Horsepower Formula

Calculate horsepower from torque and RPM, watts, kilowatts, or force and speed, with unit conversions, worked examples, efficiency checks, and practical engineering guidance.

By Turn2Engineering Editorial Team Updated August 12, 2026 11 min read

Key Takeaways

Torque + RPM: use $\text{HP}=\dfrac{T\times\text{RPM}}{5252}$ when torque is in lb·ft.
SI rotational power: use $P=T\omega$, then convert watts or kilowatts to horsepower if needed.
Linear motion: use $P=Fv$; in U.S. customary units, $\text{HP}=Fv/550$ for lbf and ft/s.
Watch for: calculated load power, shaft horsepower, motor input power, and nameplate horsepower are not automatically the same.

Table of Contents

What is the horsepower formula?

Horsepower is a unit of power, not force or torque by itself. It describes the rate at which mechanical work is performed. A machine can produce high torque at low speed and still have modest horsepower, or produce similar torque at much higher speed and transmit much more power.

The correct horsepower formula depends on the quantities you know. Rotating machinery is usually handled with torque and rotational speed, while conveyors, hoists, towing systems, and other linear-motion problems are often handled with force and velocity.

Main horsepower formulas

The common U.S. customary torque-and-speed formula is:

$$ \text{HP}=\frac{T\times\text{RPM}}{5252} $$

This form requires torque $T$ in lb·ft and speed in revolutions per minute.

The general rotational-power relationship is:

$$ P=T\omega $$

where angular speed in SI calculations is commonly obtained from:

$$ \omega=\frac{2\pi(\text{RPM})}{60} $$

Useful power conversions include:

$$ 1\,\text{hp}\approx745.7\,\text{W}\approx0.7457\,\text{kW} $$

For straight-line motion:

$$ P=Fv $$

$$ \text{HP}=\frac{Fv}{550} $$

Senior engineer check

Match the equation to the units. The constants 5252 and 550 are unit-specific conversion constants, not universal physical constants.

Which horsepower formula should you use?

Horsepower formula selector by known inputs
If you know	Use	Required units	Typical applications
Torque + RPM	$\text{HP}=\dfrac{T\,\text{RPM}}{5252}$	lb·ft and rpm	Engines, motors, shafts, pumps, fans, reducers
Torque + angular speed	$P=T\omega$	N·m and rad/s gives watts	SI rotating-machine calculations
Watts	$\text{HP}=\dfrac{W}{745.7}$	W	Power conversion
Kilowatts	$\text{HP}=\dfrac{\text{kW}}{0.7457}$	kW	Motor and equipment datasheets
Force + speed	$\text{HP}=\dfrac{Fv}{550}$	lbf and ft/s	Conveyors, hoists, towing, traction

Fast rule

Use torque × angular speed for rotation and force × linear speed for translation. Convert to horsepower only after the physical power relationship is correct.

Variables, units, and constants

Key variables

HPMechanical horsepower.
$T$Torque. Common units: lb·ft or N·m.
RPMRotational speed in revolutions per minute.
$P$Power, typically expressed in watts or kilowatts in SI.
$\omega$Angular speed in radians per second.
$F$Linear force, such as lbf or N.
$v$Linear velocity, such as ft/s or m/s.

Horsepower unit conversion reference
Conversion	Approximate relationship	Use
Mechanical hp → W	$1\,\text{hp}\approx745.7\,\text{W}$	Convert U.S. mechanical horsepower to SI power
Mechanical hp → kW	$1\,\text{hp}\approx0.7457\,\text{kW}$	Compare hp and metric equipment ratings
kW → hp	$1\,\text{kW}\approx1.341\,\text{hp}$	Quick datasheet conversion
lb·in → lb·ft	$\text{lb·ft}=\text{lb·in}/12$	Prepare torque for the 5252 formula

Unit tip

Do not put N·m directly into the 5252 formula. For SI torque, use $P=T\omega$ to obtain watts, then convert watts to horsepower.

Why does the horsepower formula use 5252?

The constant 5252 comes from combining the definition of mechanical horsepower with the conversion from revolutions per minute to angular speed.

$$ 1\,\text{hp}=550\,\text{ft·lbf/s}=33{,}000\,\text{ft·lbf/min} $$

One revolution corresponds to $2\pi$ radians. Combining the rotational work rate with 33,000 ft·lbf/min gives:

$$ \frac{33{,}000}{2\pi}\approx5252 $$

That is why torque in lb·ft and rotational speed in rpm can be converted to mechanical horsepower by dividing their product by approximately 5252.

How to rearrange the horsepower formula

Starting with:

$$ \text{HP}=\frac{T\times\text{RPM}}{5252} $$

Solve for torque:

$$ T=\frac{5252\,\text{HP}}{\text{RPM}} $$

Solve for rotational speed:

$$ \text{RPM}=\frac{5252\,\text{HP}}{T} $$

Interpretation check

At a fixed horsepower, torque decreases as rotational speed increases. A gearbox can trade speed for torque, but ideal gearing does not create power.

Worked horsepower examples

Example 1: horsepower from torque and RPM

A motor delivers $175\,\text{lb·ft}$ at $1800\,\text{rpm}$.

$$ \text{HP}=\frac{(175)(1800)}{5252}\approx60.0\,\text{hp} $$

The shaft is transmitting about $60\,\text{hp}$ at that operating point.

Example 2: kilowatts to horsepower

A machine is rated at $30\,\text{kW}$.

$$ \text{HP}=\frac{30}{0.7457}\approx40.2\,\text{hp} $$

This is a unit conversion only. It does not by itself establish whether the value is electrical input power or mechanical shaft output.

Example 3: horsepower from force and speed

A conveyor requires $850\,\text{lbf}$ of pull at $14\,\text{ft/s}$.

$$ \text{HP}=\frac{(850)(14)}{550}\approx21.6\,\text{hp} $$

The ideal mechanical load is about $21.6\,\text{hp}$ before drivetrain efficiency, startup demand, duty cycle, or service margin are considered.

Example 4: SI torque and speed

A shaft transmits $120\,\text{N·m}$ at $1500\,\text{rpm}$. Find the power in kilowatts and mechanical horsepower.

$$ \omega=\frac{2\pi(1500)}{60}\approx157.1\,\text{rad/s} $$

$$ P=T\omega=(120)(157.1)\approx18{,}850\,\text{W}=18.85\,\text{kW} $$

$$ \text{HP}=\frac{18.85}{0.7457}\approx25.3\,\text{hp} $$

Horsepower, efficiency, and motor sizing

Load horsepower, shaft horsepower, electrical input power, brake horsepower, and motor nameplate horsepower describe different points in an energy-conversion system. Real equipment has losses.

$$ \eta=\frac{P_{\text{out}}}{P_{\text{in}}} $$

$$ P_{\text{in}}=\frac{P_{\text{out}}}{\eta} $$

Motor sizing warning

Do not select a motor solely by rounding a calculated load horsepower upward. Starting torque, duty cycle, thermal limits, ambient conditions, drive efficiency, service factor, VFD operation, and manufacturer application limits can control the final selection.

Where engineers use horsepower calculations

Motors and engines: connect torque-speed operating points to delivered mechanical power.
Pumps and fans: compare shaft-power requirements with driver capability and efficiency.
Gearboxes and reducers: understand torque-speed tradeoffs while accounting for transmission loss.
Conveyors and hoists: convert force and linear speed into ideal mechanical power.
Procurement: compare hp and kW equipment ratings across U.S. and metric datasheets.
Troubleshooting: compare expected shaft power with measured electrical or mechanical performance.

Decision logic

Start from the physical quantities you actually know. Use $T\omega$ for rotating power, $Fv$ for linear power, and power-unit conversions only when the underlying power value is already known.

Common horsepower mistakes and engineering checks

Using lb·in in the 5252 formula: convert to lb·ft first.
Using N·m with 5252: use $P=T\omega$ in SI instead.
Confusing torque with power: torque alone does not determine horsepower without speed.
Ignoring efficiency: input and output power are different in real machines.
Treating calculated load hp as final motor hp: application requirements may demand additional capability.
Using the wrong horsepower definition: mechanical horsepower and metric horsepower are not numerically identical.

Sanity check

At the same torque, doubling RPM doubles horsepower. At the same RPM, doubling torque doubles horsepower. If your calculation does not follow those proportional relationships, check the setup.

Horsepower calculation sanity checks
Check item	What to verify	Why it matters
Torque units	lb·ft vs lb·in vs N·m	Determines which formula or conversion is valid
Speed units	rpm vs rad/s vs ft/s	Rotational and linear power use different forms
Power location	Input, shaft output, or load requirement	Losses separate these values
Machine duty	Startup, continuous duty, intermittent duty, overload	Can control final equipment selection

Related equations and tools

Horsepower and related mechanical power equations
Equation / topic	Best used for	Key relationship	Main caution
Horsepower from torque	U.S. rotating machinery	$\text{HP}=T\,\text{RPM}/5252$	Torque must be lb·ft
Rotational power	General/SI rotating systems	$P=T\omega$	Use angular speed in rad/s
Linear power	Conveyors, towing, hoists	$P=Fv$	Force and velocity must be compatible units
Efficiency	Input/output power comparison	$\eta=P_{\text{out}}/P_{\text{in}}$	Efficiency varies with operating point

References and further reading

Frequently asked questions

What is the formula for horsepower from torque and RPM?

Use $\text{HP}=T\times\text{RPM}/5252$ when torque is in lb·ft and rotational speed is in rpm.

Why is 5252 used in the horsepower formula?

The constant comes from the mechanical horsepower definition of 33,000 ft·lbf/min combined with the $2\pi$ radians in one revolution: $33{,}000/(2\pi)\approx5252$.

How do you convert kilowatts to horsepower?

For mechanical horsepower, divide kilowatts by approximately $0.7457$, or multiply kilowatts by approximately $1.341$.

Is horsepower the same as motor nameplate size?

No. A calculated mechanical load horsepower is only one input to motor selection. Efficiency, startup torque, duty cycle, service factor, thermal limits, ambient conditions, and manufacturer requirements may affect the final motor size.

Is metric horsepower the same as mechanical horsepower?

No. Mechanical horsepower is about $745.7\,\text{W}$, while metric horsepower is about $735.5\,\text{W}$. Confirm which definition a specification uses before converting.

Summary and next steps

Horsepower is a power-rate measurement. For rotating equipment, start with $P=T\omega$ or the lb·ft/rpm shortcut $\text{HP}=T\times\text{RPM}/5252$. For linear systems, use $P=Fv$.

The most important engineering checks are unit consistency, distinguishing input from output power, and recognizing that calculated horsepower is not automatically the final equipment nameplate size.

Where to go next

Horsepower Calculator
Calculate horsepower directly from common inputs.
Torque Calculator
Connect torque, force, radius, rotational speed, and power.
Engineering Equations Hub
Browse additional engineering equations and reference pages.

Turn2Engineering Editorial Team

Engineering Education & Editorial Team

The Turn2Engineering Editorial Team develops engineering reference content using standard mechanics relationships, practical unit checks, and application-focused examples.

This page distinguishes rotational power, linear power, unit conversion, and equipment efficiency so the formulas are applied to the correct physical quantity.

Final motor, engine, pump, fan, or drivetrain selection should follow manufacturer data and application-specific requirements for duty, efficiency, thermal loading, startup, overload, and environmental conditions.