About this calculator
The angle converter is used to convert between three angle units: degree, radian, and gradient. Degree is the most commonly used unit of angle in daily life, and a circle is 360 degrees. Radian is a unit commonly used in mathematics and physics, and a circle is 2π radians. Gradient (also called percentile) is mainly used in European surveying and engineering, and a circle is 400 gradients. Our free online angle converter provides a simple, fast and accurate solution.
The relationship between different angle units: 180° = π rad = 200 grad. Degree is the most intuitive unit. Radian is directly related to the radius and arc length of a circle (arc length = radius × radian). The gradient defines a right angle as 100 gradients. In trigonometric calculations, radians are the most natural unit; in engineering measurements, both degrees and gradients are commonly used.
Using the angle converter is very simple and intuitive. Just enter the angle value, select the input unit, hit the convert button and get instant results in other units. This tool is particularly suitable for students to learn trigonometric functions, engineers to perform measurement calculations, and programmers to process angle data.
What it calculates
The angle converter changes values between degrees, radians, gradians, and turns for trigonometry, engineering, and geometry.
Formula
- radians = degrees * pi / 180.
- degrees = radians * 180 / pi.
- 1 turn = 360 degrees = 2pi radians.
Inputs
- Angle value.
- Source angle unit.
- Target angle unit.
Example
| Input | Conversion | Result |
|---|---|---|
| 180° | to rad | pi |
| 90° | to rad | pi/2 |
| 2pi rad | to ° | 360° |
How to interpret the result
Different angle units describe the same rotation. Radians are common in calculus and trig functions, while degrees are easier for everyday angles.
Common mistakes
- Check angle mode before using trig functions.
- pi radians equals 180°, not 360°.
- Do not mix angle units with length units.
How to use
Using the angle converter is very easy. First, enter the angle value in the input box. You can enter any real number, including negative numbers and decimals. For example, 90, -45, 3.14159, etc.
Then, select the input unit: Degree, Radian, or Gradian. Click the "Convert" button.
The converter immediately displays the value of the angle in all three units. For example, if you enter 90 degrees, the result is: 90° in degrees, 1.570796 rad in radians (π/2), and 100 grad in gradient. Enter π radians, the result is: degrees 180°, radians 3.141593 rad, gradient 200 grad. The result is retained to 6 decimal places to ensure accuracy. Click the "Reset" button to clear all inputs and start a new conversion.
Main features
This angle converter has the following features: supports three units of degrees, radians, and gradients; displays all unit results in one conversion; high-precision calculation (retains 6 decimal places); supports negative numbers and decimals; displays unit conversion relationships; automatically detects invalid input; simple and intuitive interface, easy to use; fast response speed, conversion results are displayed instantly; completely free, no registration or download required; supports desktop and mobile device access; suitable for students, engineers, and programmers.
Use cases
Angle converters are very useful in several scenarios. When students learn trigonometric functions, they need to convert between degrees and radians. For example, sin(30°) = sin(π/6 rad) = 0.5. In programming, many trigonometric functions in programming languages use radians as parameters and require converting degrees to radians.
In engineering surveying, angle measurements may be in degrees or gradients and need to be converted to unified units. In geographic information systems (GIS), latitude and longitude are expressed in degrees, but some calculations require conversion to radians. In physics, physical quantities such as angular velocity and angular acceleration use radians.
In game development, rotation angles may be in degrees (more intuitive) or radians (easier to calculate). In robot control, joint angles need to be converted accurately. In astronomy, the position of celestial bodies is expressed in degrees, minutes and seconds, and needs to be converted to radians when calculating. Whether you are studying, engineering or developing, angle converter is a useful tool.