How to use the angle converter
- 1 Type the value you want to convert.
- 2 Choose the unit to convert from and the unit to convert to.
- 3 Press ⇄ to swap the two units.
- 4 Read the result, and see the same angle in every other unit in the table below.
Degrees and radians in practice
Calculators and code often expect radians: multiply degrees by π/180 before using SIN, COS or TAN. Map coordinates may be decimal degrees or degrees, minutes and seconds; convert minutes and seconds with this tool. For percentages of a turn, use the Percentage Calculator.
- A full circle is 360°, 2π rad or 400 gon.
- A roof pitch of 1 in 12 is about 4.76°.
- Check the DEG, RAD or GRAD mode on your calculator first.
Features
Six angle units
Degrees, radians, gradians, arcminutes, arcseconds and turns.
Exact π
Uses π to full precision, so 180° is exactly π radians.
Coordinates
Convert decimal degrees to arcminutes and arcseconds for maps.
When to use it
Maths and physics
Trigonometry in calculus and physics uses radians. 30° is 0.5236 rad.
Programming
JavaScript, Python and spreadsheet functions such as SIN and COS expect radians; multiply degrees by π/180 first.
Maps and GPS
GPS coordinates may be in decimal degrees or degrees, minutes and seconds. 0.5° is 30 arcminutes.
Building and DIY
Roof pitches and cutting angles are in degrees; a 45° mitre is a quarter of a right angle doubled.
Related Unit tasks
Frequently asked questions
How do I convert degrees to radians?
Multiply by π and divide by 180. 60° is π/3, or 1.0472 radians.
How do I convert radians to degrees?
Multiply by 180 and divide by π. 1 radian is 57.2958°.
What is a gradian?
One four-hundredth of a full turn, so a right angle is 100 gradians. It is used in some surveying and on scientific calculators labelled GRAD.
How many arcminutes in a degree?
60 arcminutes, and 60 arcseconds in each arcminute, so 3,600 arcseconds in a degree.
Why does my calculator give a strange answer for sin(30)?
It is probably set to radians. Switch it to DEG mode, or convert 30° to 0.5236 rad first.
What is a radian?
The angle where the arc length equals the radius. A full circle is 2π radians, about 6.283.
How many degrees is a full turn?
360 degrees, which is 2π radians or 400 gradians.
How do I convert decimal degrees to degrees, minutes and seconds?
Keep the whole degrees, multiply the decimal by 60 for minutes, then multiply the remaining decimal by 60 for seconds. 31.55° is 31° 33′ 0″.
What is a right angle in radians?
π/2, about 1.5708 radians.
Are the results exact?
They use the full precision of π available in the browser, which is accurate to about 15 significant digits.
Where are gradians still used?
Some surveyors, especially in parts of Europe, use gradians because a right angle is a round hundred. Many scientific calculators include a GRAD mode for this reason.
Why do scientists prefer radians?
Radians make calculus formulas simpler. The derivative of the sine function is the cosine only when the angle is measured in radians.
How are angles used in construction?
Builders use angles for roof pitches, stairs, ramps and cutting timber. A wheelchair ramp, for example, is usually no steeper than about five degrees for safe use.
How do I measure an angle without a protractor?
Measure the rise and the run of a slope, divide the rise by the run, and use the inverse tangent on a calculator in degree mode. Many phones also have a level app that shows angles.
What angle is a quarter turn?
Ninety degrees, half of pi radians, or one hundred gradians.
Built and reviewed by Hamza Farooq, founder and lead developer
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