Converting DMS to decimal
Add degrees + minutes/60 + seconds/3600. Minutes and seconds must each be at least zero and below 60. Apply a negative sign to the whole angle: −7°14′ means −(7 + 14/60), not −7 + 14/60.
Degrees, minutes and seconds converter
Convert decimal degrees to degrees, minutes and seconds (DMS), or DMS to decimal degrees. Worked examples for drawing angles and CNC.
DMS degrees
1Decimal → DMS
2Result
Click a dimension to copy it
1DMS → decimal
2Result
Click a dimension to copy it
How to use this calculation
An angle of 7°14′ is not 7.14°. Angular minutes and seconds are sexagesimal fractions of a degree. Convert both ways to use a drawing angle in a sine bar setup, a taper calculation or a decimal-angle input.
Worked example
Known measurements
Drawing angle = 7° 14′ 0″
Result
Decimal degrees ≈ 7.233333°
By comparison, 7.14° equals 7° 8′ 24″. Writing minutes after the decimal point changes the angle.
Converting decimal to DMS
The integer part gives degrees. Multiply the remaining fraction by 60 to obtain minutes, then multiply that remaining fraction by 60 for seconds. When rounding, 60 seconds carry into one minute and 60 minutes into one degree.
Keeping useful angular precision
One minute is 1/60 degree and one second is 1/3600 degree. Do not confuse these symbols with time minutes or inches. Preserve enough decimal places when transferring angles: over a long distance, a small angular rounding change can alter the resulting dimension.
Frequently asked questions
Is 7°14′ the same as 7.14°?
No. Fourteen minutes are 14/60 degree, so 7°14′ ≈ 7.233333°, whereas 7.14° = 7°8′24″.
How many seconds are in a degree?
A degree contains 60 minutes and a minute contains 60 seconds: 3,600 angular seconds per degree.
Do I need millimetres or inches?
No. This converts angles only, so length units do not apply.
Related tools
Hole circle (PCD)
Calculates X/Y coordinates of a bolt hole circle (PCD/BCD), preview, CSV and G-code for Fanuc G81/G83, Siemens CYCLE81/83 or Heidenhain CYCL 200.
RPM, feeds and machining time calculator
Calculate cutting speed, RPM, feeds and pass time for milling, turning and drilling. Adjust values with linked scales and look up starting values by material.
ISO fits
Calculates indicative ISO 286 tolerances for shaft and hole, H7/g6, H7/h6, H7/k6 and H7/p6 fits with clearance, transition and interference graph.