About the Angle Converter
This page converts an angle between degrees, radians, gradians, turns, arcminutes, arcseconds and milliradians. When you convert to radians it also shows the answer as a multiple of pi if it is a simple one, such as π/2 or 3π/4. Separate sections change decimal degrees into degrees, minutes and seconds and back again, read a coordinate typed in one box such as 40° 26′ 46″ N, and bring any angle into the range 0 to 360 or −180 to 180. Results are floating-point approximations with about twelve reliable digits. The π form appears only for simple multiples, and latitude and longitude limits are not enforced because this handles angles in general.
Updated September 2026
How to use the Angle Converter
- 1Type a value and choose the unit you have and the unit you want.
- 2Read the result, the π form for radians, and the table of every unit.
- 3For map coordinates, use the degrees-minutes-seconds boxes or the one-box coordinate field.
- 4Use Normalise an angle to wrap any angle into 0–360° or −180–180°.
- 5Press Copy to keep the answer.
Degrees and radians
A full circle is 360 degrees or 2π radians. One radian is the angle whose arc is as long as the radius, about 57.2958 degrees. Degrees are convenient for everyday use, and radians make formulas in trigonometry and calculus simpler, which is why calculators and programming languages use radians for sine and cosine.
To convert by hand, multiply by π/180 for degrees to radians and by 180/π for the other way. The table on this page lists the angles you meet most: 30, 45, 60, 90, 180, 270 and 360 degrees.
Degrees, minutes and seconds for maps
Maps and GPS often show a position as degrees, minutes and seconds, where a degree is split into 60 minutes and a minute into 60 seconds. A coordinate such as 40° 26′ 46″ N is the same as 40.4461 in decimal degrees. North and east are positive, south and west negative.
The one-box reader accepts degree, minute and second marks in several styles, plain numbers separated by spaces, or a hemisphere letter at the end. Anything with minutes or seconds of 60 or more is rejected, because that would be a typing mistake.
Other angle units
- Gradians: 400 to a full turn, so a right angle is 100
- Turns: one turn is a full circle, handy for rotations and animations
- Arcminutes and arcseconds: fine divisions used in astronomy and navigation
- Milliradians: used for rifle scopes and small-angle estimates
Normalising an angle
Angles can be turned past a full circle or in the negative direction, so 450° points the same way as 90°. Normalising removes the extra turns. The 0 to 360 range suits compass bearings, and the −180 to 180 range suits longitude and steering. For other kinds of units, try the Unit Converter, and for sums with the values you find, the Online Calculator. The Percentage Calculator helps if a slope is quoted as a percent, and the Number Base Converter covers binary and hex.
Features
- Seven angle units in one place
- Radians written as a multiple of π when simple
- Decimal degrees to degrees, minutes, seconds and back
- One-box coordinate reader with N, S, E and W
- Normalise to 0–360° or −180–180°
- Table of common angles with radians and gradians
- Swap button for reversing the units
- Runs in your browser
Frequently asked questions
How do I convert degrees to radians?
Multiply the degrees by π and divide by 180. So 180° is π radians, about 3.141593, and 90° is π/2. Type the degrees, pick Radians as the target, and the tool also writes simple answers in terms of π.
How do I convert decimal degrees to degrees, minutes and seconds?
The whole part is the degrees. Multiply the remainder by 60 for the minutes, then multiply what is left of that by 60 for the seconds. For 40.446111 that gives 40° 26′ 46″. The seconds are rounded to two decimals, with a carry into minutes if they reach 60.
How do I write radians in terms of pi?
Divide the radians by π and look for a simple fraction. 1.5708 divided by π is 0.5, so it is π/2. The tool shows this for denominators up to 12; other values such as 1 radian have no neat π form and appear as decimals.
What is a gradian?
A gradian, or gon, is one hundredth of a right angle, so a full circle is 400 gradians and 90° is exactly 100. It is used in some surveying and civil-engineering work.
How do I read GPS coordinates in degrees, minutes, seconds?
Type the coordinate into the one-box field, for example 33°52'7.68"S. The page reads the marks, treats S and W as negative, and shows the decimal degrees, here −33.8688. Minutes and seconds must be below 60.
What is the difference between 0-360 and −180 to 180?
Both describe the same direction. The 0–360 form never goes negative, so −90° is 270°. The −180 to 180 form is often used for longitude and rotation, so 270° is −90°.
How many arcseconds are in a degree?
There are 3,600 arcseconds in a degree: 60 arcminutes, each made of 60 arcseconds. A full turn is 1,296,000 arcseconds.