Free Online Calculators
Degrees, Radians, Gradians
Angles appear in virtually every field of science, engineering, and everyday life. Whether you're a student working through trigonometry homework, an engineer programming a robotic arm, or a surveyor measuring terrain, you'll inevitably encounter different angle units. Our free Angle Converter makes it effortless to switch between degrees (°), radians (rad), and gradians (gon) in real time.
Before diving into the converter, it helps to understand what each unit represents and where each is commonly used.
Degrees are the most widely recognized angle unit in everyday life. A full circle contains 360 degrees, a convention that traces back to ancient Babylonian astronomy. Degrees are used in navigation, architecture, carpentry, and most school-level mathematics. A right angle is 90°, a straight angle is 180°, and a full rotation is 360°.
Radians are the standard unit of angular measurement in mathematics and physics, and they form part of the International System of Units (SI). One full circle equals 2π radians (approximately 6.2832 rad). A radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius. Most scientific software, programming languages like Python and JavaScript, and advanced calculators use radians by default.
Gradians, also called gon or grad, divide a full circle into 400 equal parts. This decimal-based system was introduced during the French Revolution as part of an effort to decimalize measurement. It remains widely used in surveying, civil engineering, and cartography, where a right angle equals exactly 100 gon — making mental arithmetic much easier in those fields.
Our converter is designed for speed and simplicity. Here's how to get started:
There's no need to press a calculate button — the live conversion updates as you type. The tool works on all devices, including smartphones, tablets, and desktop computers, and requires no registration or download.
Understanding the math behind angle conversion can deepen your grasp of geometry and trigonometry. Here are the essential formulas:
While these formulas are straightforward, manually computing them — especially with π — is error-prone. Our converter handles all calculations automatically, saving you time and preventing mistakes.
High school and university math courses typically introduce angles in degrees, but calculus and advanced mathematics almost exclusively use radians. If you need to evaluate cos(60°) in a programming environment, you must first convert: 60 × π/180 ≈ 1.0472 rad. Our tool streamlines this process for students and educators alike.
Land surveyors rely heavily on gradians because the 400-gon system aligns naturally with decimal calculations. A slope of 45 degrees equals exactly 50 gon, simplifying field measurements and data recording. Converting between degrees and gradians is a routine task that our tool handles in an instant.
Functions like Math.sin() in JavaScript or math.sin() in Python expect angles in radians. A common source of bugs is forgetting to convert degrees to radians before calling these functions. For example, a rotation of 90 degrees must be entered as π/2 ≈ 1.5708 rad. Use our converter to get the exact value before writing your code.
Pilots and navigators express directions in degrees (e.g., a heading of 045° means northeast). However, onboard computers and autopilot systems often process angles in radians internally. Understanding how to convert between these units is essential for anyone working in aviation or maritime navigation.
Degrees divide a circle into 360 arbitrary parts, while radians are based on the geometry of the circle itself — specifically, the ratio of arc length to radius. Radians are considered more mathematically natural and are preferred in scientific and engineering contexts.
The gradian system (400 units per circle) is a decimal system, which simplifies calculations in the field. Since a right angle is exactly 100 gon, it's easy to work with fractions and multiples of right angles without messy arithmetic.
Use the formula: rad = 45 × (π / 180) = π/4 ≈ 0.7854 rad. This is one of the most common conversions in trigonometry and is worth memorizing for quick mental calculations.
Yes, this tool is completely free, requires no account, and works directly in your browser. It's available 24/7 on any device with an internet connection.
Absolutely. The converter handles any angle value, whether it's a fraction of a degree, a full rotation, or multiple revolutions. This is useful in fields like robotics and animation where cumulative angles often exceed 360°.