Speed and torque calculator
What your spindle actually delivers at the speed you cut at — not what the box says at maximum. Set the power, poles and frequency limits and read the torque across the whole range.
Torque across the speed range
Two-pole and 400 Hz is the usual router spindle. Change it to match your nameplate.
Reading the result
- The base frequency row is where the two regions meet: below it torque is flat and power climbs; above it power is flat and torque falls.
- The torque at max speed is the number to judge a high-speed spindle by. It is always smaller than buyers expect.
- The slip correction turns synchronous speed into the rpm you will actually measure. A few per cent is typical at rated load on a small spindle.
Unit converter
Power, torque and speed
1 hp = 0.7457 kW · 1 N·m = 0.7376 ft·lb = 8.851 in·lb · rpm = 120 f / p.
Worked example: is 2.2 kW enough for what I cut?
Suppose you want to run a 6 mm cutter in aluminium at 18,000 rpm and you have been told you need about 1.2 N·m there.
- A 2.2 kW two-pole spindle at 18,000 rpm gives
9550 × 2.2 / 18000 ≈ 1.17 N·m— right on the line, and that is the theoretical envelope. After iron losses, windage and slip it will be under it. - A 3.0 kW spindle at the same speed gives
9550 × 3.0 / 18000 ≈ 1.59 N·m— comfortable. - Going the other way, if you could drop to 12,000 rpm the 2.2 kW spindle would give about 1.75 N·m. Speed is the expensive thing you are buying with torque, and the trade is visible in one line of arithmetic.
None of this is in the power figure on the box. That is the whole reason the calculator exists.
Related
- Constant torque and constant power regions explained
- VFD sizing calculator — drive class and supply current
- Where rated frequency and poles go in the drive
Parts
Spindles
Questions
Why is my 2.2 kW spindle so weak at 24,000 rpm?
Because above the base frequency the drive holds power constant, so torque falls as speed rises. A 2.2 kW two-pole spindle makes under 1 N·m at 24,000 rpm — that is the arithmetic, not a fault.
What does constant torque mean?
Below the base frequency the V/f ratio is held constant, so the spindle makes full torque at any speed and power climbs with speed. The two regions meet at the base frequency.
Is the number this calculator prints the real torque?
It is an upper bound. Iron losses, windage, bearing drag and slip all pull the real curve below it, increasingly towards the top of the range. If the maker publishes a torque curve, use that instead.
Sources and method
Three kinds of statement appear on this page, and each is labelled where it occurs:
- Derived — synchronous speed is 120 f / p and torque is 9550 P / n; both are printed with the result rather than hidden in the script.
- Rule of thumb — workshop practice, not a standard. Given with the range it is meant to hold over, and it loses to your manual wherever the two disagree.
- Maker-specific — parameter numbers, connector pin numbers, minimum brake resistance, maximum cable length, bearing speed limits. Not published here. They move between firmware revisions of the same model, and a wrong one is worse than none.
Standards and documents
- IEC 60034-1 — rotating electrical machines: rating and performance
- ISO 1940-1 — balance quality requirements for rotors (G grades)
- The manual for your own drive and spindle — the only valid source for maker-specific values