BIZOMAT MAKEOS · Units
Degrees, Minutes and Seconds Converter
What is this angle in degrees–minutes–seconds, decimal degrees and radians?
Convert an angle between degrees–minutes–seconds, decimal degrees and radians, for drawings, sine bar set-ups and survey data.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Convert from | choice | The form of the angle you have. |
| Degrees | ° | Whole degrees (negative for negative angles). |
| Minutes | ′ | Minutes (0–59). |
| Seconds | ″ | Seconds (0–59.99). |
| Decimal degrees | ° | Angle in decimal degrees. |
| Radians | rad | Angle in radians. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Convert from
- What it is
- The form the angle is already written in: degrees, minutes and seconds, decimal degrees, or radians. Only the inputs for that form are read.
- Units and format
- Choose one of 3 options from the list: Degrees, minutes, seconds; Decimal degrees; Radians.
- Example
- The form opens with “Degrees, minutes, seconds” selected as a worked example. Choose the option that matches your case.
- Get it right
- Leave the other inputs as they are; they are ignored in this mode.
What this means: Degrees
- What it is
- The whole-degree part of an angle written as degrees, minutes and seconds. A minus sign here makes the whole angle negative.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -36000° to 36000°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only in DMS mode. With 0 whole degrees the angle is always taken as positive.
What this means: Minutes
- What it is
- The minutes part of the angle, where one minute is one sixtieth of a degree.
- Units and format
- Enter a number in ′: ′. The form accepts 0 ′ to 59.999999 ′. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 ′ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not put a sign here; give the sign on the degrees. Used only in DMS mode.
What this means: Seconds
- What it is
- The seconds part of the angle, where one second is one sixtieth of a minute (one 3600th of a degree).
- Units and format
- Enter a number in ″: ″. The form accepts 0 ″ to 59.999999 ″. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 ″ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not put a sign here; give the sign on the degrees. Used only in DMS mode.
What this means: Decimal degrees
- What it is
- The angle written as a single decimal number of degrees, as many CAD and CNC systems show it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -36000° to 36000°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12.504167° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only when converting from decimal degrees.
What this means: Radians
- What it is
- The angle in radians, the unit used by most programming languages and maths libraries; a full turn is 2π radians.
- Units and format
- Enter a number in rad: rad. The form accepts -1000 rad to 1000 rad. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.218239 rad as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only when converting from radians.
Method and formulas
- Decimal = degrees + minutes ÷ 60 + seconds ÷ 3600.
- Minutes = fractional degrees × 60; seconds = fractional minutes × 60.
- Radians = degrees × π ÷ 180.
- Example: 12° 30′ 15″ = 12.504167°.
Limitations
- Seconds are rounded to three decimals in the display.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Convert drawing angles in DMS for calculations
- Express a calculated angle in DMS for the shop
- Convert to radians
Who it is for
- Machinists
- Toolmakers
- Engineers
What you get
- Degrees–minutes–seconds
- Decimal degrees
- Radians
Interpreting the result
- Sine bar and dividing head work usually needs seconds; drawings often state minutes.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 103–104. Topic reference; no source tables or recommended settings are reproduced.
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