Angle Converter: Degrees, Radians, Gradians, Turns and Mils

What is it?

The Angle Converter converts degrees, radians, gradians, arcminutes, arcseconds, turns and mils.

Who is it for?

Students of maths and physics, programmers using trigonometry, surveyors, carpenters, and anyone converting GPS degrees-minutes-seconds.

How to use it

1. Type the Value and pick the From unit.
2. Every other unit is shown under In every unit; tap a value to copy it, or use Copy result.
3. Tap ⇅ Swap to convert the other way.

Which unit where?

• Degrees: everyday use, maps and construction. A full turn is 360°.
• Radians: maths and code. Math.sin() in JavaScript, Python and Excel’s SIN() expect radians. 180° = π rad ≈ 3.1416.
• Gradians: some surveying instruments; a full turn is 400 gon.
• Mils: military and artillery; NATO uses 6,400 mils per turn.

Degrees, minutes and seconds

GPS coordinates like 30° 54′ 36″ are degrees, arcminutes and arcseconds. 1° = 60′ and 1′ = 60″. So 30° 54′ 36″ = 30 + 54/60 + 36/3600 = 30.91°.

Wrong answer on a calculator?

Scientific calculators have a DEG/RAD mode. sin(90) is 1 in degree mode but 0.894 in radian mode. Check the mode first.

Worked examples

• 45° = π/4 ≈ 0.7854 rad.
• 2 rad ≈ 114.59°.
• 90° = 100 gradians = 1/4 turn = 1,600 NATO mils.
• 12.5° = 12° 30′ 0″.

Common mistakes

• Typing degrees-minutes as a decimal: 30° 30′ is 30.5°, not 30.30°.
• Feeding degrees into a function that expects radians in Excel or code: use RADIANS() or multiply by π/180.

Open the tool: Angle Converter

Still stuck?

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