Angle Converter

About Angle converter

Converts angles between degrees, radians, gradians, turns, arcminutes, arcseconds and NATO mils, and translates between decimal degrees and degrees-minutes-seconds notation. It also shows the sine, cosine and tangent of the angle, which helps when you are checking trigonometry homework.

How to use it

1. Enter a number in the Value box and choose its Unit. The page opens on 45 degrees.
2. Look down the All units table to see the angle expressed in every unit.
3. Under Convert a pair, choose Convert to, or press Swap to exchange the two units.
4. In the Degrees, minutes, seconds section, parse a DMS string or format decimal degrees, choosing 0 to 4 decimals for the seconds.

A 45 degree angle in other units

45°

0.78539816 rad, 50 gon, 0.125 turn, 2700 arcminutes, 162000 arcseconds, 800 mil

When to use it

• Moving between degrees and radians for trigonometry or graphics code.
• Converting GPS coordinates written as 45°30'15" into decimal degrees for a map app.
• Reading a surveying angle given in gradians.
• Checking a rifle scope or artillery value in NATO mils.

Questions about Angle converter

Which mil does the tool use?

The NATO mil, with 6400 to a full turn. Other armies use 6000 or 6300, and the true milliradian is about 6283.19 per turn, so confirm which one your source means.

What DMS formats can it read?

45°30'15", 45 30 15, 45d30m15s, -12° 5' 3.5" and plain 45.5. A leading minus applies to the whole angle, and minutes and seconds must each be below 60.

How does it avoid showing 60 seconds?

Seconds are rounded first and then carried, so 59.999 seconds at two decimals becomes the next minute instead of printing as 60.

What does the Normalized badge mean?

It wraps your angle into the range 0 to 360 degrees, so 450 degrees is shown as 90 and -90 as 270.

Why is the tangent enormous near 90 degrees?

The tangent grows without limit there, so a value like 89.9999 can be huge. That is a property of the function, not an error.

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