🐎 Horsepower Calculator

Horsepower is one of those units everybody hears and few people can derive. The horsepower calculator covers the three situations you are most likely to meet. For a rotating shaft, HP = T · RPM / 5,252 where T is torque in lb-ft. For a hydraulic motor, HP = (P · Q) / 1,714 where P is pressure in psi and Q is flow in gallons per minute. For a vehicle engine measured on a dynamometer, the same rotating formula applies once torque at the flywheel is known. All three return results in horsepower and kilowatts.

Rent a water pump and the nameplate gives you its horsepower; convert it to kilowatts to size a generator. Spec a hydraulic motor for a conveyor and you need to move from pressure and flow to power. Compare two car engines and their torque curves tell you which one accelerates harder at highway speed. The torque-to-horsepower relationship at the bottom of the torque calculator page explains the rest of the story.

Each mode applies the standard engineering formula for that machine type. The rotating mode is the mechanical definition: power equals torque times angular speed, with the 5,252 constant that converts RPM and lb-ft into horsepower. The hydraulic mode starts from pressure times flow rate, which is pressure energy delivered per second, then converts psi·gpm into horsepower with the 1,714 constant. The engine mode uses the same rotating formula but also accepts kilowatts as an input so you can convert between DIN, SAE and metric ratings.

A quick sanity check: a hydraulic pump delivering 3,000 psi at 10 gpm needs about 17.5 HP before pump losses. An electric motor of 20 HP (15 kW) is the nearest standard size. The calculator also returns the mechanical efficiency-adjusted output for hydraulic motors—if you know the motor efficiency, enter it to get the shaft output rather than the hydraulic input.

1. Choose the mode: rotating shaft, hydraulic motor, or engine.
2. Enter torque and RPM (or pressure and flow for hydraulic).
3. Optionally enter an efficiency percentage for the hydraulic motor.
4. Click Calculate to get horsepower and kilowatts.
5. Compare with the nearest standard motor size from the table.

Why is the constant 5,252 in the rotating formula?

One horsepower equals 550 ft-lb/s. Torque in lb-ft times RPM, divided by 5,252, converts the work per revolution into that power unit—the constant comes from 550 × 60 / (2π), which is 5,252.1.

What is the difference between horsepower and kilowatts?

1 HP = 745.7 W, so 1 HP is about three quarters of a kilowatt. European machines are usually rated in kW, American machines in HP. The calculator shows both so you can compare nameplates directly.

Why does my hydraulic motor need a bigger electric motor?

Because the pump and the motor each have internal losses (leakage and friction). If the pump is 90% efficient and the motor 90% efficient, you need roughly 1/0.81 = 1.23 times the theoretical hydraulic power from the electric motor.

What is the difference between brake horsepower and wheel horsepower?

Brake horsepower is measured at the engine flywheel with a dynamometer. Wheel horsepower is measured at the tires and is lower because the transmission, driveshaft and axle bearings consume energy—typically 10–15% in a car, more in 4WD.

Can I calculate the power of a pump without knowing efficiency?

Yes, you get the theoretical hydraulic power. For the electric motor size, divide by the combined pump and motor efficiency—use 0.85 as a first estimate, then refine with the nameplate values.

How is horsepower related to torque in a car?

Horsepower = torque × RPM / 5,252. An engine producing 300 lb-ft at 3,000 RPM makes 171 HP; the same torque at 6,000 RPM makes 343 HP. High RPM is why racing engines can have modest torque yet huge power.

Horsepower ratings on motors are mechanical output at the shaft; electrical input from the grid is always higher because of motor and drive losses (typically 85–92%). When you convert hydraulic flow and pressure to horsepower, remember the pump and motor each have their own efficiency, so the installed electric motor must be larger than the theoretical hydraulic power. Dynamometer ratings are measured at the flywheel; losses through the drivetrain mean wheel horsepower is typically 10–15% lower on a car.