# Angle Converter

Free angle converter. Convert between degrees, radians, gradians, turns, arcminutes, and arcseconds with precise calculations.

## What this calculates

Convert between all common angle measurement units including degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians. Essential for math, engineering, navigation, and astronomy.

## Inputs

- **Value**
- **From** — options: Degrees (°), Radians (rad), Gradians (gon), Turns, Arcminutes (′), Arcseconds (″), Milliradians (mrad)
- **To** — options: Degrees (°), Radians (rad), Gradians (gon), Turns, Arcminutes (′), Arcseconds (″), Milliradians (mrad)

## Outputs

- **Result** — The converted angle value.
- **Conversion** — formatted as text — Step-by-step conversion explanation.

## Details

Angle measurements are used across mathematics, engineering, navigation, and astronomy. Different fields prefer different units.

Key Conversion Factors

- 1 full circle = 360° = 2π radians = 400 gradians = 1 turn

- 1 radian = 180/π ≈ 57.2958°

- 1 degree = π/180 ≈ 0.01745 radians

- 1 gradian = 0.9° (400 gradians in a circle)

- 1 degree = 60 arcminutes = 3,600 arcseconds

Unit Applications

- Degrees: everyday use, navigation, geography

- Radians: mathematics, physics, engineering

- Gradians: surveying, civil engineering

- Arcminutes/arcseconds: astronomy, precision optics

- Milliradians: military ballistics, telescopic sights

## Frequently Asked Questions

**Q: How do I convert degrees to radians?**

A: Multiply the degree value by π/180. For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians. Common values: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π.

**Q: What is a gradian and where is it used?**

A: A gradian (also called a gon or grade) divides a right angle into 100 parts, so a full circle is 400 gradians. It is primarily used in surveying and civil engineering because the decimal-based system simplifies calculations involving right angles and slopes.

**Q: What are arcminutes and arcseconds?**

A: Arcminutes and arcseconds subdivide degrees for precision. 1 degree = 60 arcminutes (′), and 1 arcminute = 60 arcseconds (″). They are extensively used in astronomy (star positions), navigation (latitude/longitude), and optics.

**Q: Why do mathematicians prefer radians?**

A: Radians are the natural unit for angles because they simplify calculus formulas. The derivative of sin(x) is cos(x) only when x is in radians. Similarly, the Taylor series expansions and many physics equations assume radian measure.

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Source: https://vastcalc.com/calculators/conversion/angle-converter
Category: Conversion
Last updated: 2026-04-21