Angle Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, revolutions, and other angle units used in math, navigation, surveying, and engineering.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
180 ° = 3.1415927 rad
1 Degree = 0.017453293 Radians
1 Radian = 57.29578 Degrees
180 ° in every supported unit
What is an Angle Converter?
An angle measures the amount of rotation between two rays that share a common starting point — like the hands of a clock swinging open from the center, or a wheel turning through part of a circle. An angle converter translates that amount of rotation from one measurement system into another, for example turning degrees into radians, or gradians into arcminutes.
Several angle units coexist because different fields grew up around different needs. Degrees are the everyday, intuitive choice for navigation, surveying, and geometry because a full circle divides neatly into 360 whole-number parts. Radians are the unit calculus and physics reach for, because they make formulas involving circles and rotation simplify cleanly without an extra conversion constant. Gradians were a metric-era attempt at decimal simplicity, splitting a right angle into a clean 100 parts instead of 90 — still used in some surveying and engineering contexts today. Every unit below is defined relative to the degree, so any conversion between them reduces to a single multiplication.
Conversion chart: Degree to Radians
Conversion table
| Degree (°) | Radian (rad) |
|---|---|
| 0.01 ° | 0.00017453293 rad |
| 0.1 ° | 0.0017453293 rad |
| 1 ° | 0.017453293 rad |
| 2 ° | 0.034906585 rad |
| 3 ° | 0.052359878 rad |
| 5 ° | 0.087266463 rad |
| 10 ° | 0.17453293 rad |
| 20 ° | 0.34906585 rad |
| 50 ° | 0.87266463 rad |
| 100 ° | 1.7453293 rad |
| 1000 ° | 17.453293 rad |
Supported Units
| Unit | Symbol | In Degrees |
|---|---|---|
| Degree | ° | 1 ° |
| Radian | rad | 57.29578 ° |
| Gradian | grad | 0.9 ° |
| Minute of Arc | ' | 0.016666667 ° |
| Second of Arc | " | 0.0002777778 ° |
| Revolution | r | 360 ° |
| Quadrant | quad | 90 ° |
| Sextant | sext | 60 ° |
| Mil (angular) | mil | 0.05625 ° |
| Sign (zodiac) | sign | 30 ° |
About These Parameters
- Value
- The number you want to convert, expressed in the "From" unit. Accepts decimals.
- From Unit
- The unit your input angle is currently measured in.
- To Unit
- The unit you want the result converted into. Use the swap button to flip From and To instantly.
How Angle Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the degree. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Degree → Radian: multiply by 0.017453293. For example, 180 ° × 0.017453293 = 3.1415927 rad.
Why Radians Are the Natural Unit
In calculus and physics, the radian is the unit angles are "supposed" to be measured in, because it removes an awkward conversion constant from the math. If an angle is measured in radians, the length of the arc it traces on a circle is simply the radius multiplied by the angle (arc length = radius × angle in radians) — no factor of π/180 required. That same clean relationship is why derivatives and integrals of trigonometric functions only take their simple, familiar forms when the angle is in radians; measuring in degrees would scatter conversion constants throughout every formula.
The 360-Degree Circle: A Babylonian Legacy
Dividing a circle into 360 degrees dates back roughly 4,000 years to Babylonian astronomers, who counted using a base-60 (sexagesimal) number system rather than the base-10 system most of the world uses today. 360 is convenient in base-60 because it divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, and many other numbers, and it sits close to the roughly 365-day length of a solar year used in early calendars. That ancient choice survived the fall of Babylon and traveled through Greek and Islamic astronomy into the modern world, which is why circles still split into 360 parts instead of a rounder base-10 number like 100 or 1,000.
Example
180 ° equals 3.1415927 rad. For scale, that's about 2× a right angle (90°, or 90 °) — a half turn of 180° works out to π radians, and a full turn of 360° works out to 2π radians.
Frequently Asked Questions
Why does a circle have 360 degrees?
The 360-degree circle comes from ancient Babylonian astronomers, who used a base-60 counting system and a roughly 365-day calendar year; 360 divides evenly by many small numbers, which made it a practical choice for hand calculation long before calculators existed, and the convention simply stuck through Greek and later Western science.
What is a radian in plain terms?
A radian is the angle you get when you wrap a circle's radius along its own edge — the arc traced out is exactly as long as the radius. That works out to about 57.3 degrees, and it's the unit that makes calculus formulas involving circles and rotation come out clean and simple.
How accurate are these conversions?
Every conversion factor used here is an exact, mathematically defined relationship (for example, 1 radian = exactly 180/π degrees) — results are limited only by floating-point display precision, not by rounded conversion constants.