Angle Unit Converter — Degrees, Radians, Gradians and More
Convert angle units fast — degrees, radians, gradians, minutes of arc, seconds of arc, and turns. Includes formulas, a reference table, and practical use cases.
Most people learned angles in degrees in school and never thought much about it again. Then you open a programming language, start doing trigonometry, work with a surveying instrument, or read a technical paper — and suddenly angles are in radians, gradians, or milliradians, and the familiar numbers are nowhere to be seen.
The CalcHub angle converter translates between degrees, radians, gradians, arcminutes, arcseconds, and full turns without requiring you to remember the formulas.
Angle Conversion Reference Table
| From | To | Multiply by |
|---|---|---|
| 1 degree (°) | radians (rad) | π/180 ≈ 0.0174533 |
| 1 radian (rad) | degrees (°) | 180/π ≈ 57.2958 |
| 1 degree (°) | gradians (grad) | 10/9 ≈ 1.11111 |
| 1 gradian (grad) | degrees (°) | 0.9 |
| 1 turn (full rotation) | degrees | 360 |
| 1 turn | radians | 2π ≈ 6.28318 |
| 1 degree | arcminutes (') | 60 |
| 1 arcminute | arcseconds ('') | 60 |
| 1 degree | arcseconds | 3,600 |
| 1 radian | gradians | 200/π ≈ 63.6620 |
Angles at Common Reference Points
| Angle in Degrees | In Radians | In Gradians | What It Looks Like |
|---|---|---|---|
| 0° | 0 | 0 | Flat, no rotation |
| 30° | π/6 ≈ 0.5236 | 33.33 grad | One-twelfth of a circle |
| 45° | π/4 ≈ 0.7854 | 50 grad | Half a right angle |
| 60° | π/3 ≈ 1.0472 | 66.67 grad | Equilateral triangle corner |
| 90° | π/2 ≈ 1.5708 | 100 grad | Right angle |
| 120° | 2π/3 ≈ 2.0944 | 133.33 grad | Interior angle of equilateral triangle |
| 180° | π ≈ 3.14159 | 200 grad | Straight line |
| 270° | 3π/2 ≈ 4.7124 | 300 grad | Three-quarter turn |
| 360° | 2π ≈ 6.2832 | 400 grad | Full circle |
Why Different Angle Units Exist
Degrees are the everyday unit — a full circle is 360°. The 360 degree convention comes from ancient Babylonian astronomy and the approximate number of days in a year. Radians are the natural unit for mathematics and physics. A radian is the angle subtended by an arc equal in length to the radius of the circle. The entire circle spans 2π radians, which is why so many physics and engineering formulas drop the unit entirely — radians are dimensionless. Trigonometric functions in programming languages (sin, cos, tan) almost universally expect radians, not degrees. Gradians (also called gon or grade) divide a right angle into 100 units, making a full circle 400 gradians. This was developed during the French Revolution alongside the metric system and is still used in surveying, particularly in Europe and for civil engineering work. Arcminutes and arcseconds subdivide degrees for precision. Astronomy, navigation, and cartography use these for very small angle measurements. GPS coordinates use decimal degrees, but older formats use degrees + arcminutes + arcseconds (e.g., 40°26′47″N).How to Use the CalcHub Angle Converter
- Open calchub.in and go to the Angle Converter
- Type in your angle value
- Select the unit you're working with
- View the equivalent in all other angle units instantly
Common Situations Where This Matters
Programming and game development —Math.sin(angle) in JavaScript, Python, C++, and most languages expects radians. Passing in 90 (thinking degrees) gives you sin(90 radians) which is approximately 0.894 — not 1.0. The fix: convert 90° to π/2 rad first.
CNC machining and robotics — motor rotation and tool angles are often specified in radians or degrees depending on the control software. Getting this wrong wastes material or damages equipment.
Navigation and GPS — latitude/longitude is in degrees, arcminutes, and arcseconds (DMS format) or decimal degrees (DD format). 48°51'24"N = 48.8567°N. Surveyors in Europe might record the same bearing in gradians.
Why do radians make math simpler?
With radians, arc length = radius × angle. Simple and clean. The derivative of sin(x) is cos(x) only when x is in radians — in degrees it becomes cos(x) × π/180, which clutters every formula. Physics equations involving waves, oscillations, and rotation assume radians throughout.
What is a milliradian, and who uses it?
A milliradian (mrad) is 1/1000 of a radian. At 1,000 meters distance, 1 mrad corresponds to 1 meter of lateral displacement. This makes it extremely useful for long-range shooting, artillery, and military optics — a scope adjustment of 1 mrad moves the point of impact by 1 cm per 10 meters of range.
How do I convert degrees to radians in my head?
Multiply by π/180, which is approximately 0.01745. Or use the fact that 180° = π rad, so 90° = π/2, 45° = π/4, 30° = π/6, 60° = π/3. Memorizing those five benchmarks covers the most common trig problems.
Related Converters
- Length Converter — meters, feet, miles (useful with arc length calculations)
- Speed Converter — angular velocity relates to linear speed
- Time Converter — rotational speed (rpm) involves both angle and time