Practical guide · 6 min read

Degrees vs Radians

Understand angle modes, conversions, and why a correct calculation can still produce the wrong answer.

Degrees divide a circle into 360 parts; radians measure an angle by the arc-length-to-radius ratio.

01

Convert between modes

Multiply degrees by π/180 to obtain radians. Multiply radians by 180/π to obtain degrees.

02

Know the expected context

Geometry exercises often use degrees, while calculus and physics formulas generally assume radians.

03

Quick error check

If sin(30) is not 0.5, the calculator is probably interpreting 30 as radians.

Put it into practice

Try the related calculator

Use the method above with an interactive tool that keeps the equation and units visible.

Open calculator

Editorial note

This guide is educational. Examples are deliberately compact and cannot cover every model, course convention, or laboratory condition. See our methodology for how formulas and examples are reviewed.