Angle Converter

Enter a value to instantly convert between angle units.

Angle conversions are needed in fields ranging from navigation and surveying to programming and mathematics — converting between degrees (the everyday unit), radians (used throughout mathematics and programming, especially in trigonometric functions), and gradians (used in some surveying and engineering contexts). Anyone who has gotten unexpected results from a programming language's trigonometric functions has likely run into the degrees-radians distinction, since most programming languages' math libraries expect radians, not degrees.

From

Precision4 dp

1 Degree = 0.0175 Radian

Key Formulas

Degree → Radian

rad = ° × 0.0174533

Radian → Degree

° = rad × 57.2958

Degree → Gradian

grad = ° × 1.11111

Gradian → Degree

° = grad × 0.9

Popular Conversions

Degree to Radian Degree to Gradian Radian to Degree Gradian to Degree

All Angle Conversions

Degree to Radian Degree to Gradian Radian to Degree Gradian to Degree Degree to Arcminute Degree to Arcsecond Degree to Turn Degree to Milliradian Radian to Gradian Radian to Arcminute Radian to Arcsecond Radian to Turn Radian to Milliradian Gradian to Radian Gradian to Arcminute Gradian to Arcsecond Gradian to Turn Gradian to Milliradian Arcminute to Degree Arcminute to Radian Arcminute to Gradian Arcminute to Arcsecond Arcminute to Turn Arcminute to Milliradian Arcsecond to Degree Arcsecond to Radian Arcsecond to Gradian Arcsecond to Arcminute Arcsecond to Turn Arcsecond to Milliradian Turn to Degree Turn to Radian Turn to Gradian Turn to Arcminute Turn to Arcsecond Turn to Milliradian Milliradian to Degree Milliradian to Radian Milliradian to Gradian Milliradian to Arcminute Milliradian to Arcsecond Milliradian to Turn

About Angle Conversions

History & Background

The division of a circle into 360 degrees dates back to ancient Babylonian astronomy, likely connected to their base-60 number system and an approximation of the number of days in a year. The radian, by contrast, is a much more modern unit (formalized in the 19th century) defined purely mathematically — one radian is the angle subtended when the arc length equals the radius, making 2π radians equal to a full circle (360°). This makes the radian the 'natural' unit for mathematics, since many formulas (derivatives of trigonometric functions, for example) are simplest when angles are expressed in radians, while degrees remain the practical unit for everyday and navigational use. The gradian (also called the gon), dividing a circle into 400 units, was introduced as part of early metric system proposals to make a right angle equal to a round 100 units — it never achieved the widespread adoption of the meter or kilogram but persists in some surveying equipment and software.

How to Use This Converter

Select your starting and target angle units and enter a value for an instant conversion. If you're working with a programming language or spreadsheet formula, double check whether its trigonometric functions expect radians or degrees — this converter is useful for translating a degree value (which is how most people think about angles) into the radians a function expects, or vice versa for interpreting a function's output.

Frequently Asked Questions

Why do programming languages use radians instead of degrees for trig functions?

Radians are the 'natural' unit for calculus and analysis — many formulas involving trigonometric functions (such as derivatives and Taylor series) take their simplest form when angles are measured in radians, because the radian is defined directly from the geometry of the circle (arc length divided by radius) rather than an arbitrary division like 360 degrees. Most programming language math libraries follow mathematical convention and expect radians.

How many degrees are in a radian?

One radian is approximately 57.2958 degrees (exactly 180/π degrees). A full circle (360°) equals 2π radians (approximately 6.2832 radians). These conversion factors come directly from the radian's geometric definition, not from an arbitrary standard.

What is a gradian and where is it used?

A gradian (or gon) divides a full circle into 400 units, making a right angle exactly 100 gradians — a deliberately 'metric-friendly' design from early metric system proposals. While it never became as widespread as the meter or liter, gradians are still used in some surveying instruments and software, particularly in parts of Europe, which is why a converter to translate gradians into the more familiar degrees is useful.

Popular Use Cases

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