Angle Converter

Convert between degrees, radians, gradians, minutes, seconds, and milliradians. View π equivalence for radian values.

About this Calculator

Convert between degrees, radians, gradians, minutes, seconds, and milliradians. View π equivalence for radian values.

Formula & Calculations

Formula

Result = Input value × (Conversion factor from unit / Conversion factor to unit), normalized to degrees

Where:

deg=Degrees (360° = full circle)
rad=Radians (2π rad = full circle, base unit for calculations)
grad=Gradians / gon (400 grad = full circle)
′=Arcminutes (60′ = 1°, 21,600′ = full circle)
″=Arcseconds (60″ = 1′, 3,600″ = 1°)
mrad=Milliradians / mils (about 6283.19 mrad = full circle)

Assumptions

All conversions pass through degrees as the intermediate base unit.
Gradians follow the definition of 400 grad = 360°.
π is approximated to 15 decimal places for precision.

Calculation Examples

Example 1

Inputs:180 degrees to radians

Result:3.14159 rad (π rad)

180° × π ÷ 180 = π ≈ 3.14159 rad.

Example 2

Inputs:π/2 radians to degrees

Result:90°

π/2 × 180 ÷ π = 90°.

Example 3

Inputs:30 degrees to arcminutes

Result:1800′

30 × 60 = 1800 arcminutes.

Frequently Asked Questions

What are gradians used for?

Gradians (also called gon or grade) divide a circle into 400 units instead of 360. They are primarily used in surveying and some European engineering fields because each quadrant is exactly 100 gradians.

What is the difference between arcminutes and time minutes?

An arcminute is 1/60 of a degree and measures angles. A time minute is 1/60 of an hour. They are unrelated — one measures space/angles, the other measures time.

What are milliradians used for?

Milliradians (mils) are widely used in military optics and long-range shooting. One mil subtends approximately 1 meter at 1000 meters distance, making range estimation straightforward.