Degrees to Radians Converter

Use Degrees to Radians Converter to Convert ° to rad Instantly. Get instant browser-based results, clear steps, and copy-ready output without sign-up.
Degrees to Radians Converter

Convert angles in both directions, work with decimal values or pi-based radian input, and see exact fractions, decimal output, normalized angles, and quick-reference values without leaving the page.

Degrees to radiansrad = deg x pi / 180
Radians to degreesdeg = rad x 180 / pi

Tip: the radians field accepts plain decimals and simple pi expressions such as pi/2, 3*pi/4, and -2*pi. The output below updates live while you type.

Common Angles Reference
DegreesRadians (exact)Radians (decimal)Notes
0 deg00zero angle
30 degpi/60.5235987756special triangle angle
45 degpi/40.7853981634isosceles right triangle
60 degpi/31.0471975512special triangle angle
90 degpi/21.5707963268right angle
120 deg2pi/32.0943951024obtuse reference angle
180 degpi3.1415926536straight angle
270 deg3pi/24.7123889804three-quarter turn
360 deg2pi6.2831853072full rotation

What Does This Tool Do?

The Degrees to Radians Converter turns angle values from degree form into radians and from radians back into degrees without forcing you to remember the formula every time. It is designed for the real search intent behind this topic: fast conversion, exact pi-based values when available, dependable decimal output, and a quick way to sanity-check common angles like 30 deg, 45 deg, 90 deg, and 180 deg.

Many online converters only show a decimal answer, which is enough for rough work but weak for math homework, trigonometry, physics, engineering notes, or code where radians are the required unit. This page does more than that. When the input simplifies cleanly, it shows the exact fraction in terms of pi, the decimal result, and the normalized angle so you can immediately tell whether your answer matches the expected quadrant or turn.

It also works in both directions on the same page. You can start with degrees and move to radians, or paste a radian expression such as pi/2, 3*pi/4, or -2*pi and convert it back to degrees. That makes the tool useful for classroom problems, calculator verification, programming, CAD work, and any situation where one source uses degrees while the next formula expects radians.

Key Features

deg
Two-Way Angle Conversion
Switch between degrees-to-radians and radians-to-degrees without opening another page or using a different calculator.
pi
Exact Pi Fractions
Shows compact expressions such as pi/6, pi/4, pi/2, and 2pi when the converted value simplifies cleanly.
rad
Pi-Aware Input
Accepts radian expressions like pi/2, 3*pi/4, and decimals such as 1.5708 for faster math workflow.
ref
Reference and Normalization Help
Displays common-angle references, normalized degrees, and turn values so you can confirm the result in context instead of reading a raw number only.

How to Use This Tool

  1. Choose the conversion direction at the top of the tool. Use Degrees to Radians when your source value is in degree form and use Radians to Degrees when your source value is already in radians.
  2. Enter the angle value. In degree mode you can type whole numbers, decimals, positive values, or negative values. In radian mode you can type decimals or pi-based expressions like pi/6, pi, or 3*pi/2.
  3. Set the number of decimal places you want in the answer. This is useful when you need a short rounded result for a report or a more detailed decimal for calculator verification.
  4. Use the preset buttons if you are testing common reference angles. They are faster than typing and help students, teachers, and developers check expected outputs quickly.
  5. Read the full result block. It shows the converted value, any exact simplification that can be expressed cleanly, normalized degrees, and a short formula explanation that confirms how the answer was produced.

A good habit is to compare the decimal answer with the exact expression rather than relying on one format alone. For example, 90 deg converting to pi/2 tells you far more than seeing 1.570796 by itself, especially when you are checking trigonometric identities, unit-circle problems, or function arguments in code.

How It Works

The core conversion is straightforward. To move from degrees to radians, the tool multiplies the degree value by pi / 180. To move from radians back to degrees, it multiplies the radian value by 180 / pi. Those two formulas are mathematically equivalent inverses because 180 deg = pi rad and one full turn is 360 deg = 2pi rad.

The upgraded tool then adds interpretation on top of the raw formula. It attempts to simplify degree-based results into a short pi fraction when the value lands on a familiar rational multiple of pi. Likewise, when you enter a radian expression that is a clean fraction or multiple of pi, the tool can display an exact degree form instead of only a decimal approximation. That matters for trigonometry, calculus, geometry, and technical documents where exact notation is preferred.

Radian input is also parsed intelligently rather than treated as a plain number only. Expressions such as pi/4 or 3*pi/2 are converted into their decimal equivalents internally, then processed through the same calculation path as any other input. Finally, the tool normalizes the degree output into the familiar 0-360 range so you can quickly understand where the angle sits around the circle even if the source value was negative or greater than one full turn.

Common Use Cases

Math and Trigonometry Practice
Students use it to check homework, verify unit-circle angles, and convert textbook degree values into radian form before evaluating sine, cosine, or tangent.
Programming and Graphics
Developers often work with libraries that expect radians even when design specs, UI controls, or human-readable settings are given in degrees.
Engineering, Physics, and CAD
Technical workflows regularly move between formulas written in radians and drawings or measurements described in degrees, so a fast converter prevents preventable unit mistakes.

The tool is also useful for quick review during calculator-heavy work. If a graphing calculator shows a strange result, you can check whether the issue came from using degrees where radians were expected. If a coding project rotates an object too far, you can confirm the radian constant you passed into the animation or geometry function. And if you are teaching or documenting formulas, the common-angle table makes it easy to include both exact and decimal forms on the same page.

Frequently Asked Questions

What is the formula for converting degrees to radians?

Multiply the degree value by pi / 180. For example, 90 deg becomes 90 x pi / 180, which simplifies to pi/2.

What is the formula for converting radians to degrees?

Multiply the radian value by 180 / pi. For example, pi radians becomes 180 deg, and pi/4 becomes 45 deg.

Can I enter values like pi/2 or 3*pi/4?

Yes. The radian mode accepts simple pi-based expressions as well as decimal input. That is useful when your source comes from the unit circle, a trigonometry textbook, or code constants that already use radians.

Why does math often prefer radians over degrees?

Radians are the natural angle unit in many mathematical formulas. Derivatives of trigonometric functions, arc-length calculations, rotational motion formulas, and many calculus expressions are cleaner and more direct when angles are measured in radians.

What are the most common degree-to-radian conversions?

Some of the most common are 30 deg = pi/6, 45 deg = pi/4, 60 deg = pi/3, 90 deg = pi/2, 180 deg = pi, and 360 deg = 2pi.

Does the tool handle negative angles and values above 360 degrees?

Yes. The converter accepts negative inputs and large angles. It also shows a normalized degree value so you can see the equivalent position within a single full turn.

Is this converter accurate enough for school and technical work?

Yes for normal browser-based use. The tool uses JavaScript's floating-point math for decimal output and also shows exact forms when they simplify cleanly, which makes it practical for education, coding, and everyday technical checks.

Related Tools

Degrees to Radians Converter Competitor SEO Guide

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Manual Method Without This Tool

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Detailed Degrees to Radians Converter FAQs

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