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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.

Instant result
Result

Enter values to convert.

Inputs
Mode
Formula

Formulas

Core equations used by this converter.

Formularadians = degrees × π / 180
iFollow the formulas shown. Calculation runs locally in your browser.

How to use

1

Choose ° → rad or rad → °

Use the tabs to switch direction. Forward mode needs °; reverse uses the opposite unit.

2

Enter the value

Type a non-negative value in the active unit field.

3

Convert and read the result

Use Convert or let the result update automatically.

Example conversions

Common values with formula and result.

ϟ

30°

30°

30 × π / 180 = π/6 ≈ 0.5235987756 rad
π/6 ≈ 0.5235987756 rad
ϟ

90°

90°

90 × π / 180 = π/2 ≈ 1.5707963268 rad
π/2 ≈ 1.5707963268 rad
ϟ

180°

180°

180 × π / 180 = π ≈ 3.1415926536 rad
π ≈ 3.1415926536 rad
ϟ

45°

45°

45 × π / 180 = π/4 ≈ 0.7853981634 rad
π/4 ≈ 0.7853981634 rad

Degrees to Radians conversion specification

Version 1.1.0 · Engine tested

Calculation status
  • Engine tested 4 published cases
  • Named expert review Not performed
  • Calculation version 1.1.0

Review policy

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.)
00
30°π/60.523599
45°π/40.785398
60°π/31.047198
90°π/21.570796
120°2π/32.094395
135°3π/42.356194
150°5π/62.617994
180°π3.141593
270°3π/24.712389
360°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.

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.