Horsepower Calculator
Calculate horsepower from torque and RPM using \(HP = T \times RPM \div 5252\), or switch modes for power conversion, electric motors, hydraulic systems, and vehicle estimates.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Start with Torque & RPM for engines and rotating shafts. Use the other modes for power conversion, motors, pumps, or vehicle estimates.
Enter the known values
Only fields required for the selected calculation are shown. Change answer units in Advanced Options.
Visual Check
Use the diagram to connect the inputs, equation, and result.
Solution
Live result, quick checks, warnings, and full solution steps.
Quick checks
- Check—
Show solution steps See the equation, substitutions, assumptions, and result path
- Enter values to see the full solution steps and checks.
Source, Standards, and Assumptions
Calculation basis, constants, assumptions, and limitations.
Source/standard information updates based on the selected calculation type.
- Assumptions will appear after a valid calculation.
On this page
Calculator Guide
How to Use the Horsepower Calculator
The Horsepower Calculator above estimates horsepower from torque and RPM, converts power units, and helps check motor, hydraulic, and vehicle horsepower relationships. For the most common use case, select Torque & RPM, enter torque, choose the correct torque unit, enter RPM, and read horsepower, kW, and watts in the result panel.
Horsepower is a unit of power, which means it measures how quickly work is being done. In rotating equipment, horsepower depends on both torque and rotational speed. High torque at low RPM can produce the same horsepower as lower torque at higher RPM, so both inputs matter.
Quick Answer
To calculate horsepower from torque and RPM, use \(HP=(Torque \times RPM)/5252\) when torque is in lb-ft. For example, \(350\) lb-ft at \(5000\) RPM gives about \(333.2\) hp. If you enter torque in N-m or lb-in, convert it to lb-ft before using the 5252 constant.
Most common use
Most users use this page to calculate horsepower from torque and RPM. The other modes help convert power units, estimate electric motor horsepower, calculate hydraulic horsepower, or compare crank horsepower and wheel horsepower.
When not to rely on the simplified result
Do not use a quick horsepower estimate alone for final motor sizing, pump selection, drivetrain design, electrical code compliance, or pressure-system design. Final equipment selection should also check manufacturer curves, efficiency, duty cycle, service factor, thermal limits, voltage/current ratings, and field operating conditions.
Horsepower Calculator Inputs and Outputs
The calculator uses different inputs depending on the selected mode. The basic rotating-equipment mode uses torque and RPM, while other modes may use watts, kilowatts, voltage, current, hydraulic pressure, flow rate, or drivetrain loss.
| Type | Value | What It Means | Common Unit |
|---|---|---|---|
| Input | Torque | Twisting force applied to a rotating shaft. | lb-ft, N-m, lb-in |
| Input | Rotational speed | How fast the shaft rotates. | RPM, rad/s |
| Input | Power | Known horsepower, watts, kilowatts, or metric horsepower for conversion or reverse solving. | hp, W, kW, PS |
| Input | Voltage and current | Electrical inputs used for simplified motor horsepower estimates. | V, A |
| Input | Pressure and flow | Hydraulic inputs used to estimate fluid power and required input horsepower. | psi, GPM |
| Input | Efficiency | Loss adjustment used for electric motor and hydraulic input horsepower estimates. | % or decimal ratio |
| Input | Drivetrain loss | Estimated power loss between engine crankshaft and wheels. | % |
| Output | Horsepower | Mechanical power output or estimated input power depending on the mode. | hp |
| Output | Equivalent power | The same power expressed in watts, kilowatts, or metric horsepower. | W, kW, PS |
How the select boxes work
When you change Calculation Type or Solve For, the calculator changes the visible inputs and available answer units. For example, solving for torque changes the answer unit options to lb-ft, N-m, and lb-in. Solving for RPM changes the answer unit options to RPM and rad/s.
Practical note
The most common user mistake is mixing torque units. The 5252 formula is only directly valid when torque is in lb-ft and speed is in RPM. If the input is N-m or lb-in, the value must be converted before applying the formula.
Horsepower Formula
The standard horsepower formula for rotating equipment relates torque and shaft speed. It is commonly used for engines, motors, gearboxes, dyno readings, pumps, and rotating machinery.
Main Torque and RPM Formula
Use this form when torque \(T\) is in pound-feet and rotational speed is in revolutions per minute.
Rearranged Formula for Torque
Use this form to estimate required shaft torque when horsepower and speed are known.
Rearranged Formula for RPM
Use this form to estimate the rotational speed required to produce a target horsepower at a known torque.
SI Torque and Angular Speed Formula
Use this form when torque is in N-m and angular speed is in rad/s. Then convert watts to horsepower using \(HP=P_W/745.699872\).
N-m and RPM Shortcut
This shortcut is useful when torque is in N-m and speed is in RPM. It comes from \(P_W=\tau(2\pi RPM/60)\), then converting watts to horsepower.
Power Conversion
Mechanical horsepower converts to watts using approximately \(745.699872\) watts per horsepower.
Where the 5252 constant comes from
One mechanical horsepower is \(33{,}000\) ft-lb per minute. Rotating work uses \(2\pi\) radians per revolution, so the constant is approximately \(33{,}000/(2\pi)=5252\). That is why torque and horsepower are numerically equal at about 5252 RPM when torque is measured in lb-ft.
Zero-RPM warning
Torque can exist without horsepower. If a shaft is stalled at \(0\) RPM, it may still have torque, but mechanical horsepower is \(0\) because horsepower requires motion. For this calculator, use positive torque and RPM magnitudes for basic horsepower estimates.
Horsepower Formula by Calculator Mode
The calculator includes multiple horsepower workflows. Use the table below to understand which formula is being used for each mode and when that mode is appropriate.
| Calculator Mode | Main Formula | Best For | Important Assumption |
|---|---|---|---|
| Torque & RPM | \(HP=\frac{T \times RPM}{5252}\) | Engines, shafts, dynos, gearboxes, and rotating machinery. | \(T\) must be in lb-ft and speed must be in RPM. |
| Power Conversion | \(kW=HP \times 0.745699872\) | Converting hp, W, kW, and metric horsepower. | Mechanical hp and metric PS are not identical. |
| DC Motor | \(HP=\frac{V I \eta}{746}\) | Simple DC motor horsepower estimates. | Efficiency must be entered as a decimal ratio internally. |
| Single-Phase AC Motor | \(HP=\frac{V I PF \eta}{746}\) | Approximate single-phase motor output horsepower. | Power factor and efficiency strongly affect the result. |
| Three-Phase AC Motor | \(HP=\frac{\sqrt{3} V I PF \eta}{746}\) | Approximate three-phase motor output horsepower. | Use line-to-line voltage and running current. |
| Hydraulic Horsepower | \(Input\ HP=\frac{PSI \times GPM}{1714 \times \eta}\) | Pumps, hydraulic power units, and fluid power checks. | Input HP is higher than theoretical fluid HP when efficiency is below 100%. |
| Vehicle Performance | \(Crank\ HP=\frac{WHP}{1-L}\) | Wheel horsepower, crank horsepower, and power-to-weight estimates. | Drivetrain loss is only an estimate and varies by vehicle and test method. |
Hydraulic input HP vs. theoretical hydraulic HP
Theoretical hydraulic horsepower is \(PSI \times GPM / 1714\). Required input horsepower is higher because pumps and hydraulic systems are not perfectly efficient. If efficiency is 85%, divide theoretical hydraulic horsepower by \(0.85\) to estimate required input horsepower.
Motor nameplate caution
A motor rated at 10 hp does not always output 10 hp at every moment. Actual operating horsepower depends on load, speed, voltage, current, efficiency, power factor, duty cycle, and nameplate rating conditions.
Variables Used in the Formula
Every variable must use the correct unit system. The formula itself is simple, but the result is only accurate when torque and speed represent the same shaft and operating point.
| Symbol | Meaning | How to Enter It |
|---|---|---|
| \(HP\) | Mechanical horsepower. | Use the result when solving from torque and RPM, or enter it when solving backward for torque or speed. |
| \(T\) | Torque at the rotating shaft. | Use lb-ft for the 5252 formula. Convert N-m or lb-in before using the formula manually. |
| \(RPM\) | Revolutions per minute. | Use shaft speed at the same operating point as the torque value. |
| \(\tau\) | Torque in SI notation. | Use N-m when calculating \(P_W=\tau\omega\). |
| \(\omega\) | Angular speed. | Use rad/s for SI power calculations. |
| \(P_W\) | Power in watts. | Use for SI conversion, electrical comparison, and motor power checks. |
| \(\eta\) | Efficiency as a decimal. | Use \(0.90\) for 90% efficiency when estimating electric motor or hydraulic input power. |
| \(PF\) | Power factor for AC motor estimates. | Use a decimal between 0 and 1 when estimating AC motor horsepower from voltage and current. |
| \(L\) | Drivetrain loss as a decimal. | Use \(0.15\) for a 15% drivetrain loss estimate. |
How to Use the Calculator
Start by selecting the calculation type that matches your problem. Most users should begin with Torque & RPM, then switch modes only if they are doing a power conversion, electric motor estimate, hydraulic horsepower estimate, or vehicle performance check.
Select the calculation type
Choose Torque & RPM, Power Conversion, Electric Motor, Hydraulic Horsepower, or Vehicle Performance.
Select what to solve for
Choose whether you want horsepower, torque, RPM, motor current, hydraulic pressure, hydraulic flow, crank horsepower, wheel horsepower, or power-to-weight ratio.
Check the unit selectors
Make sure torque is entered as lb-ft, N-m, or lb-in correctly. If speed is entered as rad/s, it must be converted internally to RPM before using the standard formula.
Review the result and quick checks
Compare horsepower, kW, watts, angular velocity, torque conversions, suggested motor size, and warning messages to decide whether the answer is physically reasonable.
Default examples by mode
The calculator uses practical example defaults: \(350\) lb-ft and \(5000\) RPM for Torque & RPM, \(100\) hp for conversion, \(480\) V and \(10\) A for a three-phase motor estimate, \(1500\) psi and \(5\) GPM for hydraulic horsepower, and \(300\) WHP with \(15\%\) drivetrain loss for vehicle estimates.
How to Interpret Horsepower Results
A horsepower result tells you the rate of doing work, not just how “strong” a machine feels. Torque describes twisting force; RPM describes how quickly that force is applied repeatedly.
| Result Pattern | What It May Mean | What to Check Next |
|---|---|---|
| Low HP, high torque | The machine may produce strong turning force at low speed. | Check gearing, duty cycle, and whether speed is intentionally low. |
| High HP, moderate torque | The machine may produce power through high rotational speed. | Verify RPM rating, bearings, balance, and operating limits. |
| Zero HP with torque present | The shaft may be stalled or not rotating. | Remember that horsepower requires motion; at \(0\) RPM, mechanical horsepower is \(0\). |
| Unexpectedly high HP | Torque or RPM may be entered with the wrong units. | Check N-m versus lb-ft and rpm versus rad/s. |
| Electric estimate seems too high | Efficiency, power factor, phase, or voltage/current assumptions may be wrong. | Compare against motor nameplate horsepower and current. |
| Hydraulic HP seems too high | Pressure, flow, or efficiency may be unrealistic for the pump system. | Check pump curves, relief settings, fluid losses, and motor service factor. |
What to do with the result
Use the calculated horsepower as a power estimate, then compare it to equipment ratings. For a shaft or engine, check whether the torque and RPM are from the same operating point. For motors and pumps, compare the result to nameplate data, efficiency assumptions, service factor, and operating duty.
What changes horsepower the most?
Horsepower changes in direct proportion to both torque and RPM. Doubling torque doubles horsepower if RPM stays the same. Doubling RPM also doubles horsepower if torque stays the same. In real machines, torque usually changes with speed, which is why horsepower curves are often more useful than one isolated point.
Quick sanity check
At 5252 RPM, horsepower and torque in lb-ft are numerically equal. If torque is \(300\) lb-ft at \(5252\) RPM, horsepower should be about \(300\) hp. Use that checkpoint to catch unit mistakes quickly.
Input Quality Checklist
Horsepower errors usually come from mismatched units, mismatched operating points, or using a simplified formula outside its intended range.
Torque Unit
Confirm whether the torque value is lb-ft, N-m, or lb-in. Using N-m as if it were lb-ft overstates the horsepower.
Same Operating Point
Use torque and RPM measured at the same point on the curve. Peak torque and peak RPM usually do not occur together.
Positive Magnitudes
For this calculator, use positive torque and RPM magnitudes. Negative torque or reverse rotation may matter in advanced machine analysis, but not for basic horsepower magnitude.
Efficiency Assumptions
For motors and hydraulics, efficiency matters. Required input horsepower is higher than useful output horsepower when losses are included.
Nameplate Comparison
For equipment sizing, compare the result against rated horsepower, rated speed, current, service factor, and manufacturer data.
Actual Operating Load
A motor rated for a certain horsepower does not always output that horsepower. Actual horsepower depends on load, speed, and operating conditions.
Step-by-Step Horsepower Example
The most common horsepower calculation uses torque and RPM. This example calculates mechanical shaft horsepower from \(350\) lb-ft of torque at \(5000\) RPM.
Formula
Substitution
Final Calculation
Result
350 lb-ft at 5000 RPM is approximately 333 horsepower. This is reasonable because the speed is slightly below 5252 RPM, so the horsepower is slightly lower than the torque value.
| Example | Calculation | Result |
|---|---|---|
| 100 hp to kW | \(100 \times 0.745699872\) | \(74.57\,kW\) |
| 10 kW to hp | \(10 / 0.745699872\) | \(13.41\,hp\) |
| 100 N-m at 3000 RPM | \((100 \times 3000)/7127\) | \(42.1\,hp\) |
| 1500 psi and 5 GPM at 85% efficiency | \((1500 \times 5)/(1714 \times 0.85)\) | \(5.15\,hp\) |
Horsepower Diagrams
The two visuals below are intentionally placed as full-width learning aids instead of small side-by-side thumbnails. The first image explains the relationship between torque, RPM, and horsepower. The second image explains the calculator workflow: enter torque and speed, apply the formula, and interpret the horsepower result.
How to read the diagrams
Use the diagrams as concept checks, not as replacement formulas. The equations in the calculator and article should control the final result. The visuals are meant to help you understand why torque and RPM both matter.
The first image is most useful when you are trying to understand why an engine or motor can have a high torque value but not necessarily a high horsepower value. If RPM is low, the machine may have strong turning force but still produce limited power. If RPM increases while torque remains high, horsepower increases quickly.
Key takeaway from the torque/RPM visual
At \(5252\) RPM, horsepower and torque in lb-ft are numerically equal. Below 5252 RPM, horsepower is lower than torque for the same lb-ft value. Above 5252 RPM, horsepower becomes higher than torque for the same lb-ft value.
The second image is most useful when you are checking whether your inputs are in the correct order. Torque describes the twisting force. RPM describes how often that torque is applied each minute. The calculator combines those two values to estimate power. If either input is wrong, the horsepower result will also be wrong.
Image readability note
These figures should display full width in the article column and stack vertically on all screen sizes. Avoid placing them side by side because the labels and formula callouts become too small on tablets and mobile screens.
Typical Horsepower Reference Values
Horsepower ranges vary widely by application. Use these values only as broad checks, not as design limits. The best reference value is the manufacturer rating for the specific equipment, not a generic horsepower range.
| Application | Typical Range | How to Interpret It |
|---|---|---|
| Small appliance or fractional motor | Less than 1 hp | Often used for fans, small pumps, tools, and light-duty equipment. |
| Residential or light commercial pump | 0.5 to 5 hp | Actual sizing depends strongly on flow, pressure, duty, and efficiency. |
| Industrial electric motor | 1 to 500+ hp | Nameplate horsepower should be checked with voltage, current, enclosure, service factor, and duty cycle. |
| Passenger vehicle engine | 100 to 500+ hp | Peak horsepower occurs at a specific RPM and is not the same as wheel horsepower. |
| Hydraulic power unit | Varies widely | Pressure and flow dominate the result; efficiency and duty cycle affect required motor size. |
Practical insight competitors often miss
Peak horsepower is not always the best design point. Pumps, conveyors, industrial motors, and hydraulic systems often need horsepower checked at the worst continuous operating condition, not just at one peak or marketing value.
Design Ranges and Practical Checks
A mathematically correct horsepower result can still be practically incomplete. Equipment selection also depends on service factor, thermal loading, startup torque, intermittent versus continuous duty, and safety margins.
Shaft Power
Torque and RPM give shaft power at a specific point. They do not automatically include gearbox, belt, drivetrain, or pump losses.
Motor Sizing
Required motor horsepower should normally be checked against continuous load, starting load, service factor, and manufacturer data.
Hydraulic Systems
Hydraulic input horsepower rises when pressure or flow rises, and real systems also lose power through heat, leakage, restrictions, and inefficiency.
Field-practice warning
If the calculated horsepower is close to the equipment rating, do not assume it is acceptable. Check overload capacity, service factor, ambient temperature, duty cycle, cooling, altitude, voltage drop, and starting conditions.
Horsepower Units and Conversions
The calculator may show horsepower, watts, kilowatts, and metric horsepower. These units are all power units, but they are not exactly the same.
| Conversion | Value | Use Case |
|---|---|---|
| Mechanical horsepower to watts | \(1\,hp=745.699872\,W\) | Common for engines, shafts, dyno results, and North American mechanical power. |
| Mechanical horsepower to kilowatts | \(1\,hp=0.745699872\,kW\) | Useful for SI power comparison and international equipment ratings. |
| Metric horsepower | \(1\,PS=735.49875\,W\) | Used in many vehicle and equipment ratings outside the United States. |
| Torque conversion | \(1\,N\cdot m=0.737562149\,lb\text{-}ft\) | Needed before using the 5252 constant manually. |
| Rotational speed conversion | \(RPM=\omega \times 60/(2\pi)\) | Needed when angular speed is entered in rad/s. |
Most common unit trap
Do not use \(HP=(N\cdot m \times RPM)/5252\). If torque is in N-m, convert to lb-ft first or use an SI-consistent power calculation.
Horsepower vs. Torque, Kilowatts, and Wheel Horsepower
Horsepower is often confused with related measurements. The differences matter when comparing engines, motors, pumps, and vehicles.
| Term | What It Measures | Best Use | Main Caution |
|---|---|---|---|
| Horsepower | Rate of doing work. | Compare power output at a specific operating point. | Must include RPM when derived from torque. |
| Torque | Twisting force. | Understand pulling, turning, starting, and low-speed capability. | High torque alone does not always mean high power. |
| Kilowatts | SI power unit. | International ratings and electrical/mechanical power comparison. | Convert using the correct horsepower type. |
| Wheel horsepower | Power measured at the wheels. | Vehicle dyno comparisons. | Lower than crank horsepower because of drivetrain losses. |
| Hydraulic horsepower | Fluid power from pressure and flow. | Pumps, power units, and hydraulic actuators. | Input motor HP must account for efficiency and losses. |
Common Horsepower Calculation Mistakes
Most horsepower mistakes are not algebra mistakes. They are usually unit, interpretation, or measurement mistakes.
Common Mistakes
- Using N-m directly in the lb-ft horsepower formula.
- Combining peak torque with a different RPM point from the curve.
- Assuming crank horsepower and wheel horsepower are the same.
- Ignoring motor, pump, gearbox, belt, or drivetrain losses.
- Assuming a rated motor always outputs its full nameplate horsepower.
- Using calculated horsepower as final equipment sizing without checking duty cycle.
Better Practice
- Convert torque to lb-ft before manually using the 5252 formula.
- Use torque and RPM from the same operating condition.
- Compare calculated horsepower with nameplate and manufacturer ratings.
- Account for efficiency when estimating required input power.
- Use a safety margin or service factor where equipment selection requires it.
Troubleshooting Unexpected Horsepower Results
If the result looks too high, too low, or physically unrealistic, check the input assumptions before changing the formula.
| Problem | Likely Cause | Fix |
|---|---|---|
| Horsepower is far too high | Torque entered in N-m but treated as lb-ft, or RPM entered incorrectly. | Check unit selectors and convert torque correctly. |
| Horsepower is lower than expected | RPM is low, torque is from a different point, or efficiency losses are included. | Confirm torque and RPM are from the same operating condition. |
| Horsepower is zero even though torque is not zero | RPM is zero or the shaft is not rotating. | Horsepower requires motion. At \(0\) RPM, mechanical horsepower is \(0\). |
| Torque and horsepower do not match at 5252 RPM | Torque is not in lb-ft or the speed is not actually 5252 RPM. | Use lb-ft and RPM for the standard checkpoint. |
| Motor horsepower does not match nameplate | Voltage, current, efficiency, power factor, or phase selection may be wrong. | Check nameplate current, rated voltage, phase, service factor, and efficiency. |
| Hydraulic result seems unrealistic | Pressure, flow, or efficiency does not match the actual system operating point. | Review pump curve, relief pressure, flow demand, and system losses. |
Edge case to watch
A low-speed machine can have very high torque but modest horsepower. A high-speed machine can have moderate torque but high horsepower. That is why torque alone does not fully describe power output.
Assumptions, Sources, and Limitations
This calculator is intended for education, preliminary estimates, and quick engineering checks. It uses standard mechanical power relationships and fixed unit conversion constants.
Formula Assumption
The main formula assumes torque in lb-ft, speed in RPM, and mechanical horsepower as the output.
Measurement Assumption
Torque and RPM should describe the same shaft and operating point.
Efficiency Limitation
Basic torque-to-horsepower math gives shaft power. It does not automatically include drivetrain, pump, motor, or gearbox losses.
Hydraulic Limitation
Hydraulic horsepower estimates do not replace pump curves, pressure loss calculations, temperature checks, relief-valve settings, or manufacturer sizing guidance.
Final Design Warning
For motor, pump, electrical, hydraulic, or vehicle design, verify results against manufacturer data, applicable codes, safety requirements, duty cycle, and professional engineering judgment.
Calculation basis
The standard rotating power relationship used here is \(HP=(T \times RPM)/5252\), based on mechanical horsepower, \(33{,}000\) ft-lb/min, and \(2\pi\) radians per revolution. Unit conversions follow standard power relationships, including \(1\,hp=745.699872\,W\). For SI unit guidance and conversion-factor practice, see the NIST Guide to the SI conversion factors.
Glossary of Horsepower Terms
These terms help explain the calculator results and the formulas used on this page.
Horsepower
A unit of power that measures the rate of doing work. Mechanical horsepower is approximately 745.7 watts.
Torque
Twisting force applied to a shaft, commonly measured in lb-ft or N-m.
RPM
Revolutions per minute, a measure of how fast a rotating shaft turns.
Shaft Power
Mechanical power available at a rotating shaft before or after losses, depending on where it is measured.
Brake Horsepower
Power measured at an engine or motor output shaft, often before drivetrain losses.
Wheel Horsepower
Vehicle power measured at the wheels after drivetrain losses.
Hydraulic Horsepower
Fluid power based on pressure and flow, commonly calculated from psi and GPM.
Efficiency
The ratio of useful output power to input power, usually expressed as a percentage.
Frequently Asked Questions
What does a horsepower calculator calculate?
A horsepower calculator estimates power from torque and RPM, converts between horsepower and other power units, and may also estimate electric motor horsepower, hydraulic horsepower, wheel horsepower, crank horsepower, or power-to-weight ratio depending on the selected mode.
What is the standard horsepower formula from torque and RPM?
The standard mechanical horsepower formula is \(HP = Torque \times RPM \div 5252\) when torque is in pound-feet and rotational speed is in RPM.
Why is 5252 used in the horsepower formula?
The 5252 constant comes from converting rotational work into horsepower using \(33{,}000\) ft-lb/min and \(2\pi\) radians per revolution. It only applies directly when torque is in lb-ft and speed is in RPM.
How many watts are in one horsepower?
One mechanical horsepower is approximately \(745.699872\) watts. Electric horsepower is commonly treated as \(746\) watts, and metric horsepower is approximately \(735.49875\) watts.
Why does horsepower equal torque at 5252 RPM?
In the formula \(HP=(T \times RPM)/5252\), setting \(RPM=5252\) makes \(HP\) approximately equal to \(T\). This only works when torque is measured in lb-ft.
Can torque exist without horsepower?
Yes. A shaft can have torque at zero speed, but mechanical horsepower is zero if the shaft is not rotating. Horsepower measures the rate of doing work, so motion is required.
Can I use calculated horsepower for final motor or pump sizing?
Use the result as an estimate. Final sizing should also check manufacturer data, pump curves, motor service factor, duty cycle, efficiency, temperature, electrical requirements, and applicable safety or code requirements.