Angle Unit Converter
Select units from both columns and enter a value to instantly convert between 12 different angle measurement systems
From Unit
To Unit
Common Angle Conversions Reference
| Angle | Degrees | Radians | Gradians | Minutes | Seconds |
|---|---|---|---|---|---|
| Full Circle | 360° | 2π rad | 400 gon | 21,600′ | 1,296,000″ |
| Half Circle | 180° | π rad | 200 gon | 10,800′ | 648,000″ |
| Right Angle | 90° | π/2 rad | 100 gon | 5,400′ | 324,000″ |
| Acute Angle | 45° | π/4 rad | 50 gon | 2,700′ | 162,000″ |
| Straight Angle | 180° | π rad | 200 gon | 10,800′ | 648,000″ |
How to Use the Angle Unit Converter
Our angle measurement converter is designed for simplicity and precision. Here's how to use it:
- Select "From" Unit - Choose the angle unit you want to convert from in the left column
- Select "To" Unit - Choose the target angle unit in the right column
- Enter Value - Input the numerical value you want to convert in the input field
- View Results - The conversion result appears instantly in the transparent result panel
- Quick Conversions - Use the quick buttons for common conversions like 90° to radians
The converter supports all 12 angle measurement units with real-time calculation and high precision.
Features of Our Angle Measurement Calculator
12 Angle Units
Convert between degrees, radians, gradians, minutes, seconds, milliradians, points, circles, right angles, quadrants, sextants, and turns.
Real-time Conversion
Instant calculations as you type or change units - no need to press any calculate button.
Fully Responsive
Works perfectly on all devices - desktop computers, laptops, tablets, and mobile phones.
High Precision
Uses mathematical constants with 20-digit accuracy for professional and educational use.
Swap Functionality
Easily swap between "From" and "To" units with a single click for reverse conversions.
Quick Reference
Includes conversion table for common angles and quick conversion buttons for frequent calculations.
Detailed Unit Information
Understand each angle measurement unit and its applications:
Degree (°)
The most common angle unit, dividing a circle into 360 equal parts. Used in everyday applications, geometry, navigation, and most consumer applications.
Radian (rad)
The standard unit of angular measure in mathematics and physics. Defined as the angle subtended by an arc equal in length to the radius. Essential for calculus and trigonometric functions.
Gradian (gon)
Also called grad or gon, divides a right angle into 100 units. Commonly used in surveying (especially in Europe), artillery, and some engineering applications.
Minute & Second
Subdivisions of degrees: 1° = 60′ (minutes), 1′ = 60″ (seconds). Used in astronomy, navigation, cartography, and precise angular measurements.
Milliradian (mrad)
Used in military and optical applications for rifle scopes, telescopic sights, and range estimation. 1 radian = 1000 milliradians.
Navigation Points
Traditional compass points dividing the circle into 32 parts. Each point = 11.25°. Used in marine navigation and wind direction reporting.
Frequently Asked Questions (FAQs)
The fundamental relationship is: 360 degrees = 2π radians (approximately 6.283185 radians).
Key conversions:
- 1 degree = π/180 radians ≈ 0.0174533 radians
- 1 radian = 180/π degrees ≈ 57.29578 degrees
- 90 degrees = π/2 radians ≈ 1.5708 radians
- 180 degrees = π radians ≈ 3.14159 radians
Degrees are used in everyday applications, while radians are preferred in mathematics and physics because they simplify trigonometric calculations.
Gradians (also called gon or grad) are an angular measurement unit where a right angle is divided into 100 units instead of 90 degrees.
Key conversions:
- 400 gradians = 360 degrees
- 1 gradian = 0.9 degrees
- 1 degree = 1.11111 gradians
- 100 gradians = 90 degrees (right angle)
Gradians are commonly used in:
- Surveying (especially in Europe)
- Some engineering applications
- Artillery and military targeting
- The French system (centesimal system)
The advantage is simpler calculations with base-100 system.
Minutes and seconds of arc are subdivisions of degrees used for precise angular measurements:
- 1 degree = 60 minutes of arc (arcminutes, symbol ′)
- 1 minute of arc = 60 seconds of arc (arcseconds, symbol ″)
- 1 degree = 3600 seconds of arc
Applications:
- Astronomy: Measuring apparent sizes of celestial objects and angular distances between stars
- Navigation: Precise bearing measurements, nautical miles (1 nautical mile = 1 minute of latitude)
- Cartography: Map coordinates (degrees, minutes, seconds format)
- Optics: Measuring resolution and field of view
- Surveying: High-precision angle measurements
Milliradians (mrad) are thousandths of a radian:
- 1 radian = 1000 milliradians
- 1 milliradian = 0.001 radians ≈ 0.0573 degrees ≈ 3.44 minutes of arc
Applications:
- Military: Firearm sights (mil-dot reticles) for range estimation and bullet drop compensation
- Optics: Rifle scopes, telescopic sights, binocular specifications
- Surveying: Theodolites and total stations
- Physics: Small angle approximations (sin θ ≈ tan θ ≈ θ in radians)
The NATO mil (6400 in a circle) is different from the mathematical milliradian (approximately 6283.185 in a circle).
Our converter uses high-precision calculations with these key constants:
- π = 3.14159265358979323846 (20 decimal places)
- Degree-radian conversion factor: π/180 ≈ 0.017453292519943295
- Radian-degree conversion factor: 180/π ≈ 57.29577951308232
Precision features:
- Calculations performed with double-precision floating point
- No rounding until final display
- Adjustable decimal places (2-10 decimals)
- Scientific notation for very small/large numbers
- Exact fractions preserved where possible (π multiples)
For most practical applications, the precision exceeds requirements for engineering, science, and educational use.
Recommended units by application:
- Mathematics/Physics: Radians (simplifies calculus and trig functions)
- Engineering: Degrees (mechanical design), Radians (vibrations, waves)
- Navigation: Degrees (GPS, modern), Points (traditional marine)
- Astronomy: Degrees, Minutes, Seconds of arc (celestial coordinates)
- Surveying: Gradians (Europe), Degrees/minutes/seconds (US/UK)
- Military/Optics: Milliradians (sighting systems)
- Computer Graphics: Radians (OpenGL, DirectX), Degrees (some CAD)
- Everyday Use: Degrees (most intuitive for people)
- Rotational Mechanics: Revolutions/Turns (RPM, rotational speed)