Angle Converter
Convert degrees, radians, gradians, minutes, and seconds of arc instantly with this free online angle converter. Accurate results with comparison chart and breakdown table for all angle units.
About This Calculator
The Angle Converter is a versatile measurement tool that allows you to convert between five different units of angle measurement: degrees (deg), radians (rad), gradians (grad), minutes of arc ('), and seconds of arc ("). Whether you are studying geometry, working on physics problems, surveying land, navigating by the stars, or simply need a quick unit conversion, this tool provides accurate results instantly.
Angles are a fundamental concept in mathematics, physics, engineering, and navigation. Degrees divide a full circle into 360 equal parts and are the most common unit for everyday use. Radians are the standard SI unit used in calculus and physics because they simplify trigonometric formulas — one radian equals approximately 57.2958 degrees, and a full circle equals 2π radians. Gradians (also called gons) divide a right angle into 100 parts, making a full circle equal to 400 gradians; they are primarily used in surveying and some engineering fields. Minutes and seconds of arc are subdivisions of a degree (60 minutes per degree, 60 seconds per minute) and are essential in astronomy for measuring celestial angles and in navigation for precise coordinate calculations.
The conversion formula behind the tool is straightforward: every angle value is first converted to a base unit (degrees), then multiplied or divided by the appropriate conversion factor to produce the target unit. For example, to convert radians to degrees, the tool multiplies by 180/π. The results are presented in a clear result card showing the source and converted values, an interactive bar chart that compares your input value across all five units at once, and a breakdown table with precise values for every supported angle unit.
Frequently Asked Questions
How does the Angle Converter work?
Enter a numeric angle value, select the source unit from the dropdown, choose the target unit, and click Convert. The calculator uses precise mathematical conversion factors to instantly compute the equivalent value in your chosen unit. Results include a comparison chart showing the value across all supported angle units.
What angle units are supported?
The angle converter supports five units: degrees (deg), radians (rad), gradians (grad), minutes of arc ('), and seconds of arc ("). Degrees are the most common unit for everyday geometry, radians are standard in mathematics and physics, gradians are used in surveying, and minutes and seconds of arc are used in navigation and astronomy.
How do you convert degrees to radians?
To convert degrees to radians, multiply the degree value by π/180. For example, 180 degrees equals π radians, and 90 degrees equals π/2 radians. This angle converter handles the calculation automatically.
What is the difference between a gradian and a degree?
A gradian (also called gon) divides a right angle into 100 units, so a full circle equals 400 gradians. A degree divides a full circle into 360 units. One gradian equals 0.9 degrees, and one degree equals 1.111 gradians. Gradians are primarily used in surveying and civil engineering in some European countries.
How many arcminutes are in a degree?
One degree contains 60 minutes of arc (arcminutes). Each arcminute contains 60 seconds of arc (arcseconds). This sexagesimal system originated in ancient Babylon and is still used today for precise angle measurements in astronomy, navigation, and surveying.
What is a radian and why is it used?
A radian is the SI standard unit for measuring angles. One radian is the angle created when the arc length equals the radius of the circle, approximately 57.2958 degrees. Radians are preferred in calculus, trigonometry, and physics because they simplify formulas and make mathematical relationships more natural.
How do you convert degrees to degrees minutes seconds?
To convert decimal degrees to degrees, minutes, and seconds: the integer part is the degrees, multiply the decimal remainder by 60 to get minutes, then multiply the remaining decimal by 60 to get seconds. For example, 48.6311° equals 48 degrees, 37 minutes, and 52 seconds.
Is the angle converter accurate for scientific calculations?
Yes, all conversions use scientifically accepted mathematical conversion factors. Degrees to radians use the π/180 factor, gradians convert precisely at 0.9 degrees per gradian, and arcminutes and arcseconds use the standard 1/60 and 1/3600 factors. Results are displayed with up to 6 decimal places for precision.