How do you convert degrees to radians?

To convert degrees to radians, multiply by π/180. The formula is: Radians = Degrees × π ÷ 180. For example, 180° = 180 × π/180 = π ≈ 3.14159 radians, and 90° = π/2 ≈ 1.5708 radians.

What is a gradian (grad)?

A gradian (also called a gon) divides a right angle into 100 equal parts, so a full circle equals 400 gradians. Gradians were created during the French Revolution to metricate angle measurement and are still widely used in surveying, civil engineering, and geodesy across Europe.

How many degrees are in 2π radians?

2π radians = 360 degrees, which is a full rotation. This is because 1 radian = 180/π ≈ 57.2958 degrees. So 2π × 57.2958 ≈ 360 degrees. Radians are the SI unit of angle and are used in physics, engineering, and calculus.

What is the difference between NATO mils and Soviet mils?

The NATO mil divides a full circle into 6,400 units (1 mil = 0.05625°), while the former Soviet/Warsaw Pact system uses 6,000 mils (1 mil = 0.06°). Both approximate 1 milliradian but use round numbers for field artillery calculations. NATO mils are standard in Western militaries for mortars, artillery, and map reading.

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Convert from Degrees (°)

degrees to radians degrees to gradians degrees to arcminutes degrees to arcseconds degrees to milliradians degrees to revolutions degrees to mils (NATO) degrees to turns

Convert to Radians (rad)

degrees to radians gradians to radians arcminutes to radians arcseconds to radians milliradians to degrees revolutions to degrees mils (NATO) to degrees turns to degrees

All Angle Conversions from Degrees

Angle Units Explained

Degrees (°)

The most familiar angle unit. A full rotation = 360°. A right angle = 90°. Angles are used in geometry, navigation, carpentry, and astronomy. The choice of 360° for a full circle dates back to ancient Babylonian astronomy and their base-60 counting system.

Radians (rad)

The SI unit of angle. 1 radian is the angle where arc length = radius. A full circle = 2π rad ≈ 6.2832 rad. Radians simplify calculus (derivatives of sin/cos have no constants) and are the natural unit in physics, engineering, and advanced mathematics.

Gradians (grad)

Also called gons, gradians divide a right angle into 100 units (full circle = 400 grad). Created during the French Revolution to metricate angle measurement. Heavily used in surveying, civil engineering, and geodesy across Europe, especially in France and Sweden.

Arcminutes & Arcseconds

Arcminutes (1/60°) and arcseconds (1/3600°) provide fine angular precision. One arcminute of latitude = 1 nautical mile (1,852 m). Arcseconds are used in astronomy — the Hubble Space Telescope resolves 0.05 arcsecond detail. Atmospheric seeing is typically 1–2 arcseconds.

Milliradians (mrad)

1 mrad = 0.001 rad ≈ 0.0573°. At 1,000 m range, 1 mrad subtends exactly 1 m — making it ideal for military optics, long-range shooting, and artillery targeting. Most modern tactical rifle scopes use mrad (mil-dot) adjustments of 0.1 mrad per click.

Mils — NATO vs. Soviet

The NATO mil divides a full circle into 6400 units (1 mil = 0.05625°). The former Soviet/Warsaw Pact system uses 6000 mils (1 mil = 0.06°). Both approximate 1 mrad but with round numbers for field calculations. NATO mils are standard in Western militaries for artillery, mortars, and map reading.

Quick Reference: Key Conversions

180° = π rad ≈ 3.14159 rad 1 rad ≈ 57.2958° 1° = 60 arcminutes 1° = 3600 arcseconds 90° = 100 gradians 360° = 400 gradians 1 revolution = 360° = 2π rad 1° ≈ 17.4533 milliradians 360° = 6400 mils (NATO) 1 compass point = 11.25°