Angle Degrees To Radians
Calculator
Results
- Radians
- 0.785398
- Gradians
- 50
- Turns
- 0.125
- Arcminutes
- 2,700
- Arcseconds
- 162,000
Conversion results
| Radians | 0.785398 |
| Gradians | 50 |
| Turns | 0.125 |
| Arcminutes | 2,700 |
| Arcseconds | 162,000 |
formula-map diagram
- Radians
- 0.785398
- Gradians
- 50
- Turns
- 0.125
- Arcminutes
- 2,700
- Arcseconds
- 162,000
Unit relationship
Formula
rad = ° × π ÷ 180 ; gon = ° × 10/9= 0.78539816339745
Note
This result is a simplified model: it converts the single value you entered with the exact factors shown, and rounds to the display precision. It does not know your measurement's accuracy, and cooking or density conversions depend on how an ingredient is packed. Check critical figures against the original units.
More in Unit conversions
See all →Frequently asked questions
What's the formula to convert degrees to radians?+
Radians = degrees × (π / 180). This comes from the fact that a full circle is both 360 degrees and 2π radians, so dividing 2π by 360 gives the per-degree radian value of π/180.
Why does a half-turn equal π radians?+
A full circle is 2π radians by definition (the radian measures angle by arc length equal to the radius), so half of a full turn — 180 degrees — is exactly half of 2π, which is π. This is why π appears so often in trigonometry and rotational contexts.
What is a gradian, and why would I need it?+
A gradian (or gon) divides a full circle into 400 units instead of 360, making a right angle exactly 100 gradians — a convention used in surveying and some European engineering fields for simpler decimal math. The calculator converts to gradians as well as radians.
Why do calculators and programming functions often expect radians instead of degrees?+
Radians are the natural unit for angles in calculus and trigonometric derivatives — formulas like the derivative of sine simplify cleanly only when the angle is in radians. Most programming languages' math libraries (sin, cos, etc.) expect radian input by default, which is a common source of bugs when developers forget to convert.
Why is my radian result an irrational-looking decimal like 1.5708 instead of a clean number?+
Because radians are defined in terms of π, which is irrational, most degree values (except special cases like 180° = π or 90° = π/2 exactly) convert to non-terminating decimals when π is approximated numerically — this is expected, not a calculation error.