Angle Converter

Q: Can I enter a negative DMS angle?

Yes: type a minus sign −33° 52′ or a hemisphere letter 33° 52′ S . Both give −33.8667°.

Angle Converter

Convert angles between degrees, radians, gradians, turns, arcminutes and arcseconds, and switch between decimal degrees and degrees-minutes-seconds (DMS).

Value

From

–

Formula:

Significant figures

≈ means the result was rounded to the chosen number of significant figures.

1 turn = 360° = 2π rad = 400 gon. 1° = 60′ (arcminutes) = 3,600″ (arcseconds).

Degrees, minutes, seconds (DMS)

DMS angle

Type an angle such as 48° 51′ 29.6″, 48 51 29.6, 48d51m29.6s or 2°21′E. S and W make the value negative. It is converted to decimal degrees in the converter above.

Value above in DMS: –
Decimal degrees: –
Normalized to 0–360°: –

{value} in every unit

Unit	Result

Quick conversion table: {from} to {to}

From	To

Common values

Reference	Value	Result

Unit definitions

Unit

How to use the angle converter

Type an angle in Value (for example 180, 1.5 or −45) and choose its unit in From.
Choose the unit you want in To. The result appears as you type, with the Formula for the pair and the calculation with your number.
Press Swap units (⇄) to reverse the conversion, change Significant figures for more digits, and press Copy to copy a line such as “180 ° ≈ 3.1415927 rad”.
To work with degrees, minutes and seconds, type an angle in DMS angle, for example 48° 51′ 29.6″ N. It is converted to decimal degrees and loaded into the converter above, so you can read it in radians or any other unit.
Value above in DMS always shows the current value in degrees-minutes-seconds, next to Decimal degrees and the angle Normalized to 0–360°.

Further down, the tool lists your angle in every unit, a quick table for the selected pair (15°, 30°, 45°, 90° and so on), some everyday reference angles and the definition of each unit in degrees.

The units

Degree (°): 1/360 of a full turn. Used in everyday life, navigation and geography.
Radian (rad): the angle for which the arc length equals the radius. A full turn is 2π rad, so 1 rad = 180/π ≈ 57.29578°. Radians are the SI unit and the one used by calculus, physics and programming languages (Math.sin expects radians).
Milliradian (mrad): 1/1000 rad, used in optics and ballistics: 1 mrad covers about 1 m at 1 km.
Gradian or gon: 1/400 of a turn, so a right angle is exactly 100 gon. Common in surveying in continental Europe.
Turn: one full revolution, 360°.
Arcminute (′) and arcsecond (″): 1° = 60′ and 1′ = 60″. Used in astronomy, optics and coordinates.
NATO mil: 1/6400 of a turn, found on military compasses. Other armies use 6000 or 6300 mils per turn, so check your equipment.

Formulas

radians = degrees × π/180
degrees = radians × 180/π
gradians = degrees × 10/9
decimal degrees = D + M/60 + S/3600
DMS from decimal: D is the whole part, M = whole part of (fraction × 60), S = the remaining fraction × 60.

Example: 48.858222° gives D = 48, 0.858222 × 60 = 51.4933 so M = 51, and 0.4933 × 60 = 29.6 so S = 29.6″, that is 48° 51′ 29.6″.

Reading DMS coordinates

The DMS field accepts the degree sign or “d”, a prime or apostrophe or “m” for minutes, a double prime, quote or “s” for seconds, or simply three numbers separated by spaces. A hemisphere letter at the start or end sets the sign: N and E are positive, S and W are negative, which is the convention of decimal latitude and longitude. Minutes and seconds must be below 60, and only the last part may have decimals.

Frequently asked questions

How many degrees is one radian?

180/π, about 57.2958°. Conversely, 1° is about 0.0174533 rad.

Why does the tool show "≈" for radians?

π is irrational, so almost every conversion between degrees and radians gives an endless decimal. The result is rounded to the chosen Significant figures and marked with “≈”.

What is the difference between a gradian and a degree?

A gradian divides a right angle into 100 parts instead of 90, so 1 gon = 0.9°. Surveying instruments often use it because slopes and bearings then use decimal steps.

What does "Normalized to 0–360°" mean?

It removes whole turns and makes negative angles positive: −90° becomes 270° and 450° becomes 90°. Compass bearings are written this way.

Can I enter a negative DMS angle?

Yes: type a minus sign (−33° 52′) or a hemisphere letter (33° 52′ S). Both give −33.8667°.