Converters
Angle Converter
Convert degrees, radians and gradians.
About the Angle Converter
The Angle Converter switches between degrees, radians, gradians and full turns, the four common ways of measuring angles.
What you can do with the Angle Converter
- Converts both ways: Type in either box and the other one updates as you type.
- Every unit at once: The "In every unit" list shows your value in degrees, radians, gradians and turns. Tap one to switch to it.
- One-tap swap: The ⇅ button flips the two units, and the line under the boxes shows the rate for 1 unit.
- Maths and design: Useful for trigonometry homework, CSS rotations and calculator settings.
Degrees and radians
A full circle is 360 degrees or 2π radians, so one radian is about 57.3 degrees. Radians come from the circle itself: one radian is the angle where the arc length equals the radius. Maths and physics formulas, and programming functions like sine and cosine, expect radians.
Gradians and turns
Gradians divide a circle into 400 parts, so a right angle is exactly 100 gradians; they're used in some surveying work. A turn is simply one full rotation, so 0.25 turns is a right angle.
The most common calculator mistake
Scientific calculators have DEG, RAD and GRAD modes. If sin(90) gives 0.894 instead of 1, the calculator is in radian mode. Converting here tells you which value to enter for the mode you're in.
Related tools
Frequently Asked Questions
How do I convert degrees to radians?
Multiply by π and divide by 180. So 90° is π/2, about 1.5708 radians.
How many degrees is one radian?
About 57.2958 degrees.
Why do programming languages use radians?
Radians make the underlying maths of trigonometric functions simpler, so most languages' sine, cosine and tangent functions take radians.
How many gradians are in a circle?
A full circle is 400 gradians, so a right angle is 100 gradians and one gradian is exactly 0.9 degrees. Gradians, also called gons, are used in some surveying work. Pick degrees and gradians to convert between them.
Why did my calculator give the wrong sine value?
It was probably in the wrong angle mode. sin 30 is 0.5 in degree mode, but in radian mode it calculates sin of 30 radians, about -0.988. Check the DEG, RAD or GRAD setting, or convert your angle here first.
What is 90 degrees in radians?
A right angle of 90 degrees is π/2 radians, about 1.5708. Other common values: 45° is about 0.7854 rad, 180° is π, about 3.1416, and 360° is 2π, about 6.2832. The tool shows these as decimals, not in terms of π.
How do I convert degrees, minutes and seconds?
Minutes and seconds are not separate inputs here, so turn them into decimal degrees first: degrees plus minutes divided by 60 plus seconds divided by 3,600. For example, 30° 15' is 30.25°. Then type the decimal value to convert.
How many degrees is half a turn?
Half a turn is 180 degrees, π radians or 200 gradians, and a quarter turn is 90 degrees. Type 0.5 with turns selected and the "In every unit" list shows the same angle in degrees, radians and gradians.
Which angle units can I use in CSS rotate?
CSS accepts all four units this tool covers: deg, rad, grad and turn. So rotate(90deg), rotate(0.25turn), rotate(100grad) and rotate(1.5708rad) give the same rotation. Use the converter to switch between them when copying values from design tools.
Can I enter negative or very large angles?
Yes. Negative values such as -45 and values above one full turn, such as 720 degrees, convert normally. The tool does not reduce them to the 0 to 360 range, so 720° shows as 2 turns, about 12.566 radians.
Can I convert radians back to degrees in the second box?
Yes. Both boxes are editable, so you can type the radian value into the second box and the degrees in the first box update straight away. You can also tap ⇅ to swap which unit is on top.
Related tools
- Data Speed Converter, Convert bps, kbps, Mbps and Gbps.
- Temperature Converter, Convert Celsius, Fahrenheit and Kelvin.
- Number Base Converter, Binary, octal, decimal, hex.
- Unix Timestamp Converter, Unix time ⇄ human-readable date.
- CSS Unit Converter, px ⇄ em ⇄ rem ⇄ pt.
- Duration Formatter, Seconds → H:M:S.
Quick Work Studio