Horsepower (hp) - Unit Information & Conversion

Quick Answer

What is Horsepower? Horsepower (hp) is a unit of measurement for power—the rate at which work is performed. It tells you how fast an engine can apply force.

• 1 Mechanical hp $\approx$ 745.7 Watts.
• 1 Metric hp (PS) $\approx$ 735.5 Watts.

The Golden Rule:

• Torque is how much work an engine can do (Force).
• Horsepower is how fast it can do that work (Rate).

Quick Comparison Table

Unit	Symbol	Watts (W)	Description	Common Use
Mechanical HP	hp (I)	745.7	The US/UK standard	Cars, Lawnmowers (US)
Metric HP	PS / cv	735.5	The European standard	Cars (Europe/Asia)
Electrical HP	hp (E)	746.0	Exact definition	Electric Motors
Boiler HP	bhp	9,810	Thermal power	Steam Boilers
Hydraulic HP	-	-	Fluid power	Pumps/Hydraulics
Human Power	-	~75-100	Sustained effort	Cycling
Horse Power	-	~750	Sustained effort	Farming

Definition

The Original Experiment

James Watt didn't just guess. He observed horses working in coal mines, lifting coal up a shaft using a pulley system.

1. A horse could pull with a force of 180 pounds.
2. It walked in a circle with a 24-foot diameter (approx 75.4 ft circumference).
3. It completed the circle about 2.5 times per minute.

$$ \text{Work} = \text{Force} \times \text{Distance} $$ $$ \text{Power} = \frac{\text{Work}}{\text{Time}} $$

$$ 180 \text{ lbs} \times (24 \text{ ft} \times \pi \times 2.5) \approx 32,572 \frac{\text{ft}\cdot\text{lb}}{\text{min}} $$

Watt rounded this up to 33,000 ft⋅lb/min to be safe. Dividing by 60 seconds gives the classic definition: 1 hp = 550 ft⋅lb/s

Types of Horsepower

The world couldn't agree on just one "horsepower," so we have several:

1. Mechanical Horsepower (Imperial)

• Symbol: hp, hp(I)
• Value: 745.69987158227022 Watts
• Definition: 550 ft⋅lb/s
• Where used: USA, UK, Commonwealth countries. This is what you see on a Ford Mustang spec sheet.

2. Metric Horsepower (Pferdestärke)

• Symbol: PS, cv, ch, pk, ks
• Value: 735.49875 Watts
• Definition: The power to lift 75 kg by 1 meter in 1 second.
  • $75 \text{ kg} \times 9.80665 \text{ m/s}^2 \times 1 \text{ m/s} = 735.5 \text{ W}$
• Where used: Europe, Asia, South America.
  • German: Pferdestärke (PS)
  • French: Cheval-vapeur (ch)
  • Italian: Cavallo vapore (cv)
• Difference: Metric hp is about 1.4% smaller than Imperial hp. A 500 hp car is 507 PS.

3. Electrical Horsepower

• Symbol: hp(E)
• Value: 746 Watts (Exactly)
• Definition: Used for rating electric motors to simplify calculations.

4. Boiler Horsepower

• Symbol: bhp
• Value: 9,809.5 Watts (~13.1 mechanical hp)
• Definition: The power required to evaporate 34.5 lbs of water into steam in one hour at 212°F.
• Where used: Industrial steam boilers and power plants. Warning: Do not confuse this with Brake Horsepower (bhp)!

5. Hydraulic Horsepower

• Definition: Power available within a hydraulic system.
• Formula: $\text{hp} = \frac{\text{Pressure (psi)} \times \text{Flow (gpm)}}{1714}$
• Where used: Heavy machinery, drilling rigs.

History: The Marketing Genius of James Watt

The term "horsepower" is arguably the most successful marketing slogan in engineering history.

The Problem: In the late 1700s, the Industrial Revolution was just starting. Mines were flooded with water, and owners used teams of horses to drive pumps. James Watt had invented a vastly superior steam engine, but he had a hard time explaining how much better it was. Saying "it produces 20,000 foot-pounds per minute" meant nothing to a mine boss.

The Solution: Watt spoke their language. He calculated what one of their horses could do, then rated his engine in "horses." "This engine will replace 10 of your horses." Suddenly, the value proposition was clear. The mine owner could calculate the cost of feeding and housing 10 horses versus buying one engine.

The Irony: Watt actually overestimated the power of a horse.

• A typical horse can sustain about 0.7 hp for a full day.
• Watt's "1 hp" (33,000 ft-lb/min) is actually a grueling pace that a horse can only maintain for a few hours.
• By defining the unit as stronger than a real horse, Watt ensured his customers were never disappointed. If they bought a "5 hp" engine, it would easily outwork 5 real horses.

Real-World Examples

Biological Power

• Human (Resting): ~100 Watts (0.13 hp) - mostly heat.
• Human (Walking): ~0.2 hp.
• Human (Elite Cyclist): Can sustain 0.5 - 0.6 hp for an hour.
• Human (Usain Bolt): Peak power during a sprint is roughly 3.5 hp (2600 Watts) for a split second.
• Horse (Average): Sustains 0.7 - 1.0 hp for work.
• Horse (Racehorse): Peak power can reach 14-15 hp for a few seconds!

Automotive Scale

• Model T Ford (1908): 20 hp.
• VW Beetle (Classic): 40-50 hp.
• Toyota Corolla: ~169 hp.
• Ford F-150: 290 - 450 hp.
• Tesla Model S Plaid: 1,020 hp.
• Bugatti Chiron: 1,578 hp.

Industrial & Massive Scale

• Diesel Locomotive: 3,000 - 4,500 hp.
• Cruise Ship (Wonder of the Seas): ~130,000 hp (96 MW).
• Boeing 777 Engine: ~110,000 hp (per engine, equivalent power).
• Space Shuttle Main Engines: ~37,000,000 hp (at liftoff, combined).
• Saturn V Rocket: ~160,000,000 hp.

Common Uses

1. Automotive Industry

This is the domain of the horsepower. Despite the world moving to metric (kW), car enthusiasts and manufacturers in the US, UK, and even Europe still heavily market "HP" or "PS."

• BHP (Brake Horsepower): The power measured at the engine's crankshaft (before losses in the transmission). This is the number in the brochure.
• WHP (Wheel Horsepower): The power that actually reaches the tires. Usually 15-20% less than BHP due to friction in the gears and axles.

2. Aviation

• Piston Engines: Small planes (Cessna 172) are rated in hp (e.g., Lycoming O-320 is 160 hp).
• Turboprops: Often rated in Shaft Horsepower (shp).
• Jet Engines: Rated in Thrust (lbs or kN), not horsepower. However, you can calculate "equivalent horsepower" based on speed, though it varies wildly.

3. Home Appliances

• Garbage Disposal: 1/3 hp to 1 hp.
• Garage Door Opener: 1/2 hp to 1.25 hp.
• Blender: "2 Peak HP" (Marketing term—usually means the motor would produce that right before it burns out).
• Air Conditioner: Historically rated in hp, now mostly BTU/h or Tons. (1 hp $\approx$ 9000 BTU/h in cooling capacity, roughly).

4. Electric Motors

Industrial motors are strictly rated in hp (US) or kW (Global).

• 1 hp motor: Runs a small conveyor or drill press.
• 10 hp motor: Runs a large industrial fan or compressor.
• 100+ hp motor: Runs municipal water pumps or rock crushers.

Horsepower vs. Torque: The Eternal Debate

"Horsepower sells cars, torque wins races." — Carroll Shelby (attributed)

This is the most common confusion in the automotive world.

• Torque (lb-ft): The twisting force. It's what you feel when you accelerate from a stop. It's the "grunt."
• Horsepower (hp): How fast you can apply that torque. It determines your top speed and high-speed acceleration.

The Physics Connection: $$ \text{Horsepower} = \frac{\text{Torque (lb-ft)} \times \text{RPM}}{5252} $$

• Diesel Trucks: High Torque, Low RPM $\rightarrow$ Moderate HP. Great for towing heavy loads.
• Formula 1 Cars: Low Torque, Insane RPM (15,000+) $\rightarrow$ Massive HP. Great for top speed.

Why 5252? It's a constant derived from the definition of horsepower: $33,000 \text{ ft-lb/min} \div 2\pi \text{ radians/rev} \approx 5252$. At exactly 5,252 RPM, horsepower and torque (in lb-ft) are always equal.

Conversion Guide

HP to kW (The Big One)

Converting between Imperial Horsepower and Kilowatts.

Formula: $$ \text{kW} = \text{hp} \times 0.7457 $$ $$ \text{hp} = \text{kW} \times 1.341 $$

Quick Estimates:

• 1 hp $\approx$ 3/4 kW (0.75 kW)
• 1 kW $\approx$ 1.33 hp (add 1/3)

Horsepower (hp)	Kilowatts (kW)	Example
1 hp	0.75 kW	Toaster
100 hp	75 kW	Economy Car
134 hp	100 kW	Standard Sedan
300 hp	224 kW	Sports SUV
1000 hp	746 kW	Hypercar

HP to PS (Metric Horsepower)

Converting between US Horsepower and European PS.

Formula: $$ \text{PS} = \text{hp} \times 1.014 $$ $$ \text{hp} = \text{PS} \times 0.986 $$

Rule of Thumb: They are almost 1:1. Metric PS is slightly "smaller," so the number is slightly bigger.

• 500 hp $\approx$ 507 PS.

HP to BTU/hr (Heating/Cooling)

Used for boilers and AC units.

• 1 hp (Mechanical) $\approx$ 2,544 BTU/hr
• 1 hp (Boiler) $\approx$ 33,475 BTU/hr (Huge difference!)