Horsepower Calculator

Calculate horsepower (HP) from torque & RPM, watts, or force & distance. Get power conversions, step-by-step calculations, and engineering insights for vehicles, motors, and machines.

Most common for vehicles - Enter engine torque and RPM to calculate horsepower

Convert electrical or mechanical power from watts to horsepower

Physics-based calculation - Calculate horsepower from work done over time

What is Horsepower?

Horsepower (HP) is a unit of measurement for power, representing the rate at which work is done. It was originally defined by James Watt to compare steam engine output with the power of draft horses. One horsepower equals approximately 745.7 watts or the ability to move 550 pounds one foot in one second.

Horsepower Calculation Formulas

Mode 1: Torque & RPM to Horsepower

For vehicles and engines where torque and RPM are known:

For torque in lb·ft:

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

For torque in N·m:

$$\textbf{HP} = \frac{\textbf{T} \times \textbf{RPM}}{7127}$$

The constant 5252 (or 7127 for metric) comes from converting rotational motion to linear work, where 2π radians per revolution and unit conversions are factored in.

Mode 2: Watts to Horsepower

Direct conversion from electrical or mechanical power:

$$\textbf{HP} = \frac{\textbf{W}}{745.7} \quad \text{or} \quad \textbf{kW} = \frac{\textbf{W}}{1000}$$

This is a simple unit conversion. One horsepower is defined as exactly 745.7 watts. Kilowatts can be found by dividing watts by 1000.

Mode 3: Force, Distance & Time to Horsepower

Classical physics definition - work done per unit time:

For Imperial units (lb, ft, s):

$$\textbf{HP} = \frac{\textbf{F} \times \textbf{D}}{\textbf{t} \times 550}$$

For Metric units (N, m, s):

$$\textbf{HP} = \frac{\textbf{F} \times \textbf{D}}{\textbf{t} \times 745.7}$$

Power is the rate of doing work. The constants 550 (Imperial) and 745.7 (Metric) convert to horsepower units. This formula shows that 1 HP = 550 ft·lb/s.

Worked Examples

Example 1: Car Engine Power (Torque & RPM)

Problem: A car engine produces 250 lb·ft of torque at 5,200 RPM. What is the horsepower?

**Step 1:** Identify the values

$$T = 250 \text{ lb·ft}, \quad RPM = 5200$$

**Step 2:** Apply the torque & RPM formula

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

**Step 3:** Perform the calculation

$$HP = \frac{250 \times 5200}{5252} = \frac{1,300,000}{5252} = 247.5 \text{ HP}$$

**Step 4:** Convert to kilowatts (if needed)

$$kW = 247.5 \times 0.7457 = 184.5 \text{ kW}$$

**Answer:** The engine produces **247.5 HP** or **184.5 kW**

Example 2: Electric Motor (Watts to HP)

Problem: An electric motor draws 150,000 watts. What is the horsepower output?

**Step 1:** Identify the power in watts

$$W = 150,000 \text{ watts}$$

**Step 2:** Apply the watts to HP formula

$$HP = \frac{W}{745.7}$$

**Step 3:** Perform the calculation

$$HP = \frac{150,000}{745.7} = 201.1 \text{ HP}$$

**Step 4:** Convert to kilowatts

$$kW = \frac{150,000}{1000} = 150 \text{ kW}$$

**Answer:** The motor produces **201.1 HP** or **150 kW**

Example 3: Work Done (Force & Distance)

Problem: A crane lifts 500 pounds a distance of 100 feet in 10 seconds. What is the power output?

**Step 1:** Identify the values

$$F = 500 \text{ lb}, \quad D = 100 \text{ ft}, \quad t = 10 \text{ s}$$

**Step 2:** Calculate work done

$$Work = F \times D = 500 \times 100 = 50,000 \text{ ft·lb}$$

**Step 3:** Apply the power formula

$$HP = \frac{F \times D}{t \times 550} = \frac{50,000}{10 \times 550} = \frac{50,000}{5500} = 9.09 \text{ HP}$$

**Step 4:** Convert to kilowatts

$$kW = 9.09 \times 0.7457 = 6.78 \text{ kW}$$

**Answer:** The crane outputs **9.09 HP** or **6.78 kW**

Frequently Asked Questions (FAQs)

What is the difference between horsepower and torque?

Torque is the rotational force an engine produces (measured in lb·ft or N·m), while horsepower is the rate at which that force does work over time. Think of torque as strength and horsepower as the combination of strength and speed. HP = (Torque × RPM) ÷ 5252. High torque at low RPM is good for towing, while high horsepower means high performance at speed.

Why are there different types of horsepower (mechanical, metric, electrical)?

Different industries use slightly different definitions: Mechanical HP (745.7 W) is standard in the US, Metric HP or PS (735.5 W) is used in Europe, and Electrical HP (746 W) is used for electric motors. The differences are small (about 1-2%), but they exist due to historical measurement standards. This calculator uses mechanical horsepower.

At what RPM does an engine produce maximum horsepower?

Maximum horsepower typically occurs at high RPM where the engine spins fastest, even though torque may be lower. For most gasoline engines, peak HP occurs between 5,000-7,000 RPM. Diesel engines peak lower, around 3,000-4,500 RPM. The relationship is HP = (Torque × RPM) ÷ 5252, so as RPM increases, HP increases until torque drops off significantly.

How do I convert between horsepower and kilowatts?

Use these conversion formulas: 1 HP = 0.7457 kW, so multiply HP by 0.7457 to get kW. To convert back: 1 kW = 1.341 HP, so multiply kW by 1.341 to get HP. For example, 200 HP = 149.1 kW, and 100 kW = 134.1 HP. Many countries use kW instead of HP for rating engine power.

Can I calculate horsepower without knowing RPM?

Yes, if you know the power in watts (from electrical meters or power ratings), use Mode 2: simply divide watts by 745.7 to get HP. If you know force, distance, and time (physics work), use Mode 3. However, for rotating engines and motors, the torque-RPM method (Mode 1) is most accurate because it captures actual mechanical output.

Our goal is to provide accurate and user-friendly calculators for educational and informational purposes. Each calculator undergoes expert review and verification before publication, so you can use it confidently and get reliable results every time.

Expert Verified

James Patterson

James Patterson

Mechanical Engineer & Automotive Specialist

James has 15+ years of experience in automotive engineering, engine performance analysis, and powertrain design. He specializes in power calculations, engine dynamics, and performance optimization for both conventional and electric vehicles.

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