Degrees to Radians Converter
Convert between degrees and radians instantly. Edit either field to convert in both directions.
Common angles
Reference table
| Degrees | Radians (decimal) | Radians (fraction of π) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | 0.5235987756 | π/6 |
| 45° | 0.7853981634 | π/4 |
| 60° | 1.047197551 | π/3 |
| 90° | 1.570796327 | π/2 |
| 180° | 3.141592654 | π |
| 270° | 4.71238898 | 3π/2 |
| 360° | 0 | 2π |
Formula
radians = degrees × (π / 180)
degrees = radians × (180 / π)
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What is the Degrees to Radians Converter?
This tool instantly converts angle values between degrees and radians. Degrees are the everyday unit for angles (a full circle is 360°); radians are the mathematical unit used by trigonometric functions in programming (a full circle is 2π radians, approximately 6.2832).
In GIS and spatial programming, the conversion arises whenever you need to pass a bearing, slope angle, or latitude value to a mathematical function written in Python, JavaScript, or SQL. The formula is simple — radians = degrees × π / 180 — but having an instant reference tool saves time and avoids errors.
Common use cases
GIS programming and scripting
Convert degree values (bearings, latitudes, angles) to radians before passing them to Python math functions, JavaScript Math.sin/cos, or SQL trigonometric functions.
Geodetic formula implementation
Implement the Haversine formula, Vincenty's formulae, or other geodetic calculations that require all angles in radians.
Slope and aspect calculations
Convert slope angles from degrees (as reported by GIS software) to radians for use in terrain analysis formulae.
Map rotation and projection parameters
Convert rotation or skew angles between degrees (used in GIS UI) and radians (used in some projection library parameters).
Frequently asked questions
Why do programming languages use radians instead of degrees?
Radians are the natural unit for angles in mathematics because they express the relationship between arc length and radius directly (arc length = radius × angle in radians). Trigonometric functions (sin, cos, tan) in all major programming languages expect radian inputs. Converting degrees to radians before calling these functions is a common requirement in GIS code.
What is the formula to convert degrees to radians?
Radians = Degrees × (π / 180). For example: 90° × (π / 180) = π/2 ≈ 1.5708 radians. To convert back: Degrees = Radians × (180 / π).
When are degrees used in GIS?
Degrees are used everywhere in GIS for geographic coordinates (latitude and longitude), bearing and azimuth values, map rotation, and slope angles. Radians are only needed when passing values to mathematical functions in code or when a tool or API explicitly requires radian input.
What is a gradian and is it used in GIS?
A gradian (or gon) divides a right angle into 100 units, giving a full circle 400 gradians. It is occasionally used in European surveying instruments and some legacy GIS datasets from countries that adopted metrication of angle units. This converter focuses on the more common degrees-radians conversion.