposite unit.
Enter the value
Type a non-negative value in the active unit field.
Convert and read the result
Use Convert or let the result update automatically.
Example conversions
Common values with formula and result.
30°
30°
90°
90°
180°
180°
45°
45°
Degrees to Radians conversion specification
Version 1.1.0 · Engine tested
- Engine tested 4 published cases
- Named expert review Not performed
- Calculation version 1.1.0
- Definition
- **Degree (°)** — full circle = 360°. Everyday angle unit. **Radian (rad)** — arc length equal to the radius; full circle = \(2\pi\) rad. Default unit in most calculus and programming trig functions.
- What it calculates
- Value between ° and rad. Switch direction with the converter tabs.
- Inputs
- ° (°) or reverse unit (rad)
- Outputs
- Converted value in rad or °
- Formula
rad = ° × 0.017453293 · 1 ° = 0.017453293 rad- Degrees to radians conversion table
Degrees (°) Radians (exact) Radians (approx.) 0° 0 0 30° π/6 0.523599 45° π/4 0.785398 60° π/3 1.047198 90° π/2 1.570796 120° 2π/3 2.094395 135° 3π/4 2.356194 150° 5π/6 2.617994 180° π 3.141593 270° 3π/2 4.712389 360° 2π 6.283185 - Assumptions
- Conversion runs locally in the browser; values are not uploaded.
- Uses the standard factor/definition for these units.
- Units
- ° → rad
- rad → °
- Boundary conditions
- Empty or non-numeric input yields no valid result.
- Non-negative values are expected for physical quantities.
- Example
- 90 ° → 1.5708 rad
- Validation cases
- 90 ° → 1.5707963 rad
- 900 ° → 15.707963 rad
- 4500 ° → 78.539816 rad
- 9000 ° → 157.07963 rad
- Sources
- SI / international unit definitions where applicable
- CalculatorX conversion factors (local runtime)
- Calculation version
- 1.1.0
Background
Interpretation and common distinctions.
Use the converter tabs to switch direction when available. Results for Degrees to Radians conversion update locally in your browser.
Related tools
Frequently asked questions
Key distinctions behind the conversion.
How do you convert using Degrees to Radians conversion?
Use radians = degrees × π / 180. Example: 30° → π/6 ≈ 0.5235987756 rad.
Can I switch direction?
Use the converter tabs when available, or open the related reverse tool from Related.
Does this run online or locally?
Calculation runs locally in your browser. Values are not uploaded.
How precise are the results?
Results follow the formulas on this page. Round to the precision your use case needs.