Angle Converter

By Suraj GiriUpdated 24 September 2026

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 degree.
2. Choose the unit you want it in. This page opens on the radian.
3. Type the value, or the value with its units, such as 45 deg to rad. 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.

Degrees, radians and gradians only measure an angle, so for a length, a time or any other quantity, pick its page on the online unit converter.

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 factor above is read from the knowledge base rather than typed for the page, and every result is worked from those factors. 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.

• Decimal degrees and degrees, minutes and seconds are different notations. Convert the minutes and seconds into a decimal before comparing two angles.
• A gradian is not a degree: a full turn holds more gradians than degrees.

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

• If you are measuring time rather than angle, convert time between hours, minutes and seconds instead.
• If you are measuring frequency rather than angle, convert a rotation rate between rpm and hertz instead.
• If you are measuring torque rather than angle, convert a tightening torque between newton-metres and pound-feet instead.
• If you are measuring parts-per ratio rather than angle, a ratio written as parts per something instead.
• If you are measuring illuminance rather than angle, convert illuminance between lux and kilolux instead.
• If you are measuring count rather than angle, convert a count between dozens, scores and gross instead.

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