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Angle Converter

Convert angles between degrees, radians, gradians, turns, arcminutes, arcseconds, SI milliradians and NATO mils, and between decimal degrees and degrees-minutes-seconds.

  • Free, no sign-up
  • Runs in your browser
  • Converters
Convert an angle
Negative angles are allowed.

Degrees, minutes, seconds to decimal degrees
Empty boxes count as 0. Degrees and minutes are whole numbers; minutes 0–59, seconds below 60.

Read the guide How to Convert Degrees to Radians (and Other Angle Units)

How to use the converter

The tool has two parts.

Convert an angle. Type an angle in the Value box, choose the unit you have and the unit you want, and press Convert. The swap button flips the two units. Below the result you also see the angle in degrees, minutes and seconds, and a table shows it in all eight units. Negative angles are allowed. The converter starts on degrees to radians.

Degrees, minutes, seconds to decimal degrees. Enter the degrees, minutes and seconds of an angle, such as a map coordinate, choose the sign and press Convert. Use the minus sign for south latitudes and west longitudes. Empty boxes count as zero.

Unit definitions

  • Degree (°): one full turn is 360°.
  • Arcminute (′) and arcsecond (″): 1° = 60′ and 1′ = 60″, so 1° = 3,600″.
  • Radian (rad): the angle whose arc is as long as the radius. A full turn is 2π rad, so 1 rad = 180/π ≈ 57.29578°.
  • Gradian (grad, also called gon): a full turn is 400 grad, so a right angle is exactly 100 grad.
  • Turn: one full revolution, 360°.
  • Milliradian (mrad, SI): one thousandth of a radian. A full turn is 2,000π ≈ 6,283.19 mrad.
  • NATO mil: one 6,400th of a turn, used for artillery and some rifle scopes. It is close to the SI milliradian but not the same: 1 NATO mil ≈ 0.981748 mrad. Some other countries have used 6,000 or 6,300 mils per turn, so always check which mil a device uses.

Worked examples

  • 90° to radians: 90 × π/180 = π/2 ≈ 1.570796 rad.
  • 1 rad to degrees: 180/π ≈ 57.29578°, which is 57° 17′ 44.806″.
  • 90° to gradians: 90 ÷ 0.9 = 100 grad.
  • 45° 30′ 15″ to decimal degrees: 45 + 30/60 + 15/3,600 = 45 + 0.5 + 0.0041667 ≈ 45.504167°.

Good to know

  • Decimal degrees are converted to degrees, minutes and seconds by taking the whole degrees, multiplying the remaining fraction by 60 for minutes, and the remaining fraction of that by 60 for seconds. Seconds are rounded to three decimal places.
  • Calculators and programming languages usually expect radians in trigonometric functions. If sin(90) does not give 1, the calculator is probably in radian mode.
  • Results show up to six decimal places; very small values are written in scientific notation. Radians involve π, so values such as 180° = 3.141593 rad are rounded.

Frequently asked questions

How do I convert degrees to radians?

Multiply the degrees by π and divide by 180. For example, 180° × π/180 = π ≈ 3.141593 rad, and 30° = π/6 ≈ 0.523599 rad.

Is a mil the same as a milliradian?

Not exactly. The SI milliradian is one thousandth of a radian, about 6,283.19 per full turn. The NATO mil divides a full turn into exactly 6,400 parts, so it is about 1.8% smaller. The two are often used loosely as the same thing, but they give different results over long distances.

How do I convert degrees, minutes and seconds to decimal degrees?

Add the degrees, the minutes divided by 60 and the seconds divided by 3,600. For example, 40° 26′ 46″ = 40 + 26/60 + 46/3,600 ≈ 40.446111°. For a south latitude or a west longitude, make the result negative.

How many gradians are in a circle?

A full circle has 400 gradians, so a right angle is 100 grad and one gradian is 0.9°.