Worked example
36.8699° is 36° and 0.8699 × 60 = 52.194′, so 52′ and 0.194 × 60 = 11.6″, which rounds to 12″: 36° 52′ 12″. Back again: 36 + 52/60 + 12/3600 = 36.8700°. The small difference is rounding in the seconds.
Where the formats show up
- Drawings and protractors usually give degrees and minutes.
- CNC controls and CAD systems take decimal degrees – 12′ is 0.2°, not 0.12°.
- Trigonometry in programs uses radians; multiply degrees by π/180 (0.017453).
- For a taper angle see the taper calculator; for a set-up angle, the sine bar calculator.
Frequently asked questions
How do I convert decimal degrees to degrees, minutes, seconds?
Keep the whole degrees. Multiply the fraction by 60 for minutes; multiply what is left by 60 for seconds. 36.8699° is 36° 52′ 12″.
How do I convert degrees, minutes, seconds to decimal degrees?
Decimal = degrees + minutes / 60 + seconds / 3600. 36° 52′ 12″ = 36.87°.
How many seconds are in a degree?
3,600: one degree has 60 minutes and each minute has 60 seconds.
How do I convert degrees to radians?
Multiply by π / 180, about 0.017453. 90° is π/2 = 1.5708 rad.
More free machinist calculators
- Inch to mm – Convert inches to millimetres and back, fractions like 1 3/8 included. Exact factor 25.4, with a chart of every 1/64 inch.
- RPM and feed – Calculate spindle RPM from surface speed and diameter, surface speed from RPM, and feed rate from chip load – metric and imperial, with formulas.
- Taper – Taper ratio, half angle and taper per foot from the large and small diameter and the length, or the small diameter from the angle.
- Bolt circle – X and Y coordinates of evenly spaced holes on a bolt circle, with the hole spacing, start angle and centre offset. Copy the table into your program.
- Sine bar – Gauge block height for a sine bar angle, or the angle from a known stack, for 5 in, 10 in, 100 mm, 200 mm or any other bar length.
- Metal removal rate – Metal removal rate in cm³/min or in³/min from depth, width and feed – milling and turning, metric and imperial, with the formulas.
- Drill point depth – Length of a drill's point cone from diameter and point angle, and the total depth needed for a full-diameter hole to depth.
- Right triangle – Hypotenuse and angles from two legs, or the legs from the hypotenuse and an angle – for chamfers, dovetails, tapers and hole positions.
- Machining time – Cutting time from length, feed and spindle speed – turning with feed per revolution, milling with feed rate and number of passes.
- Decimal to fraction – Turn a decimal inch or a millimetre value into the nearest fraction – 8ths to 128ths – with the error in millimetres.
- SFM to m/min – Convert surface feet per minute to metres per minute and back, and inches per minute to mm per minute, with the exact factors.
- TPI to pitch – Convert a thread pitch in millimetres to threads per inch (TPI) and back, for matching metric and inch threads.
- Cpk calculator – Paste measurements from Excel, enter USL and LSL and get Cp, Cpk, Pp and Ppk. Says plainly when 25 values are too few for an index.
- Tolerance stack-up – Add up the tolerances of a chain of parts: closing gap, worst case and statistical RSS for up to eight dimensions. Free, in your browser.
- Fit clearance – Enter hole and shaft limits and get minimum and maximum clearance and the kind of fit – clearance, transition or interference.
- Chip thinning – Feed per tooth to program when the radial width of cut is below half the cutter diameter, so the real chip thickness stays right.
- Ball-nose stepover – Scallop height left by a ball-nose cutter from the stepover, or the stepover for a wanted scallop height, on a flat surface.
- Surface finish – Theoretical Rt and estimated Ra of a turned surface from the feed per revolution and the tool nose radius.
- Torque and power – Torque from power and speed in newton-metres or pound-feet, and power from torque and speed. The formulas with worked examples.
- Spur gear – Pitch and outside diameter, centre distance, ratio and circular pitch of a pair of external spur gears from the module and the tooth numbers.
Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.