Angle Conversion Calculator 2026
Convert between degrees, radians, gradians, minutes, seconds & circle fractions
Conversion Result
3.14159265 rad
180° = π rad
Understanding Angle Units
📐 Degrees
The most common angle unit. A full circle = 360°. Used in navigation, geometry, and everyday measurements.
🔄 Radians
The SI unit for angles. A full circle = 2π rad ≈ 6.283 rad. Essential in calculus, physics, and engineering.
📊 Gradians
Also called gons. A full circle = 400 grad. Popular in surveying because a right angle = 100 grad exactly.
🎯 Minutes & Seconds
1° = 60 minutes ('), 1' = 60 seconds ("). Used in astronomy, navigation, and geographic coordinates.
Angle Conversion Table
| Unit | Symbol | In Degrees | In Radians |
|---|---|---|---|
| Degree | ° |
1 | π/180 ≈ 0.01745 |
| Radian | rad |
180/π ≈ 57.2958 | 1 |
| Gradian | grad |
0.9 | π/200 |
| Mil (NATO) | mil |
0.05625 | π/3200 |
| Minute | ' |
1/60 ≈ 0.01667 | π/10800 |
| Second | " |
1/3600 ≈ 0.000278 | π/648000 |
| Full Circle | rev |
360 | 2π ≈ 6.2832 |
Frequently Asked Questions
How do I convert degrees to radians?
To convert degree to radian, multiply by π/180. Formula: radians =
degrees × (π/180). For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians.
How do I convert radians to degrees?
For radian to degree conversion, multiply by 180/π. Formula:
degrees = radians × (180/π). For example, π rad = π × 180/π = 180°.
What is the relationship between degrees and radians?
A full circle equals 360° or 2π radians. Therefore, 180° = π rad, 90° = π/2 rad,
and 1 radian ≈ 57.2958°. This conversion of degree to radian is fundamental in
trigonometry.
What is a gradian (grad)?
A gradian divides a circle into 400 equal parts. One grad = 0.9°. Right angles =
100 grad exactly, making gradians useful in surveying and civil engineering.
How do I convert angles to arc length (mm)?
For angle to mm conversion, use: arc length = radius × angle (in
radians). If radius is in mm, result is in mm. Example: 45° at 100mm radius = 100 × 0.7854 = 78.54mm arc
length.
How do I convert arc length to angle?
For mm to angle conversion: angle (radians) = arc length / radius.
Then convert to degrees if needed. Example: 50mm arc at 100mm radius = 0.5 rad = 28.65°.
What are minutes and seconds in angle measurement?
These are subdivisions of degrees. 1° = 60 arcminutes ('), 1' = 60 arcseconds (").
Used in GPS coordinates, astronomy, and precise surveying.
What is a mil (military unit)?
NATO mil divides a circle into 6400 parts. 1 mil ≈ 0.05625°. Used in artillery and
military applications for precise angular measurements at long distances.
Why are radians used in physics and calculus?
Radians simplify formulas. With radians, sin(x) ≈ x for small angles, and
derivatives of trig functions work cleanly: d/dx(sin x) = cos x only when x is in radians.
What is a point in navigation?
A compass point = 11.25° (1/32 of a circle). Traditional navigation divides the
compass into 32 points. Used historically in maritime and aviation navigation.
How do circle fractions work?
Circle fractions express angles as parts of a full rotation. 1/4 circle = 90° = π/2
rad. 1/2 circle = 180° = π rad. Useful for quick mental calculations.
What's the difference between angle units?
Different fields prefer different units: degrees for everyday use, radians for
math/science, gradians for surveying, mils for military. All measure the same thing—rotation amount.
How accurate is this angle converter?
This calculator uses JavaScript's full double-precision (64-bit) floating-point
arithmetic, providing approximately 15-16 significant digits of precision.
Can I convert negative angles?
Yes! Negative angles represent clockwise rotation. The conversion formulas work
identically: -90° = -π/2 rad ≈ -1.5708 rad.
What does angle conversion mean in geometry?
Angle conversion means expressing the same angular measure in
different units. The physical angle stays the same; only the numerical representation changes.
How do I use angles to find arc length and chord length?
Arc length = r × θ (θ in radians). Chord length = 2r × sin(θ/2). This is key for
angle to length conversion in engineering and design.
What is angle unit conversion used for?
Angle unit conversion is used in CAD software, navigation systems,
physics calculations, surveying, astronomy, and any field requiring angular measurements.