SizingKitFree torque to horsepower calculator
5,252 is 33,000 ÷ 2π
Torque, speed and power are one relation with three terms, and this solves for whichever one you are missing across lbf·ft, lbf·in, N·m, kgf·m, hp, kW, W, rev/min and rad/s. The familiar 5,252 is not quoted here but derived — a horsepower is 33,000 lbf·ft every minute, a revolution is 2π radians, and the division of one by the other is the whole constant. The arithmetic is printed as it ran, including the SI form that has no constant in it. Free, no signup, nothing uploaded.
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- No signup
- Any of the three unknown
- hp, kW, lbf·ft, N·m
- 5,252 derived
Written lbf·ft here. A dyno sheet writing ft-lb means the same thing.
The speed the torque was measured at, not the motor's rated speed.
POWER, HP
39.98
POWER, KW
29.82
- Torque
- 120 lbf·ft / 163 N·m
- Also written
- 1,440 lbf·in
- Speed
- 1,750 rev/min / 183.26 rad/s
- Power
- 40 hp / 29.8 kW
THE ARITHMETIC, AS IT RAN
- 120.0 lbf·ft × 1,750 rev/min ÷ 5,252.113 = 39.984 hp
- 162.7 N·m × 1,750 rev/min ÷ 9,549.297 = 29.816 kW
- 162.7 N·m × 183.260 rad/s = 29,816 W — no constant
Where the 5,252.113 comes from. A horsepower is 33,000 lbf·ft every minute — James Watt's definition of the mechanical horsepower, 550 lbf·ft every second, which works out to 745.6999 W. It was chosen rather than measured, so it is exact and carries no tolerance. A revolution is 2π radians, so a shaft turning at N rev/min under τ lbf·ft is doing 2πτN lbf·ft of work every minute, and dividing that by 33,000 gives τN ÷ 5,252.113. Reached the other way — one lbf·ft and one rev/min converted into watts by the same unit definitions the rest of this site uses, then back out as horsepower — it is 5,252.113, the same number to every digit a double carries. The metric side never grows a constant: watts are newton-meters times radians per second and that is the whole identity, and the 9,549.297 in the second line above is nothing but the price of insisting on rev/min and kilowatts instead.
What 120.0 lbf·ft is worth at every standard motor speed
Synchronous speeds for 2 through 12 poles on both line frequencies, and the power 120.0 lbf·ft — 162.7 N·m — produces at each. Same torque all the way down the column: the power is the speed doing the work.
| Poles | 60 Hz · rev/min | 50 Hz · rev/min | 60 Hz · hp (kW) | 50 Hz · hp (kW) |
|---|---|---|---|---|
| 2 | 3,600 | 3,000 | 82.3 (61.3) | 68.5 (51.1) |
| 4 | 1,800 | 1,500 | 41.1 (30.7) | 34.3 (25.6) |
| 6 | 1,200 | 1,000 | 27.4 (20.4) | 22.8 (17.0) |
| 8 | 900 | 750 | 20.6 (15.3) | 17.1 (12.8) |
| 10 | 720 | 600 | 16.5 (12.3) | 13.7 (10.2) |
| 12 | 600 | 500 | 13.7 (10.2) | 11.4 (8.5) |
Speeds are N = 120 f ÷ p — line frequency in hertz, p the number of poles — which is the definition of synchronous speed for an AC machine and is generated here rather than transcribed. An induction motor never quite reaches it: slip of 1 to 5% at full load is why a 4-pole 60 Hz nameplate reads 1,725 or 1,750 rather than 1,800, and the torque you are converting is the one measured at that lower speed. At 5,252 rev/min the horsepower column would read the same number as the torque you entered, and at 9,549 rev/min the kilowatt column would match the newton-meters — two different crossings for one shaft, which is what a crossing made of units looks like. Every hp above is the mechanical horsepower, 33,000 lbf·ft/min. A European PS, CV or ch is a separate unit worth 735.49875 W — 75 kgf·m per second, which is 75 × 9.80665 W exactly by the definition of standard gravity. It is 1.4% smaller than the horsepower in this table, and it is left out of the select above rather than quietly mixed in with it.
How to convert between torque, speed and power
Two of the three numbers, in any units they arrived in, and the third with its arithmetic shown.
Pick the one you do not have
Power from torque and speed is the usual direction — a dyno sheet or a nameplate gives you two of the three. Torque from power and speed is what sizing a coupling, a key or a shaft needs. Speed from power and torque is the one people forget exists, and it answers where on the curve a machine drawing its rated power at a known torque is actually running.
Enter both knowns in whatever units they came in
A European motor plate in kW and a torque wrench in lbf·ft can go into the same calculation without converting anything first, and a unit written into the field beats the one selected next to it, so pasting 163 N-m into a box set to lbf·ft reads as newton-meters. Torque also takes lbf·in and kgf·m, because a small gearmotor is rated in one and an older Japanese or European spec sheet in the other.
Read the three lines of arithmetic under the answer
The panel prints your own numbers going through the customary form, the kilowatt form and the SI form, in that order. The third line has no constant in it at all — newton-meters times radians per second is watts — and comparing it with the first is the fastest way to see that the 5,252 is a units artifact rather than a fact about rotating machinery.
Technical specifications
| Solved three ways | Power from torque and speed, torque from power and speed, speed from power and torque — one identity, whichever term is missing |
|---|---|
| The constant, derived | 33,000 lbf·ft/min ÷ 2π rad/turn = 5,252.113, and the same figure reached from the unit definitions agrees to every digit a double carries |
| The metric twin | 60,000 ÷ 2π = 9,549.297 for kW against N·m and rev/min; in watts, N·m and rad/s the identity has no constant at all |
| Horsepower definition | 550 lbf·ft/s = 745.6999 W, built from the exact inch, pound and standard gravity rather than stored as a rounded decimal |
| Metric horsepower | 735.49875 W — 75 kgf·m/s exactly, 1.4% under the mechanical hp, and deliberately not offered as a unit here |
| Units accepted | Torque in lbf·ft, lbf·in, N·m and kgf·m; power in hp, kW and W; speed in rev/min, rad/s and rev/s — with the unit you type beating the one selected |
| Motor speed table | Synchronous speeds generated from N = 120f ÷ p for 2 to 12 poles at both 60 and 50 Hz, with your torque converted at each |
| Nothing transmitted | The whole conversion is a multiplication in the browser, so a nameplate reading or a dyno figure you type stays on your machine |
Frequently asked questions
Why do the torque and horsepower curves always cross at 5,252 RPM?
Because horsepower is torque times speed divided by 5,252.113, so at exactly 5,252.113 rev/min the divisor and the speed cancel and the two numbers are equal. It is a property of the units, not of the engine: the curves cross there on a diesel, a turbine and an electric motor alike, and on a machine that never reaches 5,252 rev/min they would cross there if it did. The proof is to redraw the same two curves in newton-meters and kilowatts, where they cross at 9,549 rev/min instead. One shaft, two crossings, decided entirely by which units the axes are labeled in.
Is there a metric equivalent of the 5,252?
There is 9,549.297 if you insist on rev/min and kilowatts, and nothing at all if you use SI properly. Power in watts is torque in newton-meters times angular speed in radians per second, full stop — no constant, because the SI units were chosen so that this identity has none. The 9,549.297 is 60,000 divided by 2π, and every digit of it is bookkeeping for the two conversions you asked for: seconds to minutes, and radians to revolutions. This page prints it in the second line and the bare identity in the third for exactly that reason.
Is the torque on a torque wrench the same quantity as the torque on a shaft?
The same quantity, doing a completely different job, and the two calculations share nothing else. Shaft torque is transmitted — it goes in one end, comes out the other and does work continuously, which is why multiplying it by speed gives power. A torque wrench setting is static: it is the twist needed to stretch a fastener to a target preload against thread and face friction, it does no work once the joint stops moving, and 90% of it is consumed by friction rather than tension. Multiplying a bolt torque by a speed produces a number with the units of power and no meaning whatsoever. A fastener setting comes from the preload you want, the thread and head friction and the nut factor K, none of which appear anywhere in this identity; the bolt torque page is where that calculation lives.
Is a European hp the same as the hp on this page?
No, and the gap is 1.4%. The horsepower here is the mechanical one, defined as 550 lbf·ft per second or 33,000 per minute, which works out to 745.6999 W. The metric horsepower written PS in Germany, CV in France and ch elsewhere is defined as 75 kgf·m per second, which is 735.49875 W exactly. A 100 PS car is 98.6 mechanical horsepower, and a spec sheet that gives both without saying which is which is worth checking against its own kilowatt figure. This page does not offer PS as a unit, because a silently mixed pair of horsepowers is a worse failure than one extra conversion.
Do the torque and the speed have to be measured at the same moment?
Yes, and this is the most common way the calculation goes wrong. Torque is a curve, not a number: an induction motor's peak torque is at a slip well below its rated speed, and a spark-ignition engine's peak torque and peak power are hundreds of rev/min apart by design. Taking peak torque from one line of a data sheet and rated speed from another gives a power figure the machine has never produced at any point in its operating range. If you have a curve, convert it point by point — the shape of the resulting power curve is the interesting part, and it always rises to the right of the torque peak.
How do I get from shaft horsepower to the current the motor draws?
Divide by the efficiency, then treat it as an electrical problem rather than a mechanical one. Shaft power is what comes out of the motor; input power is that divided by efficiency, which is 85 to 95% for a modern integral-horsepower induction machine. Only then does current come into it, and on an AC circuit it also needs the voltage, the phase count and the power factor, which is a separate ratio from efficiency and is regularly confused with it. This page stops at the shaft on purpose: everything past it belongs to the kW-to-amps and conductor sizing pages, where the phase multiplier and the terminal temperature rating decide the answer.
Does the same relation work for a linear actuator?
The idea does, the formula does not. Power is force times velocity in a straight line just as it is torque times angular velocity in rotation, and the two are the same statement in different coordinates — but the numbers do not interchange, because a force in pounds times a speed in feet per minute needs its own divisor of 33,000 to come out in horsepower and has no π in it anywhere. That missing 2π is the whole difference between the two constants, and it is why a hydraulic cylinder or a conveyor pull is worked out on its own terms rather than by borrowing this page's arithmetic.
About the 5,252, and what it is actually made of
James Watt needed to sell steam engines to people who owned horses, so he measured what a horse could lift out of a mine and rounded it up: 33,000 pounds raised one foot every minute, which is 550 every second. That is the entire definition, and every other form of the horsepower is arithmetic on it — 745.6999 watts falls out of the exact inch, the exact pound and standard gravity without anybody measuring anything. Now put a shaft under a torque of one pound-foot and turn it one revolution: the work done is 2π pound-feet, because torque times angle is work and a revolution is 2π radians of angle. A shaft at N rev/min under τ pound-feet is therefore doing 2πτN pound-feet of work a minute, and dividing that by Watt's 33,000 gives τN ÷ 5,252.113. There is nothing else in it. No engine, no efficiency, no assumption about how the torque was produced.
The clearest way to see that the constant belongs to the units is to change them. Written in watts, newton-meters and radians per second the same relation is P = τω, with no coefficient at all, because the SI units were defined to make it come out that way. Insist on rev/min and kilowatts instead and a 9,549.297 appears — 60,000 divided by 2π, carrying the minute and the revolution exactly as the 5,252 does. This is also the honest answer to the internet's favorite engine question. Torque and power curves cross at 5,252 rev/min because that is where the divisor equals the speed, and the same two curves for the same engine cross at 9,549 rev/min when drawn in metric units. A crossing that moves when you relabel the axis is not telling you anything about combustion.
What the identity cannot tell you is whether anything can survive the numbers. A shaft carrying 400 lbf·ft has a diameter and a key and a coupling to justify, none of which appear in the arithmetic, and neither does the fact that torque is what fails a drivetrain while power is what heats it. It also says nothing about where the torque goes: through a gear train it is traded against speed at whatever ratio the tooth counts give, and across a belt drive it is traded the same way by two pitch diameters. On the other side of the motor the same shaft power becomes an electrical problem, and turning kilowatts into amps needs an efficiency, a voltage, a phase count and a power factor before a conductor can be sized. Run that motor for a year and the interesting number is neither torque nor current but what the kilowatt-hours cost, or, across a whole shop of machines, what each one contributes to the bill.
What this page keeps
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Nothing, including the unit you last had selected — reload the page and it is back to lbf·ft and rev/min, because storing that preference would mean storing something. The conversion itself is three multiplications, which is not work worth sending anywhere.