Introduction
An angle measures how much one line turns away from another. Angles are everywhere: in math class, building design, science, and art. This angle calculator helps you work with angles quickly and easily, no manual math needed.
Use the interactive dial to pick any angle from 0° to 360°, or type in a value yourself. The calculator instantly shows your angle in degrees, radians, and gradians. It also finds the angle type, quadrant, reference angle, complementary and supplementary angles, coterminal angles, and trigonometric values like sine, cosine, and tangent. Every result comes with a clear, step-by-step solution so you can follow along and learn.
You can also find the angle between two lines, convert between six different angle units, and view a live chart of sine and cosine values across the full circle. A built-in history log keeps track of your recent calculations during your session. This tool works for learning geometry and for fast angle conversions.
How to Use Our Angle Calculator
Enter any angle value to instantly see its type, quadrant, complementary and supplementary angles, reference angle, coterminal angles, and trigonometric values (sin, cos, tan) with full step-by-step solutions.
Drag the dial: Click or drag the blue handle on the interactive angle dial to set your angle visually. You can also use your keyboard arrow keys to adjust it by 1° at a time.
Type an angle: Enter any number in the "Enter Angle" field. Use the dropdown next to it to pick your unit: Degrees, Radians, or Gradians.
Use a preset angle: Click any preset button (like 30°, 45°, 90°, or 180°) to jump straight to a common angle.
Turn on Snap to 15°: Toggle this switch on to make the dial lock to the nearest 15° increment as you drag.
Click Calculate: Press the "Calculate" button to generate full results, including angle properties, a step-by-step breakdown, and an updated trigonometric chart.
Find the angle between two lines: Scroll to the "Angle Between Two Lines" section. Enter an angle for Line 1 and an angle for Line 2, each with its own unit. The calculator shows both the interior (smaller) and exterior angles between them.
Convert angle units: In the "Angle Unit Converter" section, type a value and choose the unit you are converting from. The tool instantly shows that angle in Degrees, Radians, Gradians, Turns, Arc Minutes, and Arc Seconds. Click the copy button next to any result to copy it.
Click Reset: Press the "Reset" button at any time to return the calculator to its default 45° setting.
What Is an Angle?
An angle is the space between two lines that meet at a point. That point is called the vertex. We measure angles to describe how far one line has turned from the other. Angles are everywhere: in buildings, roads, clock hands, and even the way you bend your arm.
How Angles Are Measured
The most common unit for measuring angles is the degree. A full turn around a circle is 360 degrees (360°). A half turn is 180°, and a quarter turn is 90°. Other units include radians, which are used a lot in math and science, and gradians, which are used in surveying. One full circle equals 2π radians or 400 gradians.
Types of Angles
Angles are grouped by their size:
- Zero angle: exactly 0°. The two lines overlap completely.
- Acute angle: greater than 0° but less than 90°. Think of a slightly open book.
- Right angle: exactly 90°. It looks like the corner of a square.
- Obtuse angle: greater than 90° but less than 180°. It is wider than a right angle.
- Straight angle: exactly 180°. The two lines form a flat line.
- Reflex angle: greater than 180° but less than 360°. It wraps more than halfway around.
- Full angle: exactly 360°. The line makes one complete turn back to where it started.
Related Angles
Some angles have a special link to each other. Complementary angles are two angles that add up to 90°. For example, 30° and 60° are complementary. Supplementary angles are two angles that add up to 180°. For example, 45° and 135° are supplementary. These pairs show up often in geometry problems.
Reference Angles and Quadrants
A reference angle is the smallest angle between a line and the horizontal axis. It is always between 0° and 90°. Reference angles help you find trigonometric values like sine, cosine, and tangent for any angle. The coordinate plane is split into four sections called quadrants, numbered I through IV. The quadrant an angle falls in tells you whether sine, cosine, and tangent are positive or negative.
Coterminal Angles
Coterminal angles share the same ending position on a circle but differ by full turns. You find them by adding or subtracting 360°. For instance, 45°, 405°, and −315° are all coterminal because they point in the same direction.
Angle Between Two Lines
When two lines cross or spread apart from a shared point, the space between them forms an angle. To find it, you subtract one line's angle from the other and take the smaller result. This is called the interior angle. The exterior angle is what is left when you subtract the interior angle from 360°. If you know the slope of each line, you can convert slopes to angles and use this tool to find the angle between them.
Why Angles Matter
Angles are a basic building block of geometry. Engineers use them to design bridges and buildings, for example calculating a roof pitch, planning a ramp slope, or cutting rafters at precise angles. Pilots and sailors use them for navigation, and physicists rely on angles when solving projectile motion problems. Game designers use them to control motion on screen. Learning how to measure and convert angles builds a strong base for more advanced math, including trigonometry and calculus.