Unit converter

How it is worked out

Each category has one base unit, and every conversion passes through it: the value you type is turned into the base unit, then out into each of the others. Most units are a fixed multiple of the base, so the whole calculation is one multiplication and one division. Two are not: thread pitch, where TPI is a reciprocal, and temperature, where the scales have different zero points.

Multiples:     value in B = value in A × factor(A) ÷ factor(B)

Thread pitch:  TPI = 25.4 ÷ pitch (mm)          pitch (mm) = 25.4 ÷ TPI

Temperature:   °F = °C × 9/5 + 32               °C = (°F - 32) × 5/9
               K  = °C + 273.15                 °C = K - 273.15

Worked example. A feed of 1000 mm/min in inches per minute: the factor of mm/min is 1 and the factor of in/min is 25.4, so 1000 × 1 ÷ 25.4 = 39.3701 in/min. A 1.9 N·m stepper motor in oz·in: 1.9 × 1 ÷ 0.007061551814 = 269.063 oz·in.

The factors, and where each comes from

Every number below is exact by definition except the three shown to ten significant figures, which are exact products carried at full double precision in the arithmetic. Values are one of the unit, expressed in the base unit of its category.

kg·cm means kilogram-force centimetres

Stepper and servo datasheets, especially from Asian motor makers, give holding torque in kg·cm. A kilogram is a mass, not a force, so the unit actually meant is the kilogram-force centimetre: the turning effect of a 1 kg weight hanging 1 cm from the shaft under standard gravity, 9.80665 N × 0.01 m = 0.0980665 N·m. That makes 1 N·m equal to 10.197 kg·cm, not 10. The 2% matters when two motors are being compared on paper, one rated in each unit.

TPI is the reciprocal of pitch

Pitch is the distance from one thread crest to the next. Threads per inch counts crests in one inch. So TPI = 25.4 ÷ pitch in mm, and the conversion runs the same way back. Halving the pitch doubles the TPI. A pitch or TPI of zero has no counterpart, and the converter says so instead of showing infinity.

Metric pitches rarely land on a whole TPI. The Pitch table gives the nearest TPI from the UNC, UNF, BSW, BSF and pipe thread series, picked by the smallest ratio error, and the pitch error that choice brings. The error accumulates along the thread: at +5.8%, ten turns of an M10 thread cut at 16 TPI end up 0.875 mm long. That is why a manual lathe needs a metric gear train for metric threads, while a CNC lathe, which ties the Z feed to the spindle encoder, cuts the exact pitch it is given.

IPM and inch-mode programs

IPM is inches per minute. In G-code it is what the F word means when a program runs in inch mode (G20) with feed per minute (G94); in millimetre mode (G21) the same F word is mm/min. Moving a program between the two means scaling every coordinate and every F word by 25.4, not only swapping G20 for G21. Feed per revolution (G95, in mm/rev or in/rev) is a different quantity and needs the spindle speed as well, so it is not converted here.

Revolutions per second and VFD frequency

rev/s is how many times the shaft turns in a second, which is why it is also written as Hz. It equals the output frequency of a VFD only for a two-pole spindle motor: the synchronous speed is 120 × f ÷ poles RPM, so a four-pole motor turns at half that rate, and an induction motor runs a little below synchronous speed under load.

Two horsepowers

Mechanical horsepower (hp) is 550 ft·lbf/s, 745.7 W. Metric horsepower (PS, also written CV or pk) is 75 kgf·m/s, 735.5 W, about 1.4% smaller. Motor nameplates in India and Europe usually give kW; where a horsepower figure appears beside it, check which one is meant. Electrical horsepower, 746 W exactly, is 0.04% above mechanical and is not listed separately.

Temperatures and pressures

Temperatures are converted as temperatures. A temperature difference converts without the offset: a rise of 10 °C is a rise of 18 °F and of 10 K. Anything below absolute zero (0 K, -273.15 °C, -459.67 °F) is refused. Pressure converts as given: a gauge reading stays a gauge reading, and negative values are accepted as a vacuum below atmospheric. Shop air at the tool is usually 6 to 7 bar; high-pressure through-spindle coolant runs at roughly 20 to 70 bar.

Precision

The arithmetic runs at full double precision on the exact constants above. The fields and the readout show six significant figures with trailing zeros dropped; the tables show five, or six for fractional inches, where every value is exact at that length. Round-tripping a value through any unit and back returns what you typed. Numbers may use spaces as thousands separators and e-notation such as 1e-3; a comma is refused rather than guessed at, because 1,500 reads as fifteen hundred to some people and one and a half to others.

Where these units meet Tiny Controls hardware

Feeds and spindle speeds are what you set on a mill controller such as the TNC-M34, and thread pitches on a lathe controller such as the TNC-L32. Motor torque, in whichever unit the motor's datasheet uses, is the number to check when matching a stepper motor to a drive such as the Tstep-168X. See every controller and drive on the products page.