Degrees are used for navigation and construction, radians for calculus and physics, gradians by some surveyors and milliradians for optics and ballistics. The converter also writes your angle in degrees, minutes and seconds.
How to use the Angle Converter
- Pick the unit you are starting from in the From menu and type your value.
- Pick the unit you want in the To menu. The heading changes to match – for example “Degrees to Radians Converter”.
- The most common angle units are shown below at the same time, so you can compare them at a glance.
- Type into any result to convert backwards, then use Copy results – the copied text starts with the heading for your chosen units.
Results update as you type. Everything is calculated in your browser.
How it works
Every angle unit is defined by an exact factor relative to the degree (the base unit). The calculator first turns the value you type into degrees, then turns that into the unit you picked in the “To” menu and into each of the common units below it. This two-step method means any unit can be converted to any other – 8 units are available in each menu – and you can type into any field, including a result, to work in the other direction. Changing a unit menu keeps the quantity the same and just re-expresses it, and the page heading and copied results follow your choice.
How to convert angle units
- Choose the unit you have in the From menu and type the value, for example 90 °.
- Choose the unit you want in the To menu, for example radians. The page heading changes to “Degrees to Radians Converter”.
- The calculator multiplies by the degree factor of the “from” unit and divides by the factor of the “to” unit: 90 ° × 1 ÷ 57.29578 = 1.5707963 rad.
1 degree in common units
| Unit | Value |
|---|---|
| Radians (rad) | 0.017453293 |
| Gradians (grad) | 1.1111111 |
| Arcminutes (′) | 60 |
| Arcseconds (″) | 3,600 |
| Turns (turn) | 0.0027777778 |
| Milliradians (mrad) | 17.453293 |
| Π radians (π rad) | 0.0055555556 |
Degrees conversion table
| Degrees | rad | grad | ′ | ″ |
|---|---|---|---|---|
| 1 | 0.017453293 | 1.1111111 | 60 | 3,600 |
| 15 | 0.26179939 | 16.666667 | 900 | 54,000 |
| 30 | 0.52359878 | 33.333333 | 1,800 | 108,000 |
| 45 | 0.78539816 | 50 | 2,700 | 162,000 |
| 60 | 1.0471976 | 66.666667 | 3,600 | 216,000 |
| 90 | 1.5707963 | 100 | 5,400 | 324,000 |
| 180 | 3.1415927 | 200 | 10,800 | 648,000 |
| 270 | 4.712389 | 300 | 16,200 | 972,000 |
| 360 | 6.2831853 | 400 | 21,600 | 1,296,000 |
What is a degree?
A degree is 1/360 of a full turn. Navigation, construction and geometry use degrees.
What is a radian?
The radian is the SI unit of angle: the angle at which an arc equals the radius. A full circle is 2π radians, about 6.283.
Common mistakes to avoid
Feeding degrees into a calculator set to radians (or the reverse), and reading decimal degrees as degrees and minutes.
Formula
1 ° = 0.017453293 rad1 ° = 1.1111111 grad1 ° = 60 ′1 ° = 3,600 ″1 ° = 0.0027777778 turnWorked example
Inputs — From: 90 °.
Results — To = 1.57079633 rad; Gradians = 100 grad; Arcminutes = 5,400 ′; Arcseconds = 324,000 ″; Turns = 0.25 turn; Milliradians = 1,570.79632679 mrad; Π radians = 0.5 π rad; Degrees, minutes, seconds = 90° 0′ 0″.
Frequently asked questions
How many radians in 180°?
Exactly π, about 3.14159.
What is a gradian?
1/400 of a turn, so a right angle is 100 grad.
What is an arcminute?
1/60 of a degree.
How do I change the units?
Pick any unit in the From and To menus. The value is converted in place, and the heading changes to show your conversion, for example “Degrees to Radians Converter”.
Can I type into any field?
Yes. Every field is editable, so you can start from whichever unit you have.
How many units can I convert between?
8 angle units, from the everyday to the specialised.
Which units are exact?
All factors here are exact by definition except astronomical and similar reference values, which use internationally agreed constants.
What formula does the Angle Converter use?
1 ° = 0.017453293 rad.