Worked example
A 5 kW spindle at 1,000 RPM delivers 9,549.3 × 5 / 1,000 = 47.7 N·m (35.2 lbf·ft). A 10 hp motor at 1,750 RPM delivers 5,252.1 × 10 / 1,750 = 30.0 lbf·ft (40.7 N·m). The same power at half the speed means twice the torque, which is why a gearbox that lowers the speed raises the torque.
In the shop
- The cutting force for a given metal removal rate sets the power and torque you need; low RPM with a big tool needs torque, high RPM with a small tool needs power.
- Torque at the spindle is what the datasheet's torque curve shows; check the value at the speed you intend to use, not just the peak.
- To turn cutting speed into spindle speed, see the RPM calculator.
Frequently asked questions
How do I calculate torque from kW and RPM?
T [N·m] = 9,549.3 × P [kW] / RPM. A 5 kW motor at 1,000 RPM gives 47.7 N·m.
How do I calculate torque from horsepower and RPM?
T [lbf·ft] = 5,252.1 × hp / RPM. A 10 hp motor at 1,750 RPM gives 30.0 lbf·ft.
How do I calculate power from torque and RPM?
P [kW] = T [N·m] × RPM / 9,549.3. At 47.75 N·m and 1,000 RPM that is 5 kW.
Why does a gearbox raise the torque?
Power stays the same, so halving the speed doubles the torque (and the other way round); losses in the gearbox reduce it slightly.
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.
- Degrees to DMS – Convert decimal degrees to degrees, minutes and seconds and back, with the angle in radians.
- 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.
- 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.