Angle Conversion Calculator
What Is an Angle Conversion Calculator?
An Angle Conversion Calculator is a digital tool designed to instantly convert one angular unit into another. Instead of memorizing formulas, you can simply enter your value, select the “from” and “to” units, and get accurate results.
For example:
If you have 5 radians and want to know how many degrees that equals, multiply by the conversion factor.
Formula:
S × C = E
Where:
- S = Starting value
- C = Conversion factor
- E = End result
So, 5 radians × 57.29578 = 286.4789 degrees
How to Convert Units of Angles (Step-by-Step)
All angular conversions are based on conversion factors, which are ratios that link one unit to another.
To convert any angle to degrees, multiply the given value by its corresponding factor from the table below.
If you want to convert from degrees to another unit, divide by the same factor (or multiply by its reciprocal).
Example:
To convert 286.4789 degrees back into radians:
286.4789 ÷ 57.29578 = 5 radians
This method works for all angle conversions — from radians to revolutions, degrees to mils, and beyond.
Understanding Conversion Factors
Each angular unit represents a specific part of a full circle. Knowing these relationships helps you visualize conversions intuitively.
| Convert From | Symbol | Convert To Degrees (°) | Multiply By | Convert To Unit | Multiply By |
|---|---|---|---|---|---|
| Radian | rad | 57.29578 | 57.29578 | Radian | 1 |
| Degree | ° | 1 | 1 | Radian | 0.01745329 |
| Minute | ‘ | 0.016667 | 1/60 | Radian | 0.0002908882 |
| Second | “ | 0.000277778 | 1/3600 | Radian | 0.00000484814 |
| Octant | octant | 45 | 45 | Radian | 0.7853982 |
| Sextant | sextant | 60 | 60 | Radian | 1.047196 |
| Quadrant | quadrant | 90 | 90 | Radian | 1.570796 |
| Revolution | r | 360 | 360 | Radian | 6.283185 |
| Gon | gon | 0.9 | 0.9 | Radian | 0.01570796 |
| Mil | mil | 0.05625 | 0.05625 | Radian | 0.0009817477 |
Common Angle Conversion Formulas
Here are the most useful plain text formulas for quick calculations:
- Degrees to Radians: radians = degrees × π / 180
- Radians to Degrees: degrees = radians × 180 / π
- Degrees to Revolutions: revolutions = degrees / 360
- Revolutions to Degrees: degrees = revolutions × 360
- Degrees to Minutes: minutes = degrees × 60
- Minutes to Degrees: degrees = minutes / 60
- Degrees to Seconds: seconds = degrees × 3600
- Seconds to Degrees: degrees = seconds / 3600
Why Angle Conversion Matters
Precise angle conversion is essential in many fields:
- Engineering: For torque, slope, and rotational velocity calculations.
- Astronomy: To calculate celestial object positions in arcseconds.
- Navigation: Converting bearings and courses between mils and degrees.
- Mathematics: When switching between radians and degrees in trigonometric functions.
Even small conversion errors can cascade into large inaccuracies in measurement or design.
Example: Radians to Revolutions Conversion
Let’s apply the rule to convert radians to revolutions.
Formula:
radians × (57.29578 ÷ 360) = revolutions
Example:
5 radians × 0.1591549 = 0.79577 revolutions
This shows that 5 radians cover almost 80% of a full revolution.
Pro Tip: Simplify Decimal Degrees to DMS
If you work in surveying, astronomy, or navigation, you often need to convert decimal degrees into degrees, minutes, and seconds (DMS) format.
Try the Decimal Degrees to DMS Converter for a fast and accurate breakdown.
Angle Units Explained Simply
Degrees (°): The most familiar unit; a full rotation equals 360°.
Radians (rad): Common in advanced math and physics; a full circle equals 2Ï€ radians.
Revolution (rev): A single complete turn or 360°.
Gradian (gon): Divides a circle into 400 parts — used in surveying.
Mil: Used mainly in the military for targeting; 1 revolution equals 6400 mils.
Angle Conversion in Everyday Applications
- GPS & Mapping: Systems often use radians internally but display degrees for users.
- Computer Graphics: Angles in radians define object rotations and transformations.
- Cooking & Construction Tools: Protractors and inclinometers often measure in degrees or radians.
If you frequently convert distance or area values along with angles, check out the Distance Converter and Area Converter — they complement angular calculations in spatial measurements.
Using the Angle Conversion Calculator Efficiently
- Enter the numeric value.
- Choose the input unit (like degrees or radians).
- Select the output unit you need.
- Click “Convert” — and get instant results.
Most calculators use precise constants (Ï€ = 3.14159265) to minimize rounding errors, giving you highly accurate outcomes for engineering and academic work.
Quick Reference Conversion
| From | To | Formula |
|---|---|---|
| Degrees → Radians | radians = degrees × π / 180 | 90° = 1.570796 rad |
| Radians → Degrees | degrees = radians × 180 / π | 2 rad = 114.592° |
| Degrees → Revolutions | rev = degrees / 360 | 720° = 2 rev |
| Revolutions → Degrees | degrees = rev × 360 | 0.5 rev = 180° |
| Degrees → Gradians | gon = degrees × 400 / 360 | 180° = 200 gon |
Simplify Every Angle Conversion
The Angle Conversion Calculator saves time, eliminates human error, and helps professionals and students handle angle conversions instantly. By applying the simple formulas and conversion factors discussed here, you can switch between degrees, radians, revolutions, and other angular units with total confidence.
For accurate, fast, and versatile conversions — explore the full Conversion Tools Collection and make your calculations effortless across every unit system.