Angle Converter

This page converts an angle from one unit into another. Every value passes through the radian, the SI unit angle is held in, and angle stays angle: a unit only converts inside its own dimension.

How do you convert an angle between degrees, radians and gradians?

Pick the unit you have, pick the unit you want, and type the value. The page multiplies by the factor between the two and prints the arithmetic under the result, so the answer and the working are the same object.

1. Choose the unit your value is in. This page opens on the radian.
2. Choose the unit you want it in. This page opens on the degree.
3. Type the value. The result and the factor behind it appear together.
4. Read the working. It converts into the radian first and out again, which is the same two lines you would write by hand.

Angle Conversion Table

One row per unit this page offers, each measured against the radian. The last column says whether the factor is a definition or a reading of one.

Worked Examples

The questions the bank ranked highest for this page, answered with the working.

Where These Factors Come From

Every number above is read from the knowledge base rather than computed for the page. These are the statements it holds for angle.

• A full turn is 2 pi radians, 360 degrees or 400 gradians. One degree is exactly pi/180 radians, so one radian is 180/pi degrees, about 57.29577951308232 degrees.
• One degree is 60 minutes of arc and 3600 seconds of arc, so decimal degrees = degrees + minutes/60 + seconds/3600.
• An exact factor is a definition rather than a measurement. 1 in = 25.4 mm and 1 lb = 0.45359237 kg were fixed by the 1959 international yard and pound agreement, so they never gain another digit.
• How this page reports a result result in the target angle unit; radians are given as a multiple of pi and as a decimal

SI prefixes on this page

Degrees, Radians or Gradians?

The radian is the SI unit, and it is what every trigonometric function expects. Degrees and gradians divide the same turn into different numbers of parts, so an angle carries no meaning until the unit is named beside it.

The rule behind this factor is the same for every unit - why a conversion factor is a ratio equal to one.

Frequently Asked Questions

Related Conversions

• Volume sits in the same measurement group as angle - convert a volume between litres and gallons.
• Area sits in the same measurement group as angle - convert an area between square metres and acres.
• Length sits in the same measurement group as angle - convert a length between metres and feet.
• If you are measuring parts-per ratio rather than angle, a ratio written as parts per something instead.
• If you are measuring pressure rather than angle, force spread over an area instead.
• If you are measuring mass rather than angle, kilograms and pounds side by side instead.

The rest of the family sits on every measurement family in one place.