← AskMachinist · Guides · Calculator · 🔎 Search
Degrees, Minutes and Seconds Conversion
Guide · Updated October 28, 2026
Drawings, bevel protractors and rotary tables often use degrees, minutes and seconds (DMS), while calculators, CAD and CNC controls use decimal degrees. One degree is 60 minutes and one minute is 60 seconds, so decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600. Getting this wrong is a common reason a sine bar stack or a rotary table setting is off.
Need an exact reference size?
Build any gage block stack with the free Gage Block Calculator. Free, no login.
Step by step
- Write down the DMS angle: For example 14° 30′ 00″.
- Convert to decimal: Degrees + minutes ÷ 60 + seconds ÷ 3600.
- Use the decimal angle: Enter it in the calculator for sine, cosine or tangent, with the calculator in degree mode.
- Convert back if needed: Take the decimal part × 60 for minutes, and the remaining decimal × 60 for seconds.
- Check: Plug the result back and confirm it rounds to the original.
Worked example: DMS to decimal
37° 15′ 27″ = 37 + 15 ÷ 60 + 27 ÷ 3600 = 37 + 0.25 + 0.0075 = 37.2575°.
A common mistake is writing 37° 15′ as 37.15°. It is actually 37.25°, and the 0.10° error is 6 arc-minutes, which is about 0.0017 in per inch.
Worked example: decimal to DMS
Convert 12.3456°: 0.3456 × 60 = 20.736′, so 20 minutes; 0.736 × 60 = 44.2″. Result: 12° 20′ 44″.
What an arc-minute is in inches
The offset over a length L for an angle θ is L × tan θ. For one arc-minute, tan(1/60°) = 0.000291, so 1′ is about 0.0003 in per inch of length, or 0.0035 in over 12 in. One arc-second is about 0.0000048 in per inch.
That is why a bevel protractor reading to 5′ is fine for layout, while a sine bar is needed for precision angles.
Worked example: sine bar stack
For 14° 30′ on a 5 in sine bar: decimal 14.5°, sin 14.5° = 0.25038, stack = 5 × 0.25038 = 1.2519 in. If you used 14.30° by mistake, sin 14.30° = 0.24700 and the stack would be 1.2350 in, an error of about 0.0169 in in the stack. Each arc-minute near this angle changes a 5 in sine bar stack by about 5 × cos 14.5° × 0.000291 ≈ 0.0014 in.
Worked example: rotary table
A rotary table with a 90:1 worm reads 4° per handwheel turn. To index 37° 15′: 37.25 ÷ 4 = 9.3125 turns, so 9 full turns plus 0.3125 × 4 = 1.25° = 1° 15′ on the dial. Check the table graduations; many read in minutes on the handwheel and degrees on the table.
Common problems
Treating minutes as decimals, having the calculator in radians, and rounding seconds too early on long arms where small angle errors become large offsets.
FAQ
How many minutes in a degree?
60. And 60 seconds in a minute, so 3600 seconds in a degree.
What is 30 minutes in decimal?
0.5°.
How big is one arc-minute?
About 0.00029 in per inch of length.
How do I build a sine bar stack?
Calculate L × sin θ, then build it from gage blocks; the free calculator at gageblockcalc.com finds the stack.
Related guides and calculators
- How to build a gage block stack
- How to wring gage blocks
- How to choose a gage block set
- Gage block care and wear blocks
- Carbide vs steel vs ceramic gage blocks
- How to check a height gage with gage blocks
- Machinist Christmas gift guide
- How to Indicate a Part in a 4-Jaw Chuck
- How to Indicate a Fixture
- Digital Readout (DRO) Basics for Machinists
- All free machinist calculators
- How to Use a Dial Test Indicator
- Right Triangle Trig for Machinists
- Radius from Chord and Height
- Hex and Square: Across Flats vs Across Corners
- Drill Point Length Calculation
Build your stack in seconds
The free Gage Block Calculator finds the fewest-block combination for inch and metric sets, with wear blocks. No login.
Questions? Ask a machinist.
General shop information only — follow your drawing, tool maker's data and your quality system.