Free · Angle calculators 🕑
Decimal Angle ↔ Degrees, Minutes & Seconds
Convert signed decimal degrees and compound degrees-minutes-seconds, with optional radians and other angle units.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
12.625° is 12° 37′ 30″. The decimal part becomes minutes and seconds: 0.625 × 60 = 37.5 minutes.
Decimal degrees = degrees + minutes/60 + seconds/3600; apply a leading minus sign to the whole angle
Worked example
Enter these known values and leave the other values blank.
- Angle: decimal representation
- 12.625 deg
- Angle: compound representation
- 12:37:30 deg / min / sec
Assumptions and limitations
- For compound entry, use degrees:minutes:seconds, such as 12:37:30. A leading minus sign applies to the entire angle, including the minutes and seconds.
- One degree contains 60 arcminutes and one arcminute contains 60 arcseconds. These are angle measures, not units of elapsed time.
- Angles are not restricted to a latitude, longitude or bearing range. The conversion does not wrap values into 0–360° or attach a hemisphere.
- The selected units determine the meaning of each field. Select radians when entering a radian measure; select degrees for a decimal-degree measure.
Common questions
How do I enter a negative angle?
Place one minus sign at the beginning: −12:37:30 means −12.625°, with the sign applying to all three components.
Is 12.30° the same as 12° 30′?
No. 12.30° is 12° 18′, while 12° 30′ is 12.5°.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.