TinySandyFree Online Tools

Angle Converter

Convert an angle between degrees, radians, gradians (gon), full turns, arcminutes, arcseconds, milliradians and NATO mils. Degrees and radians are related through π (180° = π rad), so those results are accurate to better than 40 digits, far beyond what is displayed. All the other angle units are exact fractions of a turn.

Unit Converters Runs in your browser

Convert an Angle

The mil used is the NATO mil (1/6400 of a turn). Other mils exist, and the milliradian is listed separately. π is carried to 45 digits.

Decimals and scientific notation such as 1.5e3 are accepted.
Automatic shows exact results in full and rounds long ones to 12 significant digits. A value too small for the chosen decimal places is shown with 3 significant digits instead of 0.

How to Use the Angle

  1. Type the value you want to convert in Value to convert.
  2. Pick the starting angle unit in From unit and the one you want in To unit. The lists are grouped by measurement system.
  3. Read the result and the formula directly under the form; it updates as you type. Use Swap units to reverse the direction.
  4. Scroll to the table to see the same value in every available unit, change Precision if you need fewer digits, or press Copy result.

About This Tool

Students in trigonometry and calculus, programmers working with rotation functions that expect radians, surveyors using gradians, navigators and astronomers using arcminutes and arcseconds, and shooters and artillery observers using mils.

Input: A number and a unit  ·  Output: The same angle in every unit.

Features and Limitations

Features

  • Exact fractions of a turn: 1 turn = 360° = 400 grad = 21 600 arcminutes = 1 296 000 arcseconds = 6400 NATO mils.
  • Radian conversions use π to 45 digits and are shown to 12 significant digits by default.
  • Negative angles are accepted (clockwise versus counter-clockwise).
  • Formula text and a table with the angle in every unit.

Limitations

  • The word “mil” has several meanings: NATO 6400 per turn, Soviet 6000, Swedish 6300 and the milliradian (6283.2 per turn). This tool uses NATO 6400 and lists milliradians separately.
  • Angles are not wrapped, so 450° stays 450° and is not reduced to 90°.
  • Results are computed in your browser; nothing you enter is sent to a server.

Example

180° = π rad = 3.14159265359 rad. 90° = 100 grad. 1 rad = 57.29577951°. 1° = 60′ = 3600″. 30° = 0.5235987756 rad. 1 turn = 2π rad = 6400 mil. 1 mil = 0.05625°.

Frequently Asked Questions

How do I convert degrees to radians?

Multiply by π/180. For example 30° × π/180 = 0.5236 rad. To convert radians to degrees multiply by 180/π, so 1 rad is 57.2958°.

What is a gradian?

A gradian, also called a gon or grade, divides a right angle into 100 parts, so a full circle is 400 grad and 90° = 100 grad. It is used in some surveying and civil engineering work, particularly in continental Europe.

Why do programming languages use radians?

Calculus formulas for sine and cosine are simplest in radians, so functions such as sin() and cos() in JavaScript, Python and C expect them. Convert degrees to radians before calling them: 90° is π/2 ≈ 1.5708.

How big is a mil?

A NATO mil is 1/6400 of a turn, 0.05625°. A milliradian is 0.0573°. Both are close to 1 m of spread per 1000 m of range, which is why they are used for aiming and rangefinding.

Related Tools

More like this: all Unit Converters tools, all Converters tools or the TinySandy home page.