Click any row to load that angle into the converter.
How to Use This Converter
Pick your source and target units from the dropdowns, type in a value, and hit Convert. The swap button (↔) flips the conversion direction if you need to go the other way.
The Quick Conversion buttons set common unit pairs. The Preset Angles fill in values like 30°, 45°, 90° so you don't have to type them. If you want to see an angle in every unit at once, switch to Convert to All mode.
Negative angles convert correctly—they represent clockwise rotation. Values over 360° represent multiple rotations. Use the Options panel if you need to adjust decimal places, turn on scientific notation, or normalize angles to a specific range.
Quick Examples
45 degrees to radians:
What about π/6 radians to degrees? Multiply by 180/π: that gives you (π/6) × (180/π) = 180/6 = 30°.
A compass bearing of 225°:
Degrees, Radians, and Gradians
Degrees go back to the ancient Babylonians and their base-60 math. Why 360 in a circle? Maybe it was close to the days in a year, or maybe they just liked that 360 divides evenly by so many numbers (2, 3, 4, 5, 6, 8, 9, 10, 12...). Degrees stuck around because they work well in everyday situations—construction, navigation, giving directions.
Calculus and physics need something different. Radians define an angle by the arc length: one radian is when the arc equals the radius. A full circle is 2π radians (about 6.283). The derivative of sin(x) equals cos(x)—but only when x is in radians. Use degrees and you'd have π/180 factors everywhere.
Gradians? French metric system, 1790s. A right angle is exactly 100 gradians, full circle is 400. Surveyors use them—slope calculations come out as clean percentages. You'll still see a GRAD mode on scientific calculators.
Key Conversion Formulas
Here's how they relate: 360° = 2π radians = 400 gradians = 1 turn. Half that is 180° = π rad = 200 grad. A right angle is 90° = π/2 rad = 100 grad.
deg = rad × 180/π
(Memorize: π rad = 180°)
Gradians to degrees: multiply by 0.9
For quick estimates: 1° ≈ 0.0175 rad, and 1 rad ≈ 57.3°
Arcminutes, Arcseconds, and DMS
One degree = 60 arcminutes (symbol: ′). One arcminute = 60 arcseconds (symbol: ″). So there are 3,600 arcseconds in a degree.
Astronomers measure star positions in arcseconds—the Moon spans about 31 arcminutes across, roughly half a degree. Rifle scopes use MOA (minute of angle) for adjustments. GPS coordinates and surveyors sometimes write angles in DMS notation: 45° 30′ 15″ instead of 45.504167°.
Why Radians Matter in Math
Radians come directly from circle geometry—the arc length divided by the radius. That's not arbitrary. Calculus relies on this: d/dx sin(x) = cos(x), but only when x is in radians. Same for d/dx cos(x) = -sin(x). The small angle approximation (sin θ ≈ θ for small θ) also requires radians. And arc length simplifies to s = rθ.
Degrees would require a π/180 factor in every derivative. More to memorize, more chances for error.
In programming: JavaScript, Python, C++, and most other languages expect radians in trig functions. Math.sin(), Math.cos(), and Math.tan() all take radians. Math.atan2() returns radians. To convert, use radians = degrees * Math.PI / 180. Interfaces may show degrees for readability, but the underlying calculation often needs radians. Angle wrapping also matters when results must stay inside a range such as -180° to 180°.
When Angle Conversions Matter
Angle conversions appear in trigonometry, navigation, mapping, surveying, CAD, robotics, astronomy, and software development. The right unit depends on the context: degrees are easy to read, radians are natural for math, gradians are still used in some surveying workflows, and DMS notation is common in coordinates.
Trigonometry and Calculators
Most classroom problems show angles in degrees, while calculus and programming libraries usually use radians. When solving trig expressions, confirm the angle mode before using sine, cosine, tangent, inverse trig functions, or graphing tools. For triangle-side and trig function work, use the Arcminutes to Degrees Converter after the angle unit is converted.
Navigation, Bearings, and Coordinates
Compass bearings are usually written in degrees from north. Latitude and longitude may appear as decimal degrees or DMS, such as 40 degrees 26 minutes 46 seconds. Converting DMS to decimal degrees makes coordinates easier to paste into maps, spreadsheets, and GIS tools.
Normalization and Rotation
An angle can describe the same direction in more than one way. For example, 450 degrees points the same direction as 90 degrees after one full rotation is removed. Normalizing to 0 to 360 degrees is common for compass-style directions, while -180 to 180 degrees is common in some programming and mapping workflows.
Quick Answers
Using Angle Converter for one defined quantity
Angle Converter compares several angular measurements units without changing the underlying measured quantity. Use one source value from one plane or rotational angle with a stated circle, direction, orientation, and notation convention.
This broader hub is useful for geometry, surveying, navigation, machining, astronomy, and rotation. Within Angle Converter, select the actual source and destination labels before interpreting the numerical difference; a familiar abbreviation is not evidence that the correct unit was selected.
Within Angle Converter, the converter performs arithmetic from the entered value and selected units. Within Angle Converter, it does not measure the source, identify its standard, inspect its context, or decide how much precision the destination record supports.
Source records for angular measurements
Distinguish degrees, radians, gradians, turns, arcminutes, and arcseconds. Sexagesimal degree notation should not be mistaken for decimal degrees.
Write the source number and unit together before opening Angle Converter. Within Angle Converter, after conversion, retain the destination symbol beside the answer and keep the original entry available for review.
Within Angle Converter, if multiple records use different units, convert each row to one agreed destination before adding, averaging, sorting, or comparing thresholds. Within Angle Converter, do not edit the source column into an unlabeled mixture.
Checking the selected unit path
Convert through a full-turn fraction or radians, then reverse the selected destination to the source angle.
Within Angle Converter, an inverse conversion should recover the source within rounding. Within Angle Converter, a second route is stronger when it uses a base unit or independently derived relationship rather than the same selected menus and value.
Within Angle Converter, test a simple benchmark such as zero, one source unit, or a known reference quantity. Within Angle Converter, for reciprocal or offset relationships, use the governing equation instead of assuming that doubling always behaves like a zero-offset multiplier.
Precision, limits, and related conversions
Important boundaries for Angle Converter include decimal versus degrees-minutes-seconds notation, signed direction, wrapped angles, plane versus solid angle, bearing conventions, and trigonometric input mode. Within Angle Converter, keep the boundary that applies to the source record beside the converted answer.
Within Angle Converter, round after the final required conversion, not at every intermediate menu change. Within Angle Converter, the source measurement limits the defensible significant digits even when the interface displays a longer decimal.
For focused follow-up calculations from Angle Converter, open Degrees To Radians Converter, Radians To Degrees Converter and Arcminutes To Degrees Converter. These linked pages keep the angular measurements source and destination visible and provide an inverse check for their specific unit pair.
Questions about Angle Converter
Can values from different units be totaled?
FAQ guidance for Angle Converter: only after all entries represent the same physical quantity and have been converted to one shared unit. FAQ guidance for Angle Converter: retain the original unit in a separate column for traceability.
What does Angle Converter change?
It changes the numerical representation and unit label for the selected angular measurements quantity. FAQ guidance for Angle Converter: it does not change or remeasure the underlying object, interval, condition, or record.
How should a result from Angle Converter be checked?
As an independent FAQ check for Angle Converter, convert through a full-turn fraction or radians, then reverse the selected destination to the source angle. FAQ guidance for Angle Converter: also confirm that the inverse returns the entered source within the chosen rounding.