Angle converter
Convert one angle between degrees, radians, arcminutes, arcseconds and degrees–minutes–seconds (DMS).
Equivalent angles
Enter an angle and convert it to see every supported form.
How to convert angle units
Use the converter
Choose the format that matches your source value. For degrees, radians, arcminutes or arcseconds, enter one number. For DMS, choose the sign separately and enter whole degrees, arcminutes and arcseconds in their own fields. Select Convert angle to show every equivalent and use Copy all results when you need a plain-text record.
The tool does not treat 12.30° as 12° 30′. Decimal degrees use ordinary base-10 decimals, so 12.30° equals 12° 18′ 0″. Choose DMS when your source is already split into degrees, minutes and seconds.
Conversion relationships
A complete turn is 360 degrees or 2π radians. Therefore radians = degrees × π ÷ 180, while degrees = radians × 180 ÷ π. One degree contains 60 arcminutes, and one arcminute contains 60 arcseconds, so one degree also contains 3,600 arcseconds.
Every input is first converted to decimal degrees and then to the other forms. The calculator keeps its internal number until the final display step. Ordinary results show two decimal places so the rounding boundary stays visible; very small nonzero values may keep the minimum useful significant digits or use scientific notation.
DMS signs, limits and carrying
In this calculator the sign belongs to the entire DMS angle, not to an individual component. Enter −12° 30′ 0″ as negative with 12 degrees, 30 minutes and 0 seconds. Do not type a minus sign into the degrees box. Degrees are whole and nonnegative, while minutes and seconds must each satisfy 0 ≤ value < 60.
DMS output rounds seconds to two decimal places. If rounding makes seconds equal 60, the tool changes them to 0 and adds one minute. If that minute reaches 60, it changes to 0 and adds one degree. This carry keeps the displayed DMS form valid.
Worked examples
Example 1: 180° × π ÷ 180 = π radians, displayed as approximately 3.14 rad. The same angle is 10,800 arcminutes, 648,000 arcseconds and 180° 0′ 0″.
Example 2: choose negative DMS and enter 12 degrees, 30 minutes and 0 seconds. Decimal degrees are −(12 + 30 ÷ 60) = −12.5°. That is displayed as approximately −0.22 rad, −750 arcminutes and −45,000 arcseconds.
Example 3: one arcsecond is 1 ÷ 3,600 degree, approximately 0.0002777778°. It is also π ÷ 648,000 radians, approximately 0.0000048481 rad. This small example shows why the result area sometimes keeps more than two decimal places: displaying 0.00 would hide a valid nonzero angle. Scientific notation is used only when it makes such a magnitude easier to preserve and read.
Scope and limitations
This is a unit converter, not a trigonometry calculator. It does not evaluate expressions such as π/4, compute sine or cosine, infer compass directions, or decide whether clockwise should be positive. Enter a decimal approximation when your source uses a symbolic multiple of π.
The converter intentionally does not normalize angles. For example, −90° remains −90° and 450° remains 450°, even though each has coterminal angles inside one turn. Browser floating-point arithmetic limits extreme precision, and the DMS display intentionally rounds seconds. For surveying, navigation or other precision-critical work, retain the source measurement and follow the rounding and sign convention required by your field.
All supported angle conversion directions
| Conversion direction | Formula or method | Example |
|---|---|---|
| Degrees to Radians (° to rad) | rad ≈ ° × 0.017453293 | 1 ° ≈ 0.017453293 rad |
| Degrees to Arcminutes (° to ′) | ′ = ° × 60 | 1 ° = 60 ′ |
| Degrees to Arcseconds (° to ″) | ″ = ° × 3600 | 1 ° = 3600 ″ |
| Degrees to Degrees, minutes, seconds (° to DMS) | ° = ° × 1; split decimal degrees into d, m and s | 1 ° = 1° 0′ 0″ |
| Radians to Degrees (rad to °) | ° ≈ rad × 57.29578 | 1 rad ≈ 57.29578 ° |
| Radians to Arcminutes (rad to ′) | ′ ≈ rad × 3437.7468 | 1 rad ≈ 3437.7468 ′ |
| Radians to Arcseconds (rad to ″) | ″ ≈ rad × 206264.81 | 1 rad ≈ 206264.81 ″ |
| Radians to Degrees, minutes, seconds (rad to DMS) | ° ≈ rad × 57.29578; split decimal degrees into d, m and s | 1 rad ≈ 57° 17′ 44.806247″ |
| Arcminutes to Degrees (′ to °) | ° ≈ ′ × 0.016666667 | 1 ′ ≈ 0.016666667 ° |
| Arcminutes to Radians (′ to rad) | rad ≈ ′ × 0.00029088821 | 1 ′ ≈ 0.00029088821 rad |
| Arcminutes to Arcseconds (′ to ″) | ″ = ′ × 60 | 1 ′ = 60 ″ |
| Arcminutes to Degrees, minutes, seconds (′ to DMS) | ° ≈ ′ × 0.016666667; split decimal degrees into d, m and s | 1 ′ = 0° 1′ 0″ |
| Arcseconds to Degrees (″ to °) | ° ≈ ″ × 0.00027777778 | 1 ″ ≈ 0.00027777778 ° |
| Arcseconds to Radians (″ to rad) | rad ≈ ″ × 0.0000048481368 | 1 ″ ≈ 0.0000048481368 rad |
| Arcseconds to Arcminutes (″ to ′) | ′ ≈ ″ × 0.016666667 | 1 ″ ≈ 0.016666667 ′ |
| Arcseconds to Degrees, minutes, seconds (″ to DMS) | ° ≈ ″ × 0.00027777778; split decimal degrees into d, m and s | 1 ″ = 0° 0′ 1″ |
| Degrees, minutes, seconds to Degrees (DMS to °) | ° = d + m/60 + s/3600; ° = ° × 1 | 1° 30′ 0″ = 1.5 ° |
| Degrees, minutes, seconds to Radians (DMS to rad) | ° = d + m/60 + s/3600; rad ≈ ° × 0.017453293 | 1° 30′ 0″ ≈ 0.026179939 rad |
| Degrees, minutes, seconds to Arcminutes (DMS to ′) | ° = d + m/60 + s/3600; ′ = ° × 60 | 1° 30′ 0″ = 90 ′ |
| Degrees, minutes, seconds to Arcseconds (DMS to ″) | ° = d + m/60 + s/3600; ″ = ° × 3600 | 1° 30′ 0″ = 5400 ″ |
Frequently asked questions
Why is a negative sign shown only once in DMS?
The sign applies to the whole angle. Separate negative signs on degrees, minutes or seconds are ambiguous, so this tool uses one sign selector and nonnegative components.
Why must minutes and seconds be less than 60?
DMS is a normalized base-60 subdivision: 60 seconds carry to one minute, and 60 minutes carry to one degree.
Does the converter wrap angles into one circle?
No. It preserves negative and multi-turn values so the output represents the same signed quantity you entered.