What is a radian, in simple terms?

Imagine wrapping the radius of a circle along its edge. The angle you sweep is one radian — roughly 57.3°. A full circle is about 6.28 radians (2π).

Why do scientists prefer radians?

Radians simplify formulas. The derivative of sin(x) is cos(x) only when x is in radians. In degrees you would need an extra π/180 factor everywhere.

How do I convert degrees to radians by hand?

Multiply the degree value by π / 180. For example, 90° × (π / 180) = π / 2 ≈ 1.5708 rad.

And radians to degrees?

Multiply by 180 / π. So π radians × (180 / π) = 180°.

Radians ↔ Degrees Converter

Convert angles between radians and degrees instantly. Type a value and see the result update in real time.

Degrees (°)

Decimal Places

Common Values

Features

Two-way conversion

Radians → degrees or degrees → radians in a single field

Common-angle shortcuts

Quick buttons for 30°, 45°, 60°, 90°, 180°, and 360° so you don't have to type

Adjustable decimal places

Show as many or as few decimals as your work requires

Formula reference

The conversion formula is displayed alongside the result for study purposes

How to use this tool

1
Pick a direction — Choose 'Degrees → Radians' or 'Radians → Degrees'
2
Enter your angle — Type the number or tap a quick-angle button
3
Read the result — The converted value updates automatically
4
Refine precision — Slide the decimal-places control if you need more or fewer digits

Common uses

Calculus homework

Trigonometric derivatives and integrals assume radians — convert first to avoid errors

Game & web development

CSS and Canvas APIs often need radians; designers think in degrees

Physics problems

Angular velocity (rad/s) and rotation (degrees) meet in nearly every mechanics problem

3-D modelling

Tools like Blender mix both units depending on the panel — convert on the fly

Frequently asked questions

Related Tools

Calculator

Basic calculator for mathematical operations

Average Calculator

Calculate the average of a set of numbers

Area Calculator

Calculate area and perimeter for 9 shapes — rectangle, circle, triangle, trapezoid, ellipse & more

GST Calculator

Calculate GST, add or remove tax from prices

Unit Converter

Convert between different units of measurement

Percentage Calculator

Calculate percentages and percentage changes