Degree Converter
Convert angles between degrees, radians, gradians, arcminutes, arcseconds, and turns. Used in trigonometry, navigation, surveying, and CAD design. See also our Degrees to Radians and Degrees to DMS converters.
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Popular Degree Converters:
What is a Degree Converter?
A degree converter is a tool that converts between different units of angle measurement such as degrees, radians, gradians, and arcminutes. It is essential for trigonometry, navigation, engineering, surveying, and any application involving angular measurements.
How to Convert Degree Units
Select the angle unit you want to convert from and the unit you want to convert to using the dropdown menus. Enter your value in the input field and the converter will instantly calculate the equivalent angle. Use the popular conversion links below for common conversions like radians to degrees.
Degree Conversion Formulas
History of Degree Measurement
The 360-degree circle originated from ancient Babylon around 2000 BCE, likely because 360 approximates the days in a year and is highly divisible. The radian was introduced in the 18th century and became standard in mathematics due to its natural relationship with the circle. The gradian was developed during the French Revolution, dividing a right angle into 100 parts.
About This Degree Converter
This degree converter supports 13 different angle units including degree, radian, gradian (gon), mil, arcminute, arcsecond, turn, circle, quadrant, sextant, sign, grad, and right angle. It serves mathematicians, engineers, surveyors, and navigators.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180 (approximately 0.0174533). For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians.
How do I convert radians to degrees?
Multiply radians by 180/π (approximately 57.2958). For example, 1 radian = 1 × 180/π ≈ 57.296 degrees.
What is a gradian?
A gradian (also called gon or grad) divides a right angle into 100 parts, so a full circle is 400 gradians. It is used in surveying because it makes percentage slope calculations easier.
How many radians are in a full circle?
A full circle contains 2π radians (approximately 6.2832 radians). This equals 360 degrees, 400 gradians, or 1 turn.
What is an arcminute and arcsecond?
An arcminute is 1/60 of a degree. An arcsecond is 1/60 of an arcminute (1/3,600 of a degree). They are used in astronomy, navigation, and precise angular measurements.
Metric Conversion Factor Tables for Degree Converter
| Units to convert | Multiply By The Number | Convert as Unit |
|---|---|---|
| Degree (°) | 0.0174532925 | Radian (rad) |
| Degree (°) | 1.1111111111 | Gradian (gon) |
| Degree (°) | 60 | Minute (') |
| Degree (°) | 3600 | Second (") |
| Degree (°) | 0.0027777778 | Turn |
| Radian (rad) | 57.295779513 | Degree (°) |
| Radian (rad) | 63.661977237 | Gradian (gon) |
| Radian (rad) | 0.1591549431 | Turn |
| Gradian (gon) | 0.9 | Degree (°) |
| Gradian (gon) | 0.0157079633 | Radian (rad) |
| Turn | 360 | Degree (°) |
| Turn | 6.2831853072 | Radian (rad) |
| Turn | 400 | Gradian (gon) |
| Quadrant | 90 | Degree (°) |
| Sextant | 60 | Degree (°) |
| Mil | 0.05625 | Degree (°) |
Degreeconverters & it's abbreviations
| Unit | Abbreviation | Unit | Abbreviation | Unit | Abbreviation |
|---|---|---|---|---|---|
| degree | ° | radian | rad | gradian | gon grad |
| mil | mil | minute of arc | ' arcmin | second of arc | " arcsec |
| turn | tr rev | circle | - | quadrant | - |
| sextant | - | sign | - | right angle | - |
| grad | ^g |
Complete list of Degree conversion units and its conversion.
- 1 degree [°] = 0.0174532925 radian [rad]
degrees to radians → - 1 radian [rad] = 57.295779513 degree [°]
radians to degrees → - 1 degree [°] = 1.1111111111 gradian [gon]
degrees to gradians →
- 1 degree [°] = 0.0027777778 turn
degrees to turns → - 1 radian [rad] = 63.661977237 gradian [gon]
radians to gradians → - 1 radian [rad] = 3437.7467708 minute of arc [arcmin]
radians to arcminutes →
- 1 turn = 6.2831853072 radian [rad]
turns to radians → - 1 turn = 400 gradian [gon]
turns to gradians → - 1 circle = 360 degree [°]
circles to degrees →
- 1 sextant = 60 degree [°]
sextants to degrees → - 1 sextant = 1.0471975512 radian [rad]
sextants to radians → - 1 sign = 30 degree [°]
signs to degrees →
- 1 right angle = 1.5707963268 radian [rad]
right angles to radians → - 1 gradian [gon] = 0.0157079633 radian [rad]
gradians to radians →
- 1 gradian [gon] = 0.9 degree [°]
gradians to degrees → - 1 degree [°] = 60 minute of arc [arcmin]
degrees to arcminutes → - 1 degree [°] = 3600 second of arc [arcsec]
degrees to arcseconds →
- 1 radian [rad] = 206264.80625 second of arc [arcsec]
radians to arcseconds → - 1 radian [rad] = 0.1591549431 turn
radians to turns → - 1 turn = 360 degree [°]
turns to degrees →
- 1 circle = 6.2831853072 radian [rad]
circles to radians → - 1 quadrant = 90 degree [°]
quadrants to degrees → - 1 quadrant = 1.5707963268 radian [rad]
quadrants to radians →
- 1 mil = 0.05625 degree [°]
mils to degrees → - 1 mil = 0.0009817477 radian [rad]
mils to radians → - 1 right angle = 90 degree [°]
right angles to degrees →