Angle Converter
Degrees to radians, gon to degrees, arcminutes – fast and precise
- Updated
You can type in either field.
Result in Radian (rad)
0.01745329rad
0.017453291 ° equals 0.01745329 rad.
In all units
Tap a unit to make it the target.
Earth’s rotation per hour is about 15 times your value.
- Your value0.01745329 rad
- Earth’s rotation per hour0.2618 rad
- Earth’s axial tilt (≈ 23.44°)0.4091 rad
- Right angle1.571 rad
- Straight angle3.142 rad
Bars on a logarithmic scale, values rounded.
How this was calculated
Both units are converted via the base unit °: 1 ° = 1 ° and 1 rad = 57.29577951 °.
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Angle units: overview and conversion factors
Degrees, radians, gon and arcminutes – mathematics, navigation and surveying
An angle describes the opening between two rays that share a common starting point. The most common unit is the degree (°), where a full circle is divided into 360 degrees. This division comes from ancient Babylon, which used a sexagesimal (base-60) number system. Because 360 is divisible by many numbers (1, 2, 3, 4, 5, 6, 8, 9, 10, 12...), it produces a practical subdivision. Right angles (90°), obtuse angles (90°–180°) and straight angles (180°) are intuitive everyday concepts.
In mathematics and physics, the radian (rad) is the dominant "natural" angle unit. One radian is the angle at which the arc length of a circle equals its radius. A full circle has 2π ≈ 6.2832 radians. The radian is a dimensionless unit (arc length divided by radius). Trigonometric functions (sin, cos, tan) are given in radians by default in calculus and signal processing, because the derivatives are then especially simple: d/dx(sin x) = cos x.
The gon (gon), also called grad or gradian, divides the full circle into 400 equal parts. That means a right angle equals exactly 100 gon – an advantage for decimal calculations. Gon is used mainly in surveying, cartography and construction planning. Theodolites – the angle-measuring instruments used by surveyors – often display their readings in gon. Gon is especially common in Switzerland and France.
The arcminute (′) is 1/60 of a degree. An arcminute measured along the Earth's meridian corresponds to one nautical mile (1,852 m) – hence the name. 1° = 60 arcminutes = 3,600 arcseconds. GPS coordinates are often given in degrees, minutes and seconds (DMS): e.g. 48° 8′ 14″ N, 11° 34′ 32″ E for Munich. In astronomy, angular distances between celestial objects are expressed in arcminutes and arcseconds. The human eye can resolve angular detail down to about 1 arcminute.
In everyday life and engineering, angles come up in many contexts: roof pitches are given in degrees (typically 15°–45°), road gradients as a percentage (tan(angle) × 100). In navigation, bearings are given in degrees (0°–360°, north = 0°). Saw blades are set to specific degrees, as are drilling angles. Our angle converter lets you quickly convert between all common angle units for mathematics, engineering and navigation.
Common angle conversions
The most important angle conversions
- 90° = π/2 rad
- Right angle = 1.5708 rad
- 180° = π rad
- Straight angle = 3.1416 rad
- 1° = 60 arcminutes
- Navigation, GPS coordinates
- 100 gon = 90°
- Right angle in the surveying system
- 360° = 400 gon
- Full circle in gon
- 1 rad ≈ 57.296°
- Radians to degrees
Calculation examples
- Formula
- degrees × (π ÷ 180) = rad
- Value
- 45°
- Factor
- π ÷ 180 = 0.017453
- Result
- π/4 ≈ 0.7854 rad
- Formula
- rad × (180 ÷ π) = degrees
- Value
- 1 rad
- Factor
- 180 ÷ π = 57.2958
- Result
- 57.296°
- Formula
- degrees × (400 ÷ 360) = gon
- Value
- 270°
- Factor
- 400 ÷ 360 = 1.1111
- Result
- 300 gon
Frequently asked questions about the angle converter
Everything about degrees, radians, gon, full circles and arcminutes
How do I convert degrees to radians?
Radians = degrees × (π / 180) ≈ degrees × 0.017453. Example: 90° = 90 × π/180 = π/2 ≈ 1.5708 rad. Conversely: degrees = radians × (180 / π) ≈ radians × 57.2958. A full circle (360°) = 2π radians ≈ 6.2832 rad.
What is a radian (rad)?
One radian is the angle at which the arc length of a circle equals its radius. A full circle has 2π radians ≈ 6.2832 rad. The radian is the SI unit of angle and is used in mathematics, physics and engineering as the "natural" angle unit, because trigonometric derivatives become especially simple with it.
What is gon (grad) and what is it used for?
One gon (also called grad or gradian) is 1/400 of a full circle: 400 gon = 360°. Gon is used mainly in surveying and cartography. A right angle equals exactly 100 gon, which simplifies calculations. Theodolites and total stations often display readings in gon.
What is an arcminute and where is it used?
One arcminute (minute of arc) = 1/60 degree ≈ 0.01667°. 1 degree = 60 arcminutes = 3,600 arcseconds. Arcminutes are used in navigation, astronomy and geography. The nautical mile historically goes back to one arcminute along the Earth's meridian and is today defined as exactly 1,852 m. GPS coordinates are often given in degrees, minutes and seconds.
How many radians and gon are in a right angle?
A right angle (90°) equals π/2 radians ≈ 1.5708 rad and exactly 100 gon. A straight angle (180°) equals π radians ≈ 3.1416 rad and 200 gon. A full circle (360°) equals 2π radians ≈ 6.2832 rad and 400 gon.