The torque-to-horsepower calculator estimates mechanical power from torque in newton-metres and rotational speed in revolutions per minute (rpm). Torque describes turning effect; power describes how quickly rotational work is performed. Either value alone is insufficient: the same torque at twice the rotational speed produces twice the power. The result uses mechanical horsepower, based on approximately 745.7 watts per horsepower. It is useful for checking a shaft operating point, not for predicting an engine or motor’s full performance curve.
Torque to Horsepower Calculator
Calculate mechanical horsepower from torque in newton-metres and rotational speed in revolutions per minute.
Torque and speed
N·m + rpm → hp
Enter torque and shaft speed
Mechanical output
Horsepower at this operating point
Horsepower will appear here
Use torque and rpm measured at the same shaft and operating point.
Mechanical horsepowerhp = torque (N·m) × rpm ÷ 7,120.9092375
- Mechanical horsepower
- — hp
Uses mechanical horsepower (745.699871582 W per hp). Both torque and rpm must be nonnegative. It does not account for drivetrain losses or infer a full performance curve; the result is rounded to six decimal places.
What is Torque to hp?
How to Use This Calculator
- Enter torque in newton-metres. Use the torque available at the same shaft and operating point as the entered speed.
- Enter rotational speed in rpm.
- Choose Calculate to obtain mechanical horsepower.
- Check whether the source torque is peak, rated, measured, or estimated. A peak value at one speed should not be combined with a different speed.
Both inputs accept zero and nonnegative decimal values. The answer is shaft power implied by the pair. It does not automatically include electrical input power, combustion fuel power, drivetrain losses, generator efficiency, or service factors.
Formula Used
Angular speed in radians per second is rpm × 2π ÷ 60. Mechanical power is torque multiplied by angular speed, and one mechanical horsepower is exactly 550 ft·lbf/s (approximately 745.699871582 watts). Converting newton-metres to foot-pounds gives:
Mechanical horsepower = torque (N·m) × rpm × 2π ÷ (60 × 745.699871582) = torque × rpm ÷ 7,120.9092375
The calculator rounds the final horsepower to six decimal places. The familiar 5,252 divisor applies when torque is in pound-feet, so it must not be used directly with newton-metres.
Variables Explained
| Value | Meaning |
|---|---|
| Torque | Turning moment at the shaft, entered in newton-metres. |
| Speed | Rotational frequency in revolutions per minute. |
| Angular speed | Rotational speed expressed in radians per second. |
| Power in watts | Torque multiplied by angular speed. |
| Mechanical horsepower | Power divided by approximately 745.70 watts per horsepower. |
| Efficiency | Not an input; losses between input and shaft output are not estimated. |
Worked Example
For 300 N·m at 1,800 rpm, angular speed is 1,800 × 2π ÷ 60 = 60π rad/s. Power is 300 × 60π = about 56,548.67 W. Dividing by 745.699871582 W per mechanical horsepower gives 75.833013 hp after six-decimal rounding. This describes the mechanical power at that exact torque-speed point. If the same 300 N·m were maintained at 900 rpm, the result would be half as large because rotational speed has halved.
Why Use This Calculator?
Read the result as the ideal mechanical relationship between the supplied torque and speed. For a real motor, torque generally changes with speed and operating condition. A nameplate horsepower does not mean the same torque is available at every rpm. For a gearbox, use values from the same side of the gearbox or account for ratio and efficiency; combining input-shaft speed with output-shaft torque overstates power.
A dynamometer measurement, manufacturer curve, duty rating, temperature limit, and service factor provide context that this two-input result cannot. Mechanical horsepower also differs from metric horsepower. Confirm which convention a specification uses before comparison. Equipment selection should follow manufacturer data and qualified engineering review, especially for lifting, braking, pressure equipment, vehicles, or machinery whose failure can injure people.
Common Mistakes
- Using pound-feet while the form expects newton-metres gives the wrong horsepower.
- Typing rpm in a field interpreted as radians per second would require a different formula.
- Combining maximum torque from one rpm with maximum speed from another invents an operating point.
- Assuming calculated shaft output equals electrical input ignores efficiency and losses.
- Mixing torque from the gearbox output with speed from its input overstates transmitted power.
- Confusing mechanical horsepower with metric horsepower creates a small but real difference.
- Reading six decimal places as measurement accuracy gives more confidence than typical torque and speed data support.
Frequently Asked Questions
Why are both torque and rpm needed?
Power is the product of torque and angular speed. Torque without speed describes turning effect but not the rate at which rotational work is done.
Can I enter torque in pound-feet?
Not directly. Convert pound-feet to newton-metres first, or use a formula designed for pound-feet. The input label here is N·m.
Is the result mechanical or metric horsepower?
It uses mechanical horsepower at about 745.7 watts per horsepower. Metric horsepower uses a different watt relationship.
Does the result include motor efficiency?
No. It calculates mechanical shaft power implied by torque and speed. Electrical input or fuel power would be higher when losses are present.
Why does horsepower change with rpm?
At unchanged torque, doubling rotational speed doubles the rate of work and therefore doubles power. Real machines may not maintain unchanged torque.
Can I use peak torque and maximum rpm?
Only if they occur together, which often they do not. Use torque and rpm from the same measured or specified operating point.
What happens when torque or rpm is zero?
Mechanical power is zero because their product is zero, even if the other value is positive.
Sources & References
The US Department of Energy’s Premium Efficiency Motor Selection and Application Guide gives the torque-speed horsepower relationship in SI and foot-pound forms. NIST discusses rpm as a widely used rotational-frequency designation in its Guide to the SI, Chapter 8. Mechanical horsepower and torque conversion factors are documented in the NIST conversion tables.